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The body structure, or anatomy, of the frog is very similar to the anatomy of man. Both man and the frog have the same kinds of organs and systems of organs. The frog's anatomy, however, is much simpler. General Body Features As in other higher vertebrates, the frog body may be divided into a head, a short neck, and a trunk (see Vertebrates). The flat head contains the brain, mouth, eyes, ears, and nose. A short, almost rigid neck permits only limited head movement. The stubby trunk forms walls for a single body cavity, the coelom. Man's internal organs are housed in one of three distinct hollow cavities--the chest, the abdomen, and the pelvis. The human chest is separated from the abdomen by a powerful muscular partition, the diaphragm (see Diaphragm). There is no such partition in the frog's coelom. All the frog's internal organs--including the heart, the lungs, and all organs of digestion--are held in this single hollow space. The Skeleton and Muscles The frog's body is supported and protected by a bony framework called the skeleton (see Skeleton). The skull is flat, except for an expanded area that encases the small brain. Only nine vertebrae make up the frog's backbone, or vertebral column. The human backbone has 24 vertebrae. The frog has no ribs. The frog does not have a tail. Only a spikelike bone, the urostyle, remains as evidence that primitive frogs probably had tails. The urostyle, or "tail pillar," is a downward extension of the vertebral column. The shoulders and front legs of the frog are somewhat similar to man's shoulders and arms. The frog has one "forearm" bone, the radio-ulna. Man has two forearm bones, the radius and the ulna. Both frog and man have one "upper arm" bone, the humerus. The hind legs of the frog are highly specialized for leaping. The single "shinbone" is the tibiofibula. Man has two lower leg bones, the tibia and the fibula. In man and in the frog, the femur is the single upper leg (thigh) bone. A third division of the frog's leg consists of two elongated anklebones, or tarsals. These are the astragalus and the calcaneus. The astragalus corresponds to the human talus. The calcaneus in the human skeleton is the heel bone. As in other vertebrates, the frog skeleton is moved by muscles (see Muscles). Skeleton-moving muscles are made of skeletal, or "striated," muscle. Internal organs contain smooth muscle tissue. The Circulatory System The frog heart is the only organ contained within the coelom which has its own protective covering. This is the pericardium (see Heart). There are two upper chambers of the heart, the right atrium and the left atrium. The frog heart, however, has only one lower chamber, a single ventricle. In man, the lower heart chamber is divided into two compartments, the right ventricle and the left ventricle. Oxygen-laden blood and oxygen-poor blood containing waste gases are present together in the frog ventricle at all times. The oxygen-laden and oxygen-poor bloods, however, do not mix. Such mixing is prevented by a unique arrangement of the frog's heart. Instead of "perching" on top of the ventricle, the right atrium dips downward into the ventricle. This causes oxygen-poor blood entering the right atrium to pass all the way down to the bottom of the ventricle. Meanwhile, oxygen-laden blood is received by the left atrium and enters the same single ventricle. The pool of oxygen-poor blood at the bottom of the ventricle holds up the oxygen-laden blood and prevents it from sinking to the bottom. When the oxygen-poor blood flows from the ventricle into vessels leading to the lungs, the oxygen-laden blood tries to "follow" it. The lung vessels, however, are filled with oxygen-poor blood, blocking the oxygen-laden blood and forcing oxygen-laden blood to detour into the arteries. These carry the oxygen-laden blood to the tissues. Frog blood has both a solid and a liquid portion. The liquid plasma carries solid elements such as red blood cells and white blood cells. (See also Blood.) The Skin and Respiratory System The frog is covered by a soft, thin, moist skin composed of two layers, an outer epidermis and an inner dermis (see Skin). The skin does not merely protect the frog but helps in respiration (see Respiratory System). An extensive network of blood vessels runs throughout the frog's skin. Oxygen can pass through the membranous skin, thereby entering directly into the blood. When a frog submerges beneath the water, all its respiration takes place through the skin. Oxygen is obtained directly from the water. The frog does not breathe through its skin alone. Adult frogs have paired, simple, saclike lungs. As in man, air enters the body through two nostrils, passes through the windpipe, and is received by the lungs (see Lungs). The mechanism of breathing, however, is different in the frog from that in man. In humans breathing is aided by the ribs, the diaphragm, and the chest muscles. The frog has no ribs or diaphragm, and its chest muscles are not involved in breathing. A frog may breathe by simply opening its mouth and letting air flow into the windpipe. However, it may also breathe with its mouth closed. The floor of the mouth is lowered, causing the frog's throat to "puff out." When the nostrils open, air enters the enlarged mouth. Then, with nostrils closed, the air in the mouth is forced into the lungs by contraction of the floor of the mouth. The Digestive and Excretory Systems The frog's mouth is where digestion begins. It is equipped with feeble, practically useless teeth. These are present only in the upper jaw. The frog's tongue is highly specialized. Normally, the tip of its tongue is folded backward toward the throat. From this position the frog can flick it out rapidly to grasp any passing prey. To better hold this prey, the tongue is sticky. (See also Tongue.) Food passes from the frog's mouth into the stomach by way of the esophagus. From the stomach, the food moves into the small intestine, where most of the digestion occurs. Large digestive glands, the liver and the pancreas, are attached to the digestive system by ducts. A gall bladder is also present (see Digestive System). Liquid wastes from the kidneys travel by way of the ureters to the urinary bladder. Solid wastes from the large intestine pass into the cloaca. Both liquid and solid waste material leave the body by way of the cloaca and the cloacal vent. The Nervous System and Sense Organs The frog has a highly developed nervous system. It consists of a brain, a spinal cord, and nerves. (See also Brain and Spinal Cord; Nervous System.) The important parts of the frog brain correspond to comparable parts in the human brain. The medulla regulates automatic functions such as digestion and respiration. Body posture and muscular co-ordination are controlled by the cerebellum. The cerebrum is very small in the frog. By comparison the human cerebrum is very large. In man the cerebrum is involved in many important life processes. Only 10 cranial nerves originate in the frog's brain. Man has 12. Similarly, the frog has only 10 pairs of spinal nerves. Man has 30 pairs. Two simple holes make up the nostrils for the frog. There are complex valves but no long nasal passages as there are in man (see Nose). The frog's sense of smell is registered by olfactory lobes. These make up the forward portion of the brain. The eye is crude. Its fixed lens cannot change its focus. Poorly developed eyelids do not move. To close its eye, the frog draws the organ into its socket (see Eye). A third eyelid, or nictitating membrane, may be drawn over the pulled-in eyeball. There is no external ear (see Ear). Both eardrums, or tympanic membranes, are exposed. There is only one bone in the frog's middle ear. The human middle ear contains three bones (ossicles). As in man, semicircular canals help to maintain body balance. Main Page - Kinds of Amphibians - Physical Characteristics - Behavior The Evolutionary Record - Anatomy of the Frog

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Future Value of Money (FV): Unveiling the Growth of Your Investments The Future Value of Money (FV) represents the worth of an investment or a sum of money at a specific future date, considering a predetermined interest rate. It’s a crucial concept in finance, indicating the value an investment will grow to over time. The FV formula is used in capital budgeting to calculate the future value of cash flows that are expected to be generated by an investment. The FV of the cash flows is then compared to the initial cost of the investment to determine whether the investment will generate a positive return. By using this concept, investors can make informed decisions about whether or not to invest in a particular project. Formula for Future Value (FV) The formula for calculating the Future Value of an investment with compound interest is: • PV (Present Value): The initial amount of money invested or deposited. • r (Interest Rate): The rate at which the investment grows per period. • t (Time Period): The duration for which the money is invested or borrowed. Time Value of Money (TVM): Unveiling the Power of Future Dollars Example Calculation: Scenario 1: An investor has $10,000 today and invests it in a mutual fund with an expected annual return of 8%. What will the FV of the investment be in 10 years? Solution: FV = PV * (1 + r)^t Where: FV = future value of money PV = present value of money r = interest rate t = time period in years Plugging in the values: FV =$10,000 * (1 + 0.08)^10 FV = $46,609.59 Therefore, the FV of the investment will be$46,609.59 in 10 years. Explanation: This scenario demonstrates how the FV formula can be used to calculate the future value of a lump sum investment over a specified time horizon. This is useful for investors planning their long-term financial goals, such as retirement. Scenario 2: An investor is considering making a monthly contribution of $500 to a retirement savings account. The account earns an annual interest rate of 6%, compounded monthly. What will the FV of the contributions be in 20 years? Solution: FV = PMT * ((1 + r/n)^(n*t) – 1) / r Where: FV = future value of money PMT = periodic payment r = annual interest rate n = number of compounding periods per year t = total time in years Plugging in the values: FV =$500 * ((1 + 0.06/12)^(12*20) – 1) / 0.06 FV = $201,661.62 Therefore, the FV of the contributions will be$201,661.62 in 20 years. Explanation: This scenario demonstrates how the FV formula can be used to calculate the future value of a series of regular payments, such as monthly savings contributions. This is crucial for planning for long-term financial goals that require consistent savings. Let’s consider an investment of $5,000 at an annual interest rate of 6% compounded annually for 5 years: FV=$5,000×(1+0.06)5=$6,760.79 After 5 years, the$5,000 investment at a 6% annual interest rate would grow to approximately $6,760.79. Scenario 4: An investor has a portfolio of investments with an expected annual return of 10%. They want to estimate the FV of their portfolio in 15 years. If the current value of their portfolio is$100,000, what will the FV be in 15 years? Solution: FV = PV * (1 + r)^t Where: FV = future value of money PV = present value of money r = interest rate t = time period in years Plugging in the values: FV = $100,000 * (1 + 0.10)^15 FV =$761,225.80 Therefore, the FV of the portfolio will be $761,225.80 in 15 years. Explanation: This scenario demonstrates how the FV formula can be used to estimate the future value of a portfolio of investments over a long-term horizon. This is valuable for investors assessing the potential growth of their wealth and planning for their long-term financial goals. Scenario 4: An investor is evaluating an investment project with an initial cost of$50,000. The project is expected to generate annual cash flows of $10,000 for the next five years. If the investor’s required rate of return is 12%, what is the FV of the project’s cash flows at the end of the five-year period? Solution: FV = PMT * ((1 + r/n)^(n*t) – 1) / r Where: FV = future value of money PMT = periodic payment r = annual interest rate n = number of compounding periods per year t = total time in years Plugging in the values: FV =$10,000 * ((1 + 0.12/1)^1*5) – 1) / 0.12 FV = $37,800.72 Therefore, the FV of the project’s cash flows at the end of the five-year period will be$37,800.72. Explanation: This scenario illustrates how the FV formula can be used to calculate the future value of cash flows generated by an investment project. This is essential for capital budgeting as it allows investors to assess the potential profitability of the project. Significance in Financial Planning and in Decision Making Understanding the Future Value of Money is essential for: • Investment Planning: It helps in estimating the potential growth of investments over time, aiding in long-term financial planning. • Savings and Retirement: Individuals use this concept to assess the growth of retirement savings or other long-term savings accounts. • Loan Planning: Lenders and borrowers utilize the FV concept to calculate loan terms, repayments, and future values of borrowing or investing money. Borrowers can project the total future cost of a loan, including interest payments, and plan their repayment strategies effectively. 1. Financial Planning: FV aids in estimating the future worth of investments, helping individuals and businesses plan for long-term financial goals. 2. Goal Setting: It assists in setting realistic savings or investment targets, guiding individuals in achieving their financial objectives. 3. Comparing Investment Options: FV allows for the comparison of various investment options by estimating their potential future values. Limitations of FV: 1. Assumed Constant Interest Rates: Similar to TVM, FV calculations presume a constant interest rate, which might not align with real-world scenarios. 2. Complexities Ignored: FV calculations might overlook various factors like taxes, fees, or changes in investment conditions, impacting the accuracy of projections. 3. Reliance on Predictions: FV is based on predictions of future interest rates and investment performance, which may vary from actual outcomes. Conclusion The Future Value of Money is a critical tool in financial decision-making, guiding individuals and businesses in making informed choices about investments, savings, and borrowing, considering the impact of time and interest rates on the value of money. By understanding these concepts empowers individuals to make informed decisions about their finances, plan for their future goals, and maximize the value of their investments. Photo credit: Monam via Pixabay Capital Budgeting Techniques: Making Smarter Investment Choices

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It is currently 25 Jun 2017, 03:42 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # If n is a positive integer, is the value of b-a at least Author Message VP Joined: 30 Sep 2004 Posts: 1480 Location: Germany If n is a positive integer, is the value of b-a at least [#permalink] ### Show Tags 12 Jan 2005, 09:02 This topic is locked. If you want to discuss this question please re-post it in the respective forum. If n is a positive integer, is the value of b-a at least twice the value of 3^n - 2^n ? 1. a = 2^n+1 and b = 3^n+1 2. n =3 Director Joined: 07 Nov 2004 Posts: 683 ### Show Tags 12 Jan 2005, 09:48 Pick A. 1) b= 3^n+1, a = 2^n+1 b-a = 3^n-2^n So, b-a is not greater than twice the value of 3^n-2^n. Sufficient. 2) n = 3 Insufficient VP Joined: 18 Nov 2004 Posts: 1433 ### Show Tags 12 Jan 2005, 11:50 Pick "A". I am assuming offcourse that you meant b= 3^(n+1), a = 2^(n+1) Statement 1 : for n = 1 we have (b-a) ==> 9 - 4 = 5 and 3^n - 2^n = 1....so ans is yes n = 2 we have (b-a) ===> 27-8 = 19 and 3^n - 2^n = 1....so ans is yes Statement 2 is insuff. ALTERNATE APPROACH: b-a = 3^(n+1) - 2^(n+1) = 3^n x 3 - 2^n x 2 = 2(3^n x 1.5 - 2^n) For all +ve n interger (3^n x 1.5 - 2^n) will be > than 3^n-2^n....So statement 1 is suff. Director Joined: 21 Sep 2004 Posts: 607 ### Show Tags 12 Jan 2005, 16:11 A . explanation as above. 12 Jan 2005, 16:11 Display posts from previous: Sort by

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Contact: Valene Marshall National Science Foundation Caption: At first glance, the bone-dry landscape of the Atacama Desert in Chile might seem inhospitable. But, it's prime real estate for astronomers. This desert is now home to the largest ground-based radio telescope in the world! The telescope is called the Atacama Large Millimeter/submillimeter Array or ALMA for short. "It's allowing us to see the universe like we never have before," says Kartik Sheth, an astronomer with the National Radio Astronomy Observatory (NRAO) in Charlottesville, Va. "ALMA will be a telescope made up of 66 antennas, at 16,500 feet, in the desert of Atacama, in Chile," he explains. With support from the National Science Foundation, Sheth is part of a team of astronomers putting this new array to work. "Together, these telescopes work as a single telescope that can be as large as 10 miles in diameter. And, it will be 10 to 100 times more powerful than any existing telescope that we have," says Sheth. From its perch in the high desert, ALMA sits above 40 percent of Earth's atmosphere and virtually all the world's water vapor. ALMA is designed to peer into a slice of the electromagnetic spectrum at millimeter wavelengths; light that is closer to a radio wave than to the optical light that is seen by the human eye. Sheth says ALMA can detect hidden gases inside galaxies; gases that might hold the key to star and planetary formation. ALMA might even detect the building blocks of life. Credit: Jon Baime, Science Nation Producer Usage Restrictions: This video may only be used with appropriate caption or credit.

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A new study from the University of California, Irvine and the University of Washington shows that water conserved by plants under high CO2 conditions compensates for much of the effect of warmer temperatures, retaining more water on land than predicted in commonly used drought assessments. According to the study published this week in the Proceedings of the National Academy of Sciences, the implications of plants needing less water with more CO2 in the environment changes assumptions of climate change impacts on agriculture, water resources, wildfire risk, and plant growth. The study compares current drought indices with ones that take into account changes in plant water use. Reduced precipitation will increase droughts across southern North America, southern Europe and northeastern South America. But the results show that in Central Africa and temperate Asia — including China, the Middle East, East Asia and most of Russia — water conservation by plants will largely counteract the parching due to climate change.

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(AP) -- With whale fins splashing in the distance, Ruth Curry hauls up her catch from the blustery deck of an icebreaker. An orange tube fixed to a metal frame breaks the surface as the motorized winch stops groaning. Inside: data on the water temperature deep down in this glacial fjord off southeast Greenland. "If you were to dip your hand in it, it doesn't seem that warm," says Curry, an American climate scientist. "But it is. It's warm enough to melt ice. And that's the important thing here." Curry and her colleagues from the Woods Hole Oceanographic Institution in Massachusetts zigzagged between majestic icebergs in the Sermilik fjord last month in search of proof that waters from warmer latitudes, or subtropical waters, are flushing through this remote and frigid region. They found it - all the way up to the base of the outlet glaciers that spill into the ocean like tongues of ice from Greenland's massive ice sheet. Coupled with similar findings off western Greenland, the discovery could help to explain why the glaciers have started flowing quicker in the past decade, a phenomenon that raised alarm because it contributes to rising sea levels. "The measurements alone are not enough to conclude that the glacial melt is to a high degree driven by subtropical water. But I think the story is (starting) to come together," says research leader Fiamma Straneo. The team found subtropical water with a temperature of about 39 Fahrenheit (4 degrees Celsius) deep inside the Sermilik fjord. The findings confirm the outcome of an undersea battle below the dark surface of the North Atlantic: Arctic waters that usually dominate this region have yielded to an influx of subtropical water carried north by westward branches of the current commonly called the Gulf Stream. Scientists say it's a natural process - in one period the cold waters will have the upper hand, and in the next it's the other way round. But the rapidly increasing temperatures of the subtropical oceans suggest that the balance could be tilted beyond natural variability, Curry says. "We've actually measured the waters at their source and have seen their temperature going up, up, up in a way that can't be explained without taking into account human influences," she says. The research underscores the complex interaction between the world's oceans and a warming atmosphere. Oceans help to contain global warming by absorbing about half of the carbon dioxide released by humans into the atmosphere, but the water also expands as it warms, raising sea levels. It could also have a big impact on climate through feedback mechanisms, such as the melting of seaside glaciers and changes to ocean currents that warm or cool different parts of the globe. In the June-August period, the world's ocean surface temperature was the warmest on record since 1880, according to the U.S. National Oceanic and Atmospheric Administration. The surface temperature was 62.5 F (17 Celsius), 1 degree F (0.6 degrees C) above the 20th century average. Meteorologists say the reason was El Nino weather patterns combined with manmade global warming. The North Atlantic has seen especially large changes in recent years. The temperature of the water that flows into the Arctic has increased by as much as 3.5 degrees F (2 degrees C) since the 1990s, says Helge Drange, professor of oceanography at Norway's University of Bergen. "This can only be understood as a combined effect of natural variability and manmade warming," he says. That has had a big impact on marine ecosystems, with fish traveling north into waters that were previously too cold for them. For example, more than 20 new species of fish have been found off Iceland, including blue sharks and flounders. Meanwhile, cod has followed the warm water as it flows around Greenland's southern tip and up the giant island's west coast. "If you talk to local people they say it's fantastic because the Atlantic cod is coming," Drange says. To many scientists, however, the shifts in ocean currents are no cause for celebration. Even if there's natural variability, there's concern that global warming may make the fluctuations more extreme. And while some species thrive in warmer water, others that live on the edge of the Arctic, such as polar bears and seals, find their habitat melting away. "We're heading off to a climate extreme and this is just going to snowball," says Curry, reflecting on the state of the global climate on the Greenpeace icebreaker hosting the Woods Hole research team. "I think that we've done it, really kicked Earth's climate system. And that says a lot," she says. "It's a beast. It's huge. And to have moved it in as short a period of time as a 100 years, basically, to have done that is enormous." ©2009 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed. Explore further: Quakes destroy or damage 83 houses in Philippines

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# Understanding Double Weave Blocks If you are lucky enough to have a loom with eight or more shafts, then double weave blocks are yours to master – but beware their addictive powers! In this post, we’ll talk through the logic of working with blocks and suggest some possibilities to get you hooked…I mean started. ## Why 8 shafts? We have already seen in our post on double cloth weave how a loom with four shafts can be used to weave two layers of plain weave. When you have eight shafts to play with, you can assign four to each layer: that makes it possible to divide your threading into two groups of two shafts each. A typical block threading looks something like this: The blue squares indicate one warp layer, which is threaded on shafts 1-4. The black squares show the other layer, threaded on shafts 5-8. The threading has been divided into blocks A and B. In block A, the blue warp layer is threaded on shafts 1 & 2, the black warp layer on shafts 5 & 6. In block B, shafts 3 & 4 are used for the blue layer, shafts 7 & 8 for the black layer. Each block consists of 4 ends but can be repeated as many times as you like: wide blocks, narrow blocks, any-size-you-please blocks. My 8-shaft sampler is threaded so that one half consists of equal width blocks, while the blocks in the other half are based on the Fibonacci sequence. ## To weave two layers Just because you have blocks, doesn’t mean you’ll want to use them all the time! You can still weave two solid plain weave layers. In the diagram below, I have indicated that the blue layer is going to be the layer on top by marking it with crosses on the threading plan – as you get involved in devising your own double weave drafts, this is quite a useful way to plan what you want to achieve and design a liftplan to bring it to life. In the adjacent grid we can see the four lifts that we will need: two lifts to make plain weave in the top layer, and two more lifts to make plain weave in the bottom layer while lifting the top layer out of the way. I’ve used my threading notation of colored squares to show which shafts are being used to make plain weave in the two layers, and simple crosses to show which shafts are simply being lifted out of the way. I have found that it helps my understanding of double weave drafting to distinguish between these two reasons for lifting shafts. Using the same notation, I can write out the following set of lifts to give me plain weave in two layers with black on the top: ### Note: Tie-ups, liftplans and all The diagrams above show two sets of lift combinations, which are necessary to make plain weave in two layers. At this stage they are neither liftplans nor tie-ups – we’ll come back to those later. If you can, it is well worth using a table loom when you explore double weave blocks. When you have the freedom to move each shaft independently then all the possibilities are open to you and you can develop your own lift combinations by thinking through the process. ## To weave blocks Let’s turn, then, to thinking about blocks. First of all, we are still going to need to make plain weave in both layers of our cloth. This gives us the starting point shown below: I have indicated with crosses my intention to have the blue layer on top in block A and the black layer on top in block B. Notice that I want the black warp on shafts 7 & 8 to form part of the top layer. This tells me that when I am weaving the blue layer I will need to lift those two shafts up, so that their warp ends remain visible on the surface of the cloth. Similarly, when I am weaving the black layer I will need to raise shafts 1 & 2 to keep those warp ends on the surface. And there we have it: a combination of lifts which will give us blue on the face of the cloth wherever block A is threaded and black wherever block B is threaded. To switch the colors over to the opposite blocks, we need to lift the opposite pairs of shafts. Note that we are continuing to make plain weave in exactly the same way as before – the only thing we have changed is our choice of which shafts carry the top layer. Of course, we have the option to go further and mix up the layers in our plain weave too, but that is a challenge for another day! ## Liftplans and tie-ups You can easily turn any of the examples shown here into a liftplan. The important thing to remember is that you need to alternate your weaving of the two layers pick by pick. To make a tie-up is a little more complex and is most easily done by splitting the treadles into two groups, one to operate shafts 1-4 and the other to operate shafts 5-8. On a jack loom you will need at least eight treadles: four for each group. Two of these treadles weave plain weave, one lifts block A and one lifts block B. If you want to lift the whole layer, then you need to use both of these treadles together, or – if you have 10 treadles – you can tie up another treadle to do this job. I’ve used the same notation as above to show what each treadle is doing – of course, you may prefer to order them differently. On a countermarche loom, if you want to have access to all these combinations, then you will need a full dozen treadles: six for each group. As you cannot use the block A and block B treadles together, you will need one treadle to raise the whole layer and another treadle to lower it. It can be quite a challenge at first to make the treadle combinations do what you want, but it is also quite exciting to mix and match! Just make sure that your treadling maintains the pick by pick alternating of layers. ## Some double weave design possibilities The popular “windows” design is achieved by arranging your threading so that you begin and end with block A. You then weave a sequence which has: • all of one layer on top • the same layer on top in block A only • all of the layer on top again Staggered blocks are visually very exciting, especially if your threading blocks are of different widths. You need to weave a sequence with: • layer 1 on top in both blocks • layer 2 on top in block A only • layer 2 on top in both blocks • layer 2 on top in block B only • layer 1 on top in both blocks

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# Force Calculations Force is push or pull. Forces on an object are usually balanced (if unbalanced the object accelerates): Balanced Unbalanced No Acceleration Acceleration ### Example: The forces at the top of this bridge tower are in balance (it is not accelerating): The cables pull downwards equally to the left and right, and that is balanced by the tower's upwards push. (Does the tower push? Yes! Imagine you stand there instead of the tower.) We can model the forces like this: And when we put them head-to-tail we see they close back on themselves, meaning the net effect is zero: The forces are in balance. Forces in balance are said to be in equilibrium: there is also no change in motion. ## Free Body Diagrams The first step is to draw a Free Body Diagram (also called a Force Diagram) Free Body Diagram: A sketch where a body is cut free from the world except for the forces acting on it. In the bridge example the free body diagram for the top of the tower is: Free Body Diagram It helps us to think clearly about the forces acting on the body. ### Example: Car on a Highway What are the forces on a car cruising down the highway? The engine is working hard, so why doesn't the car continue to accelerate? Because the driving force is balanced by: • Air resistance (put simply: the air resists being pushed around), • Rolling resistance, also called rolling friction (the tires resist having their shape changed) Like this: Free Body Diagram W is the car's weight, R1 and R2 are the rolling resistance of the tires, N1 and N2 are the reaction forces (balancing out the car's weight). Note: steel wheels (like on trains) have less rolling resistance, but are way too slippery on the road! ## Calculations Force is a vector. A vector has magnitude (size) and direction: We can model the forces by drawing arrows of the correct size and direction. Like this: Brady stands on the edge of a balcony supported by a horizontal beam and a strut: He weighs 80kg. What are the forces? Let's take the spot he is standing on and think about the forces just there: ### His Weight His 80 kg mass creates a downward force due to Gravity. Force is mass times acceleration: F = ma The acceleration due to gravity on Earth is 9.81 m/s2, so a = 9.81 m/s2 F = 80 kg × 9.81 m/s2 F = 785 N ### The Other Forces The forces are balanced, so they should close back on themselves like this: We can use trigonometry to solve it. Because it is a right-angled triangle, SOHCAHTOA will help. For the Beam, we know the Adjacent, we want to know the Opposite, and "TOA" tells us to use Tangent: tan(60°) = Beam/785 N Beam/785 N = tan(60°) Beam = tan(60°) × 785 N Beam = 1.732... × 785 N = 1360 N For the Strut, we know the Adjacent, we want to know the Hypotenuse, and "CAH" tells us to use Cosine: cos(60°) = 785 N / Strut Strut × cos(60°) = 785 N Strut = 785 N / cos(60°) Strut = 785 N / 0.5 = 1570 N Solved: Interesting how much force is on the beam and strut compared to the weight being supported! ## Torque (or Moment) What if the beam is just stuck into the wall (called a cantilever)? There is no supporting strut, so what happens to the forces? The Free Body Diagram looks like this: The upwards force R balances the downwards Weight. With only those two forces the beam will spin like a propeller! But there is also a "turning effect" M called Moment (or Torque) that balances it out: Moment: Force times the Distance at right angles. We know the Weight is 785 N, and we also need to know the distance at right angles, which in this case is 3.2 m. M = 785 N x 3.2 m = 2512 Nm And that moment is what stops the beam from rotating. You can feel moment when holding onto a fishing rod. As well as holding up its weight you have to stop it from rotating downwards. ## Friction ### Box on a Ramp The box weighs 100 kg. The friction force is enough to keep it where it is. The reaction force R is at right angles to the ramp. The box is not accelerating, so the forces are in balance: The 100 kg mass creates a downward force due to Gravity: W = 100 kg × 9.81 m/s2 = 981 N We can use SOHCAHTOA to solve the triangle. Friction f: sin(20°) = f/981 N f = sin(20°) × 981 N = 336 N Reaction N: cos(20°) = R/981 N R = cos(20°) × 981 N = 922 N And we get: ## Tips for Drawing Free Body Diagrams • Draw as simply as possible. A box is often good enough. • Forces point in the direction they act on the body • straight arrows for forces • curved arrows for moments ## Sam and Alex Pull a Box The calculations can sometimes be easier when we turn magnitude and direction into x and y: <=> Vector a in Polar Coordinates Vector a in Cartesian Coordinates You can read how to convert them at Polar and Cartesian Coordinates, but here is a quick summary: From Polar Coordinates (r,θ) From Cartesian Coordinates (x,y) to Cartesian Coordinates (x,y) to Polar Coordinates (r,θ) x = r × cos( θ ) y = r × sin( θ ) r = √ ( x2 + y2 ) θ = tan-1 ( y / x ) Let's use them! ### Example: Pulling a Box Sam and Alex are pulling a box (viewed from above): • Sam pulls with 200 Newtons of force at 60° • Alex pulls with 120 Newtons of force at 45° as shown What is the combined force, and its direction? First convert from polar to Cartesian (to 2 decimals): Sam's Vector: • x = r × cos( θ ) = 200 × cos(60°) = 200 × 0.5 = 100 • y = r × sin( θ ) = 200 × sin(60°) = 200 × 0.8660 = 173.21 Alex's Vector: • x = r × cos( θ ) = 120 × cos(-45°) = 120 × 0.7071 = 84.85 • y = r × sin( θ ) = 120 × sin(-45°) = 120 × -0.7071 = −84.85 Now we have: (100, 173.21) + (84.85, −84.85) = (184.85, 88.36) That answer is valid, but let's convert back to polar as the question was in polar: • r = √ ( x2 + y2 ) = √ ( 184.852 + 88.362 ) = 204.88 • θ = tan-1 ( y / x ) = tan-1 ( 88.36 / 184.85 ) = 25.5° And we have this (rounded) result: And it looks like this for Sam and Alex: They might get a better result if they were shoulder-to-shoulder!

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1. ## Exact Value I have to evaluate the exact value of tan(15). To give some context, I have to find the area of a dodecagon, and I used the uber super cool formula: ns^2/(4tan(180/n)) where n is the number of sides and s is the side length. Thanks. 2. Originally Posted by DivideBy0 I have to evaluate the exact value of tan(15). To give some context, I have to find the area of a dodecagon, and I used the uber super cool formula: ns^2/(4tan(180/n)) where n is the number of sides and s is the side length. Thanks. Use a half-angle formula. I can never remember the formula for tan(a/2), so I do it this way: sin(a/2) = (+/-)sqrt{1 - cos(a)}/sqrt{2} cos(a/2) = (+/-)sqrt{1 + cos(a)}/sqrt{2} (where we get the + or - from which quadrant the angle is in.) So tan(a/2) = sin(a/2)/cos(a/2) = (+/-)sqrt{1 - cos(a)}/sqrt{1 + cos(a)} In this case, a = 30: tan(15) = sqrt{1 - cos(30)}/sqrt{1 + cos(30)} = sqrt{1 - sqrt{3}/2}/sqrt{1 + sqrt{3}/2} = sqrt{2 - sqrt{3}}/sqrt{2 + sqrt{3}} You will want to rationalize this, so multiply the numerator and denominator by sqrt{2 - sqrt{3}}. I'll just give you the answer: tan(15) = sqrt{7 - 4sqrt{3}} -Dan 3. Thanks m8! 4. Originally Posted by DivideBy0 Thanks m8! I appreciate the thanks ( ), but what the heck is "m8?" -Dan 5. Originally Posted by topsquark I appreciate the thanks ( ), but what the heck is "m8?" -Dan It's a 'leet' abbreviation of 'mate' (used commonly in australia) 6. Originally Posted by DivideBy0 It's a 'leet' abbreviation of 'mate' (used commonly in australia) Ah! Obvious once it's explained. -Dan

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BE2C2 Report — This fascinating map, created by the American Museum of Natural History, shows how the world’s human population grew from 1 million in AD 1 and migrated across the globe to reach 7 billion by 2015. Each yellow dot represents 1 million people. Modern humans evolved in Africa about 200,000 years. Around 100,000 years ago, we began migrating across the globe. Once we started to farm and settle down, the human population began to spike. By the year AD 1, it had reached 170 million. In the second half of the 18th century, the population doubled from 597 million to 1 billion — thanks to the Industrial Revolution which made a leap forward in medicine and technology. There was more food too, making it cheaper and more available. In only 200 years since the Industrial Revolution, the global population rocketed to 7 billion. If the growth rate continues at the same pace, 11 billion people will be living on the planet by the turn of the next century. Land use also kept pace with population growth. The two maps below show land use in the 1700s versus in 2050. It shows that across many parts of the globe, but particularly in North and South America, sub-Saharan Africa, Europe and Asia populations have exploded. According to their prediction, by 2050 we will reach our peak, as women have fewer children. Population growth will begin to slow. According to UN DESA report titled, “World Population Prospects: The 2015 Revision”, the current world population of 7.3 billion is expected to reach 8.5 billion by 2030, 9.7 billion in 2050 and 11.2 billion in 2100). (The original article appeared in the World Economic Forum website)

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The civilization that was Rome had high demands on its people. The Roman citizen may have enjoyed rights and had room to follow his ambitions, but so too did he have duties. These were not merely legal duties, but social ones. He would have to live up to the expectations of the men at the head of his family. This didn't merely apply to the Roman nobility, but so too to the simply country peasant. A man would have to prove his virtus, his worth as a man. Whatever their social status might have been, Romans could only win the recognition and respect of their fellow Romans by doing their duty. Where better is this shown that the origins of the census, the very registration which defined a Roman citizen, were military in nature. For it was the virtues of the warrior which were demanded, be the citizen a soldier, an labourer or a senator. He was to have courage and intelligence and show discipline. The privileged and high-born Roman would embark on a political career early on. For this a series of offices and posts led gradually upwards to ever more influence and prestige. All the young nobleman's abilities and energy would be devoted to getting onto and climbing this ladder. Private life was merely a space to rest and to find friends and build personal alliances. And the more distinguished a citizen's ancestry was, the more daunting the task became. Because he was expected to live up o their example. For this he would need to excel in a whole collection of skills; gaining riches, mastering law, distinguishing himself as an officer and winning followers and respect through his ability in oratory. Nobility in Roman society was not a matter established merely by birth. Nobility could be acquired and maintained only by serving in public offices and rising to senior positions, the senior magistracies called honores. If equestrian families which had acquired sufficient wealth over time could try to enter into the struggle for such high positions in order to acquire nobility, then the pressure on the nobles to maintain their standing became ever greater. For nobility was not only something one could acquire, but something one could also lose. By failing to achieve high office, either by lack of effort or lack of ability, the nobleman's family, his children, would lose their status. Only after three successive generations achieved high office in a row, could a family be noble. And yet it took only one generation to lose this nobility again. And so the pressure was on for each son of a senatorial family to perform and reach the highest levels of Roman society. From childhood on they were raised to compete and prove themselves the best and highest of society, the optimates. In his late teens a senatorial son would usually serve as a tribune on the staff of a legionary commander. These commanders were usually relatives or friend's of the family. In this role of officer in the army, the young man would face his first major tests. His discipline, courage, his ability to undergo hardships and, very importantly, his ability to withstand the temptation of foreign cultures and foreign women. But his service in the army would also reveal if the young nobleman would be a petty tyrant, cruel and vicious to the vanquished. For ruthlessness was indeed a virtue in a Roman leader, but cruelty and brutality were seen as a weakness and lack of nobility of mind. If military life was demanding on a young noble, then civilian life offered little respite. For just as the Roman army knew many an enemy, then so too did the powerful noble families of Rome. All feuds between different households were never forgotten. Should the father have been shamed and humiliated by the act of one family then it was upon the son to avenge this disgrace. These contests took place in the court room. Most families power depended very often on their ability to bend the rules. Fraud, intrigue, bribery, corruption, embezzlement, even extortion, blackmail and assault. And so there was few powerful households which had no secrets to hide. But it was by these secrets that they might be destroyed, if a young nobleman, skilled in oratory and knowledgeable in law, should drag them through the courts. More so the destruction of a powerful foe usually led to the young man, whose standing had inevitably risen in the eyes of the public, taking the very senatorial seat of the man he had just vanquished in the courts. It was around the age of thirty that a Roman nobleman would stand a realistic chance of launching his bid on achieving high office. No doubt this was the most arduous time of his life. To build up and maintain a network of friends, supporters and voters, he would leave no stone unturned. He would shoulder enormous financial burdens (to the point of near bankruptcy if necessary), work all day long, defend his many clients in court, support them with money and spend his evenings at banquettes fulfilling his social duties of host or honoured guest. He would have to travel the rural more to visit his electors. Shaking hands, making them feel important by knowing their names and their families. Such a nobleman had to be available at all times. He would need to provide help to those who sought it, be that with money, accommodation, letters of reference to potential employers, or even by lending his horses. Most of all, much like the tv-friendly politicians of today, the Roman nobleman had to be likeable. A generous and kind leader of the poor and a courteous and respectful elderly and his more distinguished peers. This life would continue for all his time in office, though no doubt as his sons grew older, they would help him in his duties. But the responsibilities would only be taken from his shoulders once his sons achieved office too and he could finally retire. Most likely he would then retire to a villa in the countryside where he would spend the later years of his life enjoying the peace and quiet he had so longed for. Alas death would bring him an honourable funeral and he would pass on into family memory from where he would further increase the burden upon the next generations to live up to their ancestors' example. A great way of strengthening and enlarging one's network of power was through marriages, either one's own marriage or that of one's relatives. For such wedlock would bring about alliances between families, which would then lend each other mutual support. Both practical as well as political support. Adoptions too could build such alliances. More so, neither marriages nor adoptions ever severed the links between the children and their real families. Hence the individuals didn't suffer while the family unit was further strengthened and empowered. Examples of such marriages and adoptions are plenty. Scipio adopted the son of Aemilius Paullus, who then became known as Scipio Aemilianus and who would later speak of either of his two fathers with great respect and affection. The daughter of Cicero married several times, undoubtedly to build alliances for her father. Her subsequent divorces did nothing to damage the relationships between her father and his sons-in-law.

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# How do you solve -2a = 16? Mar 13, 2018 See a solution process below: #### Explanation: Divide each side of the equation by $\textcolor{red}{- 2}$ to solve for $a$ while keeping the equation balanced: $\frac{- 2 a}{\textcolor{red}{- 2}} = \frac{16}{\textcolor{red}{- 2}}$ $\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} a}{\cancel{\textcolor{red}{- 2}}} = \frac{2 \times 8}{\textcolor{red}{2 \times - 1}}$ $a = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 8}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}} \times - 1}}$ $a = \frac{8}{\textcolor{red}{- 1}}$ $a = - 8$

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In April 2001, the U.S. Census Bureau announced that the total population of the United States on April 1, 2000, was 281,421,906. The apparent precision was entirely spurious. The Director of the Census Bureau later remarked that the true population of the United States in 2000 is known only to within 5 million persons or so(so plus or minus 2%). The amount of error and uncertainty remains or increases for historical estimates, current estimates and future estimates. According to a preliminary announcement of the United Nations Population Division (2001), the difference between the medium projected population of the world in 2050 according to its 1998 projection (8.9 billion) and its 2000 projection (9.3 billion) is 413 million people, roughly 5 percent of the 1998 projected population size for 2050. The population project at the International Institute for Applied Systems Analysis projected a median (not medium) world population in 2050 of 8.8 billion. These three projections for 2050 differ in methods and assumptions. The differences in output among them of half a billion people express demographers’ ignorance of the future, not differences in genuine knowledge. The demographic present, past, and future are surrounded by uncertainty. Population projections are uncertain for several reasons. The initial data may be erroneous. The rates of birth, death, and migration in cohort-component models may be projected erroneously. (Projections for countries or small areas normally are more uncertain than those for the world because of the greater importance of migration for local areas.) External factors may change unexpectedly (such as AIDS, natural hazards, or climate). External factors may change as expected but the relationship between those factors and demographic rates may change. Policies and programs may develop to influence the rates of birth, death, and migration. Estimates or guesses about historic, current and future economic activity (GDP etc...) build upon the uncertainty around population. Most demographers would probably agree to four statements about the future of global population during the 25-50 years. 1. the population will be bigger than it is now. The world will be bigger by 2 billion to 4 billion people by the middle of the century, and nearly all of that growth will be in poor countries, not rich. 2. the population will increase less rapidly, absolutely and relatively, than it has recently. Whether population growth ends depends on choices that we make right now about reproductive health, education for women, and many other investments. 3. the population will be more urban than it is now. Practically all of the additional people will be living in cities in poor countries, and that will be an unprecedented epidemiological challenge to infectious disease control. 4. the population will be older than it is now. Canada and US Population estimates Under the scenarios considered, Canada’s population would be between 36.0 and 42.0 millions in 2031 and between 36.0 and 50.0 millions in 2056. In the medium-growth scenario, the population would be 39.0 millions in 2031 and 42.5 millions in 2056. Economic estimates for the size of China's economy can vary over 1200% for 2040. Nobel Prize winning economist Robert Fogel projects that China's economy will be $123 trillion in 2040 Albert Keidel of the Carnegie Endowment projects China to have a $45 trillion economy in 2040 Researchers at the Institute of Quantitative & Technical Economics of the Chinese Academy of Social Sciences forecasted in 2007 that China's economy would grow to about $5.9 trillion in 2030 and $6.7 trillion in 2035. An economist who could predict annual economic growth to within 1% would be doing pretty well. But if there was a consistent under-estimation or overestimation of economic growth for China, USA, Europe or the world of 2% over the course of decades then the result could easily be off by 100% by 2040. The annual economic figures themselves are inaccurate to start with. Then you start getting into surprises like a pandemic or financial crisis or surprising successes like new technology or business processes or policies which increase growth. The policies which helped India breakout of the Hindu growth rate. China shifting to opening its economy in the late 1970s and 1980s. Containerized shipping for more growth. Walmart providing economic productivity gains. The internet. Even getting a handle on how much those things helped or hindered in the past is uncertain, so it is tough to determine how much things are helped going forward. If you liked this article, please give it a quick review on Reddit, or StumbleUpon. Thanks How to Make Money

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# 12.3 Directed Graphs. A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency. ## Presentation on theme: "12.3 Directed Graphs. A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency."— Presentation transcript: 12.3 Directed Graphs A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency matrix. If the nodes are connected, you place a 1 in the matrix. Ex: TO: n 1 n 2 n 3 n 4 FROM: A finite graph may need to include info about direction. We get a directed graph. *Flights work this way. n1n1 n2n2 n3n3 n4n4 From Long Beach to Orlando on Jet Blue  Ex 1) Create the adjacency matrix. Chicago New York St. Louis TO: C N S FROM: What options do you have if you are making 2 flights? You would have the same matrix, but there would be two of them. 2 nd x –1 is MATRIX  EDIT choose 1: [A] enter dimensions 3 × 3 Now enter each element. When done, go 2 nd MODE to QUIT Calculate [A] 2 MATRIX  NAMES  1: [A] matches! If we continued this, it would be a lot of multiplying. We can use our graphing calculators to speed things up! Ex 2) Suppose the nodes in the diagram represent people and the directed edges mean the first person knows the second person’s phone number. a) Interpret the diagram in a matrix. Al Betty Fred Charles David Ellen 2 nd person: A B C D E F 1 st person: Ex 2) cont… b)In how many ways can a message get from Betty to Ellen in 3 or fewer calls? (*Use your calculator!) A B C D E F No ways 2 ways 1 way so 3 different ways Ex 2) cont… c) Is it possible to get a message from Fred to Charles? If yes, what is the minimum number of calls? A B C D E F 1 call No way 2 calls 1 way Yes, 2 calls minimum Homework #1203 Pg 616 #1–5, 7, 9, 11, 15, 17–20, 22–32 Download ppt "12.3 Directed Graphs. A finite graph is a set of points, called nodes, connected by a set of lines, called edges. We can represent the graph in an adjacency." Similar presentations

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When astronauts from the Apollo 17 mission landed on the Moon in 1972, one of their mission objectives was to analyze the tenuous atmosphere using the Lunar Atmosphere Composition Experiment, a mass spectrometer (with a shape and appearance weirdly reminiscent of a modern day printer/scanner combo) designed to detect traces of gas in the lunar firmament. At the time, readings from LACE had suggested that helium was present in the lunar atmosphere. Now, forty years later, readings from NASA's Lunar Reconnaissance Orbiter have corroborated LACE's findings — and the confirmation raises some interesting questions. For instance, does the helium originate from inside the Moon, or from an external source like solar wind? How do helium concentrations vary with altitude? And why do atmospheric helium levels tend to drop as night sets in? LRO's assessment is also a testament to its versatility as a scientific instrument. Even though the orbiter is primarily a surface-mapping tool, NASA hopes it can provide some answers to questions surrounding the Moon's helium-rich atmosphere on the side. "These ground-breaking measurements were enabled by our flexible operations of LRO as a science mission," explained LRO project scientist Richard Vondrak in a statement, "so that we can now understand the moon in ways that were not expected when LRO was launched in 2009." Read more about LRO and the Moon's mysterious, helium-rich atmosphere over at MSNBC.

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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" /> You are viewing an older version of this Concept. Go to the latest version. # Temperature ## The average kinetic energy of atoms in a piece of matter. Estimated9 minsto complete % Progress Practice Temperature Progress Estimated9 minsto complete % Temperature Students will learn the concept of temperature, where it comes from and how it relates to our everyday world. ### Key Equations $KE_{avg} = \frac{1}{2} m v ^2_{avg} = \frac{3}{2}kT$ The average kinetic energy of atoms (each of mass $m$ and average speed $v$ ) in a gas is related to the temperature $T$ of the gas, measured in Kelvin. The Boltzmann constant $k$ is a constant of nature, equal to $1.38\times10^{-23} \;\mathrm{J/K}$ $T_F = \frac{9}{5}T_C + 32^\circ \text{F}$ ; conversion from Celsius to Fahrenheit $T_C = \frac{5}{9}(T_F - 32^\circ \text{F})$ ; conversion from Fahrenheit to Celsius ### Guidance • When an object feels cold to the touch, it is because heat is flowing from you to the object. • When an object feels hot to the touch, it is because heat is flowing from the object to you. • Some objects (like metals) conduct heat better than others (like wood). Thus if you stick a metal rod in the fireplace and hold the other end, the heat is conducted well and you get burned. On the other hand, if you place a wood stick in the fire and hold the other end you’ll be OK. • The temperature of a gas is a measure of the amount of average kinetic energy that the atoms in the gas possess. • If you heat something, you increase its internal energy, so you increase the movement of molecules that make up this thing, thus it expands. This is called heat expansion; most everything expands as heated and contracts as cooled. • Most materials expand as they are heated. This can cause bridges to collapse if they are not designed to have a place to expand in the summer months (like the placing of metal ‘teeth’ at intervals on the Golden Gate Bridge). • Water contracts from $0^\circ C$ to $4^\circ C$ and then expands from $4^\circ C$ to $100^\circ C$ . Remembering that density is mass divided by volume explains why water at $4^\circ C$ is more dense than water below and above $4^\circ C$ . This also explains why lakes freeze on the top first and not throughout. As the water on the top of the lake drops below $4^\circ C$ , it is now more dense than the water below it, thus it sinks to the bottom, allowing the warmer water to rise up to the top and cool down in the winter weather. Only when the entirety of the lake is at $4^\circ C$ , then the lake can start to freeze. It freezes from the top down, because water below $4^\circ C$ is less dense than water at $4^\circ C$ . • More than 50% of the water rise expected from global warming is due to the thermal expansion of water • There are 3 different temperature scales you should know-the Kelvin scale, the Celsius scale and the Fahrenheit scale. • The Kelvin scale (K) is the one used in most scientific equations and has its zero value set at absolute zero (the theoretical point at which all motion stops). • The Celsius scale $(^\circ C)$ is the standard SI temperature scale. It is equal to the Kelvin scale if you minus 273 from the Celsius reading. Water has a boiling point of $100^\circ C$ and a freezing point of $0^\circ C$ . • The Fahrenheit scale $(^\circ F)$ is the English system and the one we are familiar with. • Newtons’ Law of Cooling: The rate of heat transfer is proportional to the difference in temperature between the two objects. For example, hot liquid that is put in the freezer will cool much faster than a room temperature liquid that is put in the same freezer. #### Kinetic Theory of Gases According to classical kinetic theory, temperature is always proportional to the average kinetic energy of molecules in a substance. The constant of proportionality, however, is not always the same. Consider: the only way to increase the kinetic energies of the atoms in a mono-atomic gas is to increase their translational velocities. Accordingly, we assume that the kinetic energies of such atoms are stored equally in the three components ( $x,y, \text{ and } z$ ) of their velocities. On the other hand, other gases --- called diatomic --- consist of two atoms held by a bond. This bond can be modeled as a spring, and the two atoms and bond together as a harmonic oscillator. Now, a single molecule's kinetic energy can be increased either by increasing its speed, by making it vibrate in simple harmonic motion, or by making it rotate around its center of mass . This difference is understood in physics through the concept of degrees of freedom : each degree of freedom for a molecule or particle corresponds to a possibility of increasing its kinetic energy independently of the kinetic energy in other degrees. It might seem that monatomic gases should have one degree of freedom: their velocity. They have three because their velocity can be altered in one of three mutually perpendicular directions without changing the kinetic energy in other two --- just like a centripetal force does not change the kinetic energy of an object, since it is always perpendicular to its velocity. These are called translational degrees of freedom. Diatomic gas molecules, on the other hand have more: the three translational explained above still exist, but there are now also vibrational and rotational degrees of freedom. Monatomic and diatomic degrees of freedom can be illustrated like this: Temperature is an average of kinetic energy over degrees of freedom, not a sum . Let's try to understand why this is in reference to our monoatomic ideal gas. In the derivation above, volume was constant; so, temperature was essentially proportional to pressure, which in turn was proportional to the kinetic energy due to translational motion of the molecules. If the molecules had been able to rotate as well as move around the box, they could have had the same kinetic energy with slower translational velocities, and, therefore, lower temperature. In other words, in that case, or assumption that the kinetic energy of the atoms only depends on their velocities, implied between equations [2] and [3], would not have held . Therefore, the number of degrees of freedom in a substance determines the proportionality between molecular kinetic energy and temperature: the more degrees of freedom, the more difficult it will be to raise its temperature with a given energy input. This is why it takes so long to boil water but so little time to heat up a piece of metal with the same mass. A note about the above discussion: Since the objects at the basis of our understanding of thermodynamics are atoms and molecules, quantum effects can make certain degrees of freedom inaccessible at specific temperature ranges. Unlike most cases in your current physics class, where these can be ignored, in this case, quantum effects can make an appreciable difference. For instance, the vibrational degrees of freedom of diatomic gas molecules discussed above are, for many gases, inaccessible in very common conditions, although we do not have the means to explain this within our theory. In fact, this was one of the first major failures of classical physics that ushered in the revolutionary discoveries of the early 20th century. #### Example 1 Convert 75 degrees Fahrenheit to Celcius. ##### Solution To do this conversion, we'll just use the equation given above. $T_c&=\frac{5}{9}(T_f - 32^\circ \text{F})\\T_c&=\frac{5}{9}(75^\circ \text{F} - 32^\circ \text{F})\\T_c&=23.8^\circ \text{C}$ #### Example 2 The mass of a neon atom is $3.34*10^{-26}\;\text{kg}$ . If the temperature of the neon atom 100 K, what is it's average velocity? ##### Solution We can solve this problem using the equation given above relating kinetic energy to the temperature of a gas. $\frac{1}{2}mv^2&=\frac{3}{2}kT\\v&=\sqrt{\frac{3kT}{m}}\\v&=\sqrt{\frac{3*1.38*10^{-23}\;\text{J/K} * 100\;\text{K}}{3.34*10^{-26}\;\text{kg}}}\\v&=352.1\;\text{m/s}\\$ ### Time for Practice 1. Convert the boiling point of water $100^\circ \text{C}$ to Fahrenheit 2. Convert $70^\circ \text{F}$ to Celsius 3. The temperature of the box is related to the average speed of the molecules. Use momentum principles to relate temperature to pressure. Explain conceptually, in words rather than with equations. 4. Explain why a lake freezes at the top first, rather than throughout or at the bottom? 5. Typical room temperature is about $300 \;\mathrm{K}$ . As you know, the air in the room contains both $O_2$ and $N_2$ gases, with nitrogen the lower mass of the two. If the average kinetic energies of the oxygen and nitrogen gases are the same (since they are at the same temperature), which gas has a higher average speed? 6. Temperature is a measure of the average kinetic energy of molecules. Consider a mixture of hydrogen and oxygen gas at a certain temperature. Use the formula for kinetic energy to explain why the hydrogen molecules move faster than the oxygen molecules. Then explain why there’s no hydrogen in the earth’s atmosphere, and why the moon has no atmosphere at all. 7. Calculate the average speed of $N_2$ molecules at room temperature $(300 \;\mathrm{K})$ . (You remember from your chemistry class how to calculate the mass (in $kg$ ) of an $N_2$ molecule, right?) 8. How high would the temperature of a sample of $O_2$ gas molecules have to be so that the average speed of the molecules would be $10$ % the speed of light? Convert this temperature to Kelvin and Fahrenheit as well. 1. $212^\circ \text{F}$ 2. $21^\circ \text{C}$ 3. . 4. . 5. . 6. . 7. $517 \;\mathrm{m/s}$ 8. $1.15 \times 10^{12}\;\mathrm{K}$

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Our language, institutions, and current obsession with the royal baby notwithstanding, the United States has not been shaped solely by its British antecedents. Fernandez-Armesto, the William P. Reynolds Professor of History at the University of Notre Dame, offers a Hispanic perspective on this country that starts with conquistadores, then moves through the colonies in Puerto Rico, Florida, and the Southwest, missionary efforts in the Far West, and the vibrant Hispanic presence today. The United States is still typically conceived of as an offshoot of England, with our history unfolding east to west beginning with the first English settlers in Jamestown. This view overlooks the significance of America's Hispanic past. In an absorbing narrative, Felipe Fernndez-Armesto begins with the explorers and conquistadors who planted Spain's first colonies in Puerto Rico, Florida, and the Southwest in the sixteenth century. Missionaries and rancheros carry Spain's expansive impulse into the late eighteenth century, settling California, mapping the American interior to the Rockies, and charting the Pacific coast. The nineteenth-century triumph of Anglo-America in the West is followed by the twentieth-century Hispanic resurgence, spreading from the Hispanic heartland in the West to major cities from Chicago to Miami and Boston. Fernndez-Armesto shows that today's plural America is the product of its past.

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7 técnicas para enseñar a los niños nuevo vocabulario en inglés. Es un interesante artículo acerca de cómo enseñar a los niños nuevas palabras en inglés. Nada que no conozcamos, pero aún así interesante. Before a child can learn to read, he needs to have a good understanding of basic words and what they mean. There are very easy ways that you can build a preschooler's vocabulary and introduce early reading concepts. Here are some vocabulary-building activities that you can do every day that will help you teach your child new words. 1. Loving the LibraryIf you are looking for a great place to start building your preschooler's vocabulary and early reading skills, look no further than your local library. 2. Synonym SubstituteAn easy way to introduce your child to new words is to use them yourself. Learn how to become a walking thesaurus and why when it comes to preschool vocabulary building, enormous is better than big. 3. Learning and Reinforcing the AlphabetThis fun ABC game provides children who are learning the alphabet with some reinforcement and confidence. The bonus -- it's a great way to keep your preschooler busy on long car rides, in waiting rooms or while waiting on lines. 4. Use Descriptive WordsWhen it comes to increasing your child's vocabulary, more is better. The more words that your child hears on a daily basis, the more she'll learn, absorb and eventually put to use herself. 5. Become a Label MakerIf you want your preschooler to learn more words, then make it easy. Say them often, sure, but show them too. Build on her basic comprehension of well-known words by labeling all of these commonly-used items so she learns to recognize what the word looks like. 6. Become a Super SorterSeeing is learning when it comes to introducing new words. Teaching your preschooler how to sort and categorize will help their logical thinking and build their vocabulary. A good way to help preschoolers learn new words is to take what they are hearing and help them to visualize it. Here's how. 7. Rhyme TimeThe fat cat sat on the mat. The white kite flew at night. How many rhyming words can your preschooler come up with? Rhyming is not only fun to do, but is an easy way to get your child to think about how words can relate to each other. Última edición por Gius; 13/01/2012 a las 12:33 Etiquetas para este Tema

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||The neutrality of this article is disputed. (June 2013) (Learn how and when to remove this template message)| Animal languages are forms of non-human animal communication that show similarities to human language. Animals communicate by using a variety of signs such as sounds or movements. Such signing may be considered complex enough to be called a form of language if the inventory of signs is large, the signs are relatively arbitrary, and the animals seem to produce them with a degree of volition (as opposed to relatively automatic conditioned behaviors or unconditioned instincts, usually including facial expressions). In experimental tests, animal communication may also be evidenced through the use of lexigrams (as used by chimpanzees and bonobos). While the term "animal language" is widely used, researchers agree that animal languages are not as complex or expressive as human language. Many researchers argue that animal communication lacks a key aspect of human language, that is, the creation of new patterns of signs under varied circumstances. (In contrast, for example, humans routinely produce entirely new combinations of words.) Some researchers, including the linguist Charles Hockett, argue that human language and animal communication differ so much that the underlying principles are unrelated. Accordingly, linguist Thomas A. Sebeok has proposed to not use the term "language" for animal sign systems. Marc Hauser, Noam Chomsky, and W. Tecumseh Fitch assert an evolutionary continuum exists between the communication methods of animal and human language. - 1 Aspects of human language - 2 Primate: studied examples - 3 Non-primates: studied examples - 4 Comparison of the terms "animal language" and "animal communication" - 5 See also - 6 References - 7 Further reading - 8 External links Aspects of human language The following properties of human language have been argued to separate it from animal communication: - Arbitrariness: there is (usually) no rational relationship between a sound or sign and its meaning (e.g. there is nothing intrinsically "housy" about the word "house"). - Discreteness: language is composed of small, repeatable parts (discrete units) that are used in combination to create meaning. - Displacement: languages can be used to communicate ideas about things that are not in the immediate vicinity either spatially or temporally. - Duality of patterning: the smallest meaningful units (words, morphemes) consist of sequences of units without meaning. This is also referred to as double articulation. - Productivity: users can understand and create an indefinitely large number of utterances. - Semanticity: specific signals have specific meanings. Research with apes, like that of Francine Patterson with Koko (gorilla) or Allen and Beatrix Gardner with Washoe (chimpanzee), suggested that apes are capable of using language that meets some of these requirements such as arbitrariness, discreteness, and productivity. In the wild, chimpanzees have been seen "talking" to each other when warning about approaching danger. For example, if one chimpanzee sees a snake, he makes a low, rumbling noise, signaling for all the other chimps to climb into nearby trees. In this case, the chimpanzees' communication does not indicate displacement, as it is entirely contained to an observable event. Arbitrariness has been noted in meerkat calls; bee dances demonstrate elements of spatial displacement; and cultural transmission has possibly occurred between the celebrated bonobos Kanzi and Panbanisha. Human language may not be completely "arbitrary." Research has shown that almost all humans naturally demonstrate limited crossmodal perception (e.g. synesthesia) and multisensory integration, as illustrated by the Kiki and Booba study. Other recent research has tried to explain how the structure of human language emerged, comparing two different aspects of hierarchical structure present in animal communication and proposing that human language arose out of these two separate systems. Claims that animals have language skills akin to humans however, are extremely controversial. As Steven Pinker illustrates in his book The Language Instinct, claims that chimpanzees can acquire language are exaggerated and rest on very limited or specious data. The American linguist Charles Hockett theorized that there are sixteen features of human language that distinguished human communication from that of animals. He called these the design features of language. The features mentioned below have so far been found in all spoken human languages and at least one is missing from all other animal communication systems. - Vocal-auditory channel: sounds emitted from the mouth and perceived by the auditory system. This applies to many animal communication systems, but there are many exceptions. Ex. An alternative to vocal-auditory communication is visual communication. An example is cobras extending the ribs behind their heads to send the message of intimidation or of feeling threatened. In humans, sign languages provide many examples of fully formed languages that use a visual channel. - Broadcast transmission and directional reception: this requires that the recipient can tell the direction that the signal comes from and thus the originator of the signal. - Rapid fading (transitory nature): Signal lasts a short time. This is true of all systems involving sound. It does not take into account audio recording technology and is also not true for written language. It tends not to apply to animal signals involving chemicals and smells which often fade slowly. For example, a skunk's smell, produced in its glands, lingers to deter a predator from attacking. - Interchangeability: All utterances that are understood can be produced. This is different from some communication systems where, for example, males produce one set of behaviours and females another and they are unable to interchange these messages so that males use the female signal and vice versa. For example, Heliothine moths have differentiated communication: females are able to send a chemical to indicate preparedness to mate, while males cannot send the chemical. - Total feedback: The sender of a message is aware of the message being sent. - Specialization: The signal produced is intended for communication and is not due to another behavior. For example, dog panting is a natural reaction to being overheated, but is not produced to specifically relay a particular message. - Semanticity: There is some fixed relationship between a signal and a meaning. Primate: studied examples - Baboons: Humans are able to distinguish real words from fake words based on the phonological order of the word itself. In a recent study, baboons have been shown to have this skill, as well. The discovery has led researchers to believe that reading is not as advanced a skill as previously believed, but instead based on the ability to recognize and distinguish letters from one another. The experimental setup consisted of six young adult baboons, and results were measured by allowing the animals to use a touch screen and selecting whether or not the displayed word was indeed a real word, or a nonword such as "dran" or "telk." The study lasted for six weeks, with approximately 50,000 tests completed in that time. The experimenters explain the use of bigrams, which are combinations of two (usually different) letters. They tell us that the bigrams used in nonwords are rare, while the bigrams used in real words are more common. Further studies will attempt to teach baboons how to use an artificial alphabet. Non-primates: studied examples ||This section's tone or style may not reflect the encyclopedic tone used on Wikipedia. (April 2013) (Learn how and when to remove this template message)| Among the most studied examples of animal languages are: - Bird songs: Songbirds can be very articulate. African grey parrots are famous for their ability to mimic human language, and at least one specimen, Alex, appeared able to answer a number of simple questions about objects he was presented with. Parrots, hummingbirds and songbirds - display vocal learning patterns. - Bee dance: Used to communicate direction and distance of food source in many species of bees. - African forest elephants: Cornell University's Elephant Listening Project began in 1999 when Katy Payne began studying the calls of African forest elephants in Dzanga National Park in the Central African Republic. Andrea Turkalo has continued Payne's work in Dzanga National Park observing elephant communication. For nearly 20 years, Turkalo has spent the majority of her time using a spectrogram to record the noises that the elephants make. After extensive observation and research, she has been able to recognize elephants by their voices. Researchers hope to translate these voices into an elephant dictionary, but that will likely not occur for many years. Because elephant calls are often made at very low frequencies, this spectrogram is able to detect lower frequencies that human ears are unable to hear, allowing Turkalo to get a better idea of what she perceives the elephants to be saying. Cornell’s research on African forest elephants has challenged the idea that humans are considerably better at using language and that animals only have a small repertoire of information that they can convey to others. As Turkalo explained on 60 Minutes’ “The Secret Language of Elephants,” “Many of their calls are in some ways similar to human speech." - Mustached bats: Since these animals spend most of their lives in the dark, they rely heavily on their auditory system to communicate. This acoustic communication includes echolocation or using calls to locate each other in the darkness. Studies have shown that mustached bats use a wide variety of calls to communicate with one another. These calls include 33 different sounds, or "syllables," that the bats then either use alone or combine in various ways to form "composite" syllables. - Prairie dogs: Dr. Con Slobodchikoff studied prairie dog communication and discovered: - different alarm calls for different species of predators; - different escape behaviors for different species of predators; - transmission of semantic information, in that playbacks of alarm calls in the absence of predators lead to escape behaviors that are appropriate to the type of predator which elicited the alarm calls; - alarm calls containing descriptive information about the general size, color, and speed of travel of the predator. - Bottlenose dolphins: It was long believed that dolphins were never able to demonstrate the ability to communicate in their own language, but in light of a recent discovery, this may have been incorrect. Research has found out that dolphins greet each other with whistles, possibly communicating information about each other's name, age or sex.[better source needed] Each dolphin has its own unique whistle sound, allowing each dolphin to maintain a separate identity, similar to humans. Dolphins are able to create new sounds and whistles when trying to attract a mate. Furthermore, there appears to be a designated leader within most pods. The leader is responsible for initiating communication when approaching another dolphin group.[better source needed] Dolphins can hear one another up to 6 miles apart underwater. In one National Geographic article, the success of a mother dolphin communicating with her baby using a telephone was outlined. Researchers noted that it appeared that both dolphins knew who they were speaking with and what they were speaking about. Not only do dolphins communicate via nonverbal cues, but they also seem to chatter and respond to other dolphin’s vocalizations. Recording of humpback whales singing and clicking. |Problems playing this file? See media help.| - Whales: Two groups of whales, the humpback whale and a subspecies of blue whale found in the Indian Ocean, are known to produce repetitious sounds at varying frequencies known as whale song. Male humpback whales perform these vocalizations only during the mating season, and so it is surmised the purpose of songs is to aid sexual selection. Humpbacks also make a sound called a feeding call, five to ten seconds in length of near constant frequency. Humpbacks generally feed cooperatively by gathering in groups, swimming underneath shoals of fish and all lunging up vertically through the fish and out of the water together. Prior to these lunges, whales make their feeding call. The exact purpose of the call is not known, but research suggests that fish react to it. When the sound was played back to them, a group of herring responded to the sound by moving away from the call, even though no whale was present. - Sea lions: Beginning in 1971 and continuing until present day, Dr. Ronald J. Schusterman and his research associates have studied sea lions’ cognitive ability. They have discovered that sea lions are able to recognize relationships between stimuli based on similar functions or connections made with their peers, rather than only the stimuli's common features. This is called “equivalence classification.” This ability to recognize equivalence may be a precursor to language. Research is currently being conducted at the Pinniped Cognition & Sensory Systems Laboratory to determine how sea lions form these equivalence relationships. Sea lions have also been proven to be able to understand simple syntax and commands when taught an artificial sign language similar to the one used with primates. The sea lions studied were able to learn and use a number of syntactic relations between the signs they were taught, such as how the signs should be arranged in relation to each other. However, the sea lions rarely used the signs semantically or logically. In the wild it's thought that sea lions use the reasoning skills associated with equivalence classification in order to make important decisions that can affect their rate of survival (e.g. recognizing friends and family or avoiding enemies and predators). Sea lions use the following to display their language: - Sea lions use their bodies in various postural positions to display communication. - Sea lion's vocal cords limit their ability to convey sounds to a range of barks, chirps, clicks, moans, growls and squeaks. - There has yet to be an experiment which proves for certain that sea lions use echolocation as a means of communication. The effects of learning on auditory signaling in these animals is of special interest. Several investigators have pointed out that some marine mammals appear to have an extraordinary capacity to alter both the contextual and structural features of their vocalizations as a result of experience. Janik and Slater (2000) have stated that learning can modify the emission of vocalizations in one of two ways: (1) by influencing the context in which a particular signal is used and/or (2) by altering the acoustic structure of the call itself. Male California sea lions can learn to inhibit their barking in the presence of any male dominant to them, but vocalize normally when dominant males are absent. Recent work on gray seals show different call types can be selectively conditioned and placed under biased control of different cues (Schusterman, in press) and the use of food reinforcement can also modify vocal emissions. “Hoover”, a captive male harbor seal demonstrated a convincing case of vocal mimicry. However similar observations have not been reported since. Still shows under the right circumstances pinnipeds may use auditory experience, in addition to environmental consequences such as food reinforcement and social feedback to modify their vocal emissions. In a 1992 study, Robert Gisiner and Ronald J. Schusterman conducted experiments in which they attempted to teach Rocky, a female California sea lion, syntax. Rocky was taught signed words, then she was asked to perform various tasks dependent on word order after viewing a signed instruction.It was found that Rocky was able to determine relations between signs and words, and form a basic form of syntax. A 1993 study by Ronald J Schusterman and David Kastak found that the California sea lion was capable of understanding abstract concepts such as symmetry, sameness and transitivity. This provides a strong backing to the theory that Equivalence relations can form without language. The distinctive sound of sea lions is produced both above and below water. To mark territory, sea lions “bark”, with non-alpha males making more noise than alphas. Although females also bark, they do so less frequently and most often in connection with birthing pups or caring for their young. Females produce a highly directional bawling vocalization, the pup attraction call, which helps mother and pup locate one another. As noted in Animal Behavior, their amphibious lifestyle has made them need acoustic communication for social organization while on land. Sea lions can hear frequencies as low as 100 Hz and as high as 40,000 Hz and vocalize between the ranges of 100 to 10,000 Hz. - Caribbean reef squid have been shown to communicate using a variety of color, shape, and texture changes. Squid are capable of rapid changes in skin color and pattern through nervous control of chromatophores. In addition to camouflage and appearing larger in the face of a threat, squids use color, patterns, and flashing to communicate with one another in various courtship rituals. Caribbean reef squid can send one message via color patterns to a squid on their right, while they send another message to a squid on their left. Comparison of the terms "animal language" and "animal communication" |This section needs additional citations for verification. (November 2010) (Learn how and when to remove this template message)| It is worth distinguishing "animal language" from "animal communication", although there is some comparative interchange in certain cases (e.g. Cheney & Seyfarth's vervet monkey call studies). Thus "animal language" typically does not include bee dancing, bird song, whale song, dolphin signature whistles, prairie dogs, nor the communicative systems found in most social mammals. The features of language as listed above are a dated formulation by Hockett in 1960. Through this formulation Hockett made one of the earliest attempts to break down features of human language for the purpose of applying Darwinian gradualism. Although an influence on early animal language efforts (see below), is today not considered the key architecture at the core of "animal language" research. Animal Language results are controversial for several reasons. (For a related controversy, see also Clever Hans.) In the 1970s John Lilly was attempting to "break the code": to fully communicate ideas and concepts with wild populations of dolphins so that we could "speak" to them, and share our cultures, histories, and more. This effort failed. Early chimpanzee work was with chimpanzee infants raised as if they were human; a test of the nature vs. nurture hypothesis. Chimpanzees have a laryngeal structure very different from that of humans, and it has been suggested that chimpanzees are not capable of voluntary control of their breathing, although better studies are needed to accurately confirm this. This combination is thought to make it very difficult for the chimpanzees to reproduce the vocal intonations required for human language. Researchers eventually moved towards a gestural (sign language) modality, as well as "keyboard" devices laden with buttons adorned with symbols (known as "lexigrams") that the animals could press to produce artificial language. Other chimpanzees learned by observing human subjects performing the task. This latter group of researchers studying chimpanzee communication through symbol recognition (keyboard) as well as through the use of sign language (gestural), are on the forefront of communicative breakthroughs in the study of animal language, and they are familiar with their subjects on a first name basis: Sarah, Lana, Kanzi, Koko, Sherman, Austin and Chantek. Perhaps the best known critic of "Animal Language" is Herbert Terrace. Terrace's 1979 criticism using his own research with the chimpanzee Nim Chimpsky was scathing and basically spelled the end of animal language research in that era, most of which emphasized the production of language by animals. In short, he accused researchers of over-interpreting their results, especially as it is rarely parsimonious to ascribe true intentional "language production" when other simpler explanations for the behaviors (gestural hand signs) could be put forth. Also, his animals failed to show generalization of the concept of reference between the modalities of comprehension and production; this generalization is one of many fundamental ones that are trivial for human language use. The simpler explanation according to Terrace was that the animals had learned a sophisticated series of context-based behavioral strategies to obtain either primary (food) or social reinforcement, behaviors that could be over-interpreted as language use. In 1984 during this anti-Animal Language backlash, Louis Herman published an account of artificial language in the bottlenosed dolphin in the journal Cognition. A major difference between Herman's work and previous research was his emphasis on a method of studying language comprehension only (rather than language comprehension and production by the animal(s)), which enabled rigorous controls and statistical tests, largely because he was limiting his researchers to evaluating the animals' physical behaviors (in response to sentences) with blinded observers, rather than attempting to interpret possible language utterances or productions. The dolphins' names here were Akeakamai and Phoenix. Irene Pepperberg used the vocal modality for language production and comprehension in an African grey parrot named Alex in the verbal mode, and Sue Savage-Rumbaugh continues to study bonobos such as Kanzi and Panbanisha. R. Schusterman duplicated many of the dolphin results in his California sea lions ("Rocky"), and came from a more behaviorist tradition than Herman's cognitive approach. Schusterman's emphasis is on the importance on a learning structure known as "equivalence classes." However, overall, there has not been any meaningful dialog between the linguistics and animal language spheres, despite capturing the public's imagination in the popular press. Also, the growing field of language evolution is another source of future interchange between these disciplines. Most primate researchers tend to show a bias toward a shared pre-linguistic ability between humans and chimpanzees, dating back to a common ancestor, while dolphin and parrot researchers stress the general cognitive principles underlying these abilities. More recent related controversies regarding animal abilities include the closely linked areas of Theory of mind, Imitation (e.g. Nehaniv & Dautenhahn, 2002), Animal Culture (e.g. Rendell & Whitehead, 2001), and Language Evolution (e.g. Christiansen & Kirby, 2003). There has been a recent emergence in animal language research which has contested the idea that animal communication is less sophisticated than human communication. Denise Herzing has done research on dolphins in the Bahamas whereby she created a two-way conversation via a submerged keyboard. The keyboard allows divers to communicate with wild dolphins. By using sounds and symbols on each key the dolphins could either press the key with their nose or mimic the whistling sound emitted in order to ask humans for a specific prop. This ongoing experiment has shown that in non-linguistic creatures brilliant and rapid thinking does occur despite our previous conceptions of animal communication. Further research done with Kanzi using lexigrams has strengthened the idea that animal communication is much more complex then we once thought. - Hockett, Charles F. (1960). "Logical considerations in the study of animal communication". In Lanyon, W.E.; Tavolga, W.N. Animals sounds and animal communication. American Institute of Biological Sciences. pp. 392–430. - Martinelli, Dario (2010). "Introduction to Zoosemiotics". Biosemiotics. 5: 1–64. doi:10.1007/978-90-481-9249-6_1. - Hauser, Marc D.; Chomsky, Noam; Fitch, W. Tecumseh (22 November 2002). "The Faculty of Language: What Is It, Who Has It, and How Did It Evolve?" (PDF). Science. American Association for the Advancement of Science. pp. 1569–1579. Retrieved 28 March 2014. We argue that an understanding of the faculty of language requires substantial interdisciplinary cooperation. We suggest how current developments in linguistics can be profitably wedded to work in evolutionary biology, anthropology, psychology, and neuroscience. We submit that a distinction should be made between the faculty of language in the broad sense (FLB)and in the narrow sense (FLN). FLB includes a sensory-motor system, a conceptual-intentional system, and the computational mechanisms for recursion, providing the capacity to generate an infinite range of expressions from a finite set of elements. We hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language. We further argue that FLN may have evolved for reasons other than language, hence comparative studies might look for evidence of such computations outside of the domain of communication (for example, number, navigation, and social relations). - Denham, Kristin; Lobeck, Anne (2010). Linguistics for Everyone: An Introduction (Instructor's ed.). Wadsworth, Cengage Learning. pp. 4–5. ISBN 9781428205833. - Fitch, WT. (Feb 2011). "Unity and diversity in human language.". 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The Mycenaean civilization art arose around the year 1600 BC, compared to the pacific and joyously Minoan Culture was of quite solemn nature and beligerant tendencies. These two cultures formed the basis of which was latter the Greek Civilization. Is necessary to study this culture to better understand the archaic period of Greek art. The history and legends of the Mycenaean people has come to us by the writings left behind by the Greek poet Homer (c. 750 BC) among other chronics that made also references about them. In those cronics is told that they became the dominant culture of the island; been their influence evident in all artistic manifestations discovered in Mycenae in the Peloponnese region which ruins and ancient artifacts give us today a glance about the interesting life and culture of this civilization. Mycenaean Cultures develop takes place in the age of bronze of the Greek peninsula and succeeded the ancient Minoan culture of Crete. Although the Mycenaean and Greek cultures were two separate entities, they occupied the same lands, successively. The archeological studies made in those territories confirm the differences between them as been to complete separate culture after for many years was considered only one. Mycenae was a society with hierarchies; the figure of the King was the Supreme exponent of the political and economical power control. The Mycenae or Achaeans, as they called themselves were a fundamentally warrior people whom were also highly specialized in the development of techniques to elaborate weapons, arrows, long sword and armor with sheets of metal and teeth of wild boar helmets (with strength and durable characteristic intended for personal protection in the fight). They created architectural elements including cyclopean masonry and “Beehive” tombs, were great engineers who designed and built remarkable bridges. Likewise stands the construction of enormous strengths of stones placed one on top of each other without mortar, which protected their palaces and buildings in general with those asthonished walls. The Mycenaean cities were built on top of the hills surrounded by these walls mentioned. This factor contributed to succesfully give them advantages from the strategic point of view. Their buildings were not complex in structure though since they were constructed ssentially destined for practical use. Were built around a central megaron (an architectural form consisting of a porch, vestibule, and large hall with a central hearth) functioned as the king’s audience chamber as well. The structural design they use was an earlier element of Helladic architecture.The Greek learned later from this previous culture, how to build gates and tombs amount other architectural construction techniques. From their architecture are remaining the Lion Gate, and the Treasury of Atreus as two example of a Tholos tomb. Pottery artisans and jewelry Mycenaean were impressive potters themselves and prodigious goldsmiths as well; they developed a simply functional ceramics; beautifully decorated with geometric motifs which applied also in the elaboration of objects for personal use. They widely used the gold (for which had special predilection), reached a high degree of mastery in the use of different other techniques and materials as well like bronce and other alloys. They assimilated elements of the previous culture (Minoan) especially in the artisanal part with naturalistic elements like flowers or animal representation principally seen in the first stage. Are supposed that Etruria’s artisans worked for the Mycenaeans leaving their mark in the pottery and jewels. Some of their inventions to develop the various objects for everyday life use were extraordinary. They make as well luxury items, such as carved gems, jewelry, vases in precious metals, and glass ornaments showing remarkable skills and attention to details resulting in formidable pieces. Many of them marvel us today for their beauty making us wander how in such remote times they could reach that mastery with pretty much rudimentary utensils and tools. They were skilled traders also carrying wine, oils and spices all over the region along many other objects of their own creation been respected and even afraid since they were fierce warriors. The fragments of Mycenaean paintings found in Tiryns, Pylos and Greece, represent what is presumed were impressive murals both Mycenaean and Minoan. These paintings were not the frescos type as traditionally has been known by the Egyptians murals, in this case the Mycenaean elaborate theirs by applying paint to tempera on dry plaster as well. Topics of Mycenaean murals include everyday life event and depictions of war scenes as well of hunting, sacrifices representations, processions, mythology and legend and of course reference to nature since they inherited this inclination from the Minoan. Their scene representation do not care particularly for the spatial order been however pretty stereotyped. They represent the figures over an essentially plain background; like is they were cut off or outlined over that background. Not much is known about the religious practices of the Mycenaean and that include the name of their Gods. It things though that Poseidon was a popular deity. Other Gods included: – The Lady of the Labyrinth. – Diwia (Sea Goddess) The scarce temples or shrines remaining where religious practices might have been performed don’t say much about the insight of their religious believes. Has been assuming all rituals took place on open ground or in sanctuaries high in the mountains although for the lack of evidence these are only assumptions. Nevertheless it is know that the Minoans had a strong influence on most of the religious rituals practiced by the Mycenaean. The Mycenaean civilization collapsed around 1100 BC. Its final marked the end of the age of bronze in Greece. It was followed by a period of one hundred to one hundred fifty years called ‘dark age’, of which very little is known. When the prehistory ends; it begins the period of recorded history. This fact marks a very important milestone in the development of the evolution of human communities and their awareness as cultural entities.

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Index: Pair of Linear Equations in Two Variables # Index: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 PDF Download ### (i) Previous Year Questions The document Index: Pair of Linear Equations in Two Variables | Mathematics (Maths) Class 10 is a part of the Class 10 Course Mathematics (Maths) Class 10. All you need of Class 10 at this link: Class 10 ## Mathematics (Maths) Class 10 116 videos|420 docs|77 tests ## FAQs on Index: Pair of Linear Equations in Two Variables - Mathematics (Maths) Class 10 1. What is a pair of linear equations in two variables? Ans. A pair of linear equations in two variables is a set of two equations that can be represented by straight lines on a graph. These equations contain two variables, usually represented by x and y, and the goal is to find the values of x and y that satisfy both equations simultaneously. 2. How to solve a pair of linear equations in two variables? Ans. To solve a pair of linear equations in two variables, you can use methods like substitution, elimination, or graphical representation. The substitution method involves solving one equation for one variable and substituting it into the other equation. The elimination method involves adding or subtracting the equations to eliminate one variable and solve for the other. The graphical method involves plotting the equations on a graph and finding the point of intersection. 3. What is the importance of solving linear equations in two variables? Ans. Solving linear equations in two variables is important because it helps in solving real-life problems that involve multiple variables. These equations can represent relationships between different quantities, such as cost and quantity, speed and time, or supply and demand. By solving these equations, we can determine the values of the variables and make informed decisions based on the given conditions. 4. Can a pair of linear equations in two variables have more than one solution? Ans. Yes, a pair of linear equations in two variables can have more than one solution. This occurs when the two equations represent the same line, meaning they are dependent on each other. In such cases, any point on the line will satisfy both equations. These infinite solutions can be represented by a single equation with one variable. 5. Are there any real-life applications of solving linear equations in two variables? Ans. Yes, there are numerous real-life applications of solving linear equations in two variables. Some examples include calculating the intersection point of two roads or railways, determining the break-even point in business analysis, optimizing production levels based on cost and demand constraints, and finding the equilibrium point in economics. These equations provide a mathematical framework for solving various problems in different fields. ## Mathematics (Maths) Class 10 116 videos|420 docs|77 tests ### Up next Explore Courses for Class 10 exam ### Top Courses for Class 10 Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests. 10M+ students study on EduRev Related Searches , , , , , , , , , , , , , , , , , , , , , ;

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Deep in a Maryland forest, George Rasberry sits on an upturned pail and peers through a camera with a calibrated lens at the trees above him. He is measuring the leaf coverage present at each level of the forest. Here and there in the wilderness, buckets are placed to catch samples of the leaves. These reveal what species are in the canopy and how much it grows annually. Nearby stands a tower so tall I nearly break my neck to see the top, 165 feet up, a good 30 feet above the canopy. Aluminum arms stick out at intervals, each bearing instruments that measure forest conditions such as light, wind speed and carbon dioxide concentration. The anemometer at the bottom is still, but the ones higher up are turning slowly. This is the world of George Rasberry, a biological science technician at the Smithsonian Environmental Research Center (SERC) in Edgewater, and of his colleague Geoffrey "Jess" Parker, a forest ecologist there. Parker specializes in the study of the canopy, the importance of which in forest science has only recently been recognized. In the early 1980s pioneer researcher Terry Erwin collected great showers of insects from the canopy of a tropical forest. "The samples occupied sorters for years. We discovered lots of new species, many of them specific to particular tree species," Parker tells me. For instance, in one tree species in Panama, they found ten times the number of tropical beetle species they expected. When their findings were applied to the whole world, one estimate of the total number of all species went from 1.5 million to 30 million. "The canopy," Parker says, "is a part of all vegetation. Even your lawn has a canopy. So do vineyards, shrubs, orchards. Most people think it's just the top, but you can't tell where the top ends, or its influence. The canopy is all the leaves, twigs, fine branches — all of the surfaces. It's the surfaces of a forest that drag the wind and make it calm, that take noise out and control rainfall. The forest canopy is home to a majority of earth's species. It combs pollutants out of the air, takes energy from the sun and in general controls the exchanges of energy or heat, and material, such as carbon dioxide and water vapor." What use is all this information? Well, for instance, I wanted to know why the streams often go dry in the summer in this part of the world. "It's a lot of invisible things," Parker says, "like taking up carbon dioxide. Everything in the forest, the wood and leaves, was once carbon dioxide. Fallen leaves represent some of the carbon dioxide that was taken up this year. And as carbon dioxide goes into the leaves and wood, water vapor is released. As it is released, there is less in the soil to supply the streams. "Also, tree roots compete for moisture. Trees are just pipes that connect groundwater to the atmosphere: they're valved pipes controlled by leaves. This area has a precipitation of about three or four inches a month. The amount that plants take up and release increases during the growing season, so in summer, streams can go dry." At SERC the objective is to study one specific area's canopies and from that learn the rules for all canopies. "It's fun to spend a decade looking at one particular forest, but we want to say powerful things about forests in general," says Parker. "One way to do this is to study the changes that a forest goes through as it ages." SERC scientists are studying some 50 different forest plots. "We know their ages from taking tree-ring cores, and by now we know pretty much what forests in this region do, from the youngest stands, 5 years old, to one that might be 350 years old. This means we can put the canopy structure into context in the general scheme of forest development."

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Park History and Stats The Grand Canyon officially became a National Park on February 26, 1919, signed into law by Woodrow Wilson. Though Theodore Roosevelt had given its status as a National Monument 1908, he was working as part of a long-going effort at preserving the park dating back to the 1880s, largely led by then-Senator Benjamin Harrison. Roosevelt is well-known for his oratory skills, and had this to say of the Grand Canyon in 1903: “The Grand Canyon fills me with awe. It is beyond comparison—beyond description; absolutely unparalleled throughout the wide world… Let this great wonder of nature remain as it now is. Do nothing to mar its grandeur, sublimity and loveliness. You cannot improve on it. But what you can do is to keep it for your children, your children’s children, and all who come after you, as the one great sight which every American should see.” The Tusayan Museum was built in 1928, and the Tusayan ruins themselves, an 800-year-old Pueblo site, would be excavated by members of the Gila Pueblo in 1930. Conservation and restoration work occurred in 1948 and 1965. It was placed on the register of National Historic Places in 1975. The Desert View Watchtower was designed by architect Mary Colter, who also designed several other buildings within Grand Canyon National Park. The Tower was completed in 1932. On May 27, 1987, it was designated a National Historic Landmark as part of a collective nomination of Mary Colter’s buildings. Date Founded: February 26, 1919; Declared a UNESCO World Heritage Site in 1979 Size: 1,901.972sq Miles Elevation: 7,461ft (Navajo Point) Rainfall: 16in a year; 60in of snow Visitors: Nearly 6 Million a year Fees: Entrance Fees are on a weekly basis and range from $15 (single, bicycle or on foot) up to $30. *We will note that these fees are covered completely by the America The Beautiful Pass, which applies to over 2,000 different sites. The Eastern portion of Grand Canyon National Park could very well be its own park were it not adjoined to one of the largest on the planet. It is comprised of the area along Desert View Drive, a 25-mile long road leading to the main campus of the South Rim. “To preserve unimpaired the natural and cultural resources and values of the national park system for the enjoyment, education, and inspiration of this and future generations.” The East Rim includes Desert View, and the Tusayan Museum, which features archeological and anthropological exhibits highlighting the history of the native culture. The ruins of the pueblo structures of Tusayan are preserved, while at the Desert View Watchtower, the legacy of Pueblo culture is brought into a modern context via educational programs and the amazing artwork of the tower’s interior. The Eastern portion of the park has 5 vistas (Desert View, Navajo Point, Lipan Point, Moran Point and Grandview point, as well as the Tusayan Ruin and Museum (Open 9-5). The Grandview Trail begins at Grandview point. Desert View facilities: Gas Station: Jan 1 to Mar 30 = Closed Mar 31 to Oct 22 = 9:00 am – 5:00 pm Oct 23 to Dec 31 = Closed *Self-service gas (pay at the pump) is available year-round, 24 hours a day. Trading Post Hours: Jan 1 to May 18 = 9-5 May 19 to Sept 3 = 8-8 Sept 4 to Dec 31 = 9-5 Desert View Deli: Jan 1 to Feb 28 = 9-4 Mar 1 to May 18 = 9-5 May 19 to Sept 3 = 8-7 Sept 4 to Dec 31 = 9-5 Marketplace: Jan 1 to Mar 30 = 8-5 Mar 31 to Sept 3 = 8-8 Sept 4 to Oct 22 = 8-6 Oct 23 to Dec 31 = 8-5 The Desert View Watchtower is the centerpiece of the campus, with the Tower shop open from 9-5 and the Tower stairs open from 9-4:30. The Desert View campus is open year-round and has ample flush toilets and fresh water. The town of Cameron, AZ is 57 miles away, however, the Southern side of the park has all of the amenities you would expect in a small town. We were able to buy craft beer to go along with our dinner that evening. There is a wide variety of prepared food and made to order meals in the store at the Desert View facility as well. Batteries, wine, firewood, first-aid and hygiene products are all available. Further amenities are to be had on the main campus of the South Rim, Grand Canyon Village, which is a small city unto itself. Desert View Campground has 50 sites which operate on a first-come, first serve basis, and the NPS site cautions that these sites are often booked up by the early afternoon. Site use is $12/night with a 7-day limit, though some discounts are offered with various ATB Passes. Payment is via an automated kiosk, which only accepts credit card (as of late 2017). While sites are able to accommodate large cars and small RVs and trailers, vehicles longer than 30′ are prohibited. This facility closes for winter in mid-October and reopens mid-April. Newbie to Novice. There are flush toilets, fresh water and a camp attendant on duty, and with a well-stocked market and kitchen just up the road, if you don’t feel like cooking, you don’t have to. We opted for a mix, making a delicious pasta dish over the fire for dinner, but spoiling ourselves with made-to-order bagel sandwiches for breakfast. Tusayan Museum and Ruins offer Ranger-guided tours in the summer months from 11-2, (information here) while the Grand Canyon Association hosts events ranging from art auctions to craft demonstrations at the Desert Watchtower every Saturday and Sunday during the summer months. A full breakdown of their calendar and timetable can be found here. Desert View is a nice, quiet campsite, and there’s nothing quite like a cold beer by the fireside- the selection at the Trading Post was a pleasant surprise. Camping here allowed us to dip our toes into the South Rim at a leisurely pace, and you have your pick of vistas for sunset and sunrise. We’d definitely camp here again. Things we’d like to try next time We missed out on some of the programming going on; a Grand Canyon Association demonstration was wrapping up as we arrived at the Tower. If we came back, we’d plan around events occurring at the Tower or other facilities. Come early, and reserve for as long as is reasonable. $12/night is mighty cheap, even cheaper if your ATB Pass gives you a discount. If we hadn’t come on the last night (and gotten the second-to-last site) of operation for the campground for the year, we would have definitely stayed there and used it as a base of operations for a longer stay on the South Rim overall. Pets are allowed at the campground, provided they are leashed. Your furry companion is not allowed near the rim, however. The ravens at the Desert Watchtower seem especially enthusiastic about showing off, and we caught a lot of impressive mid-air acrobatics. When taking pictures at the Desert Watchtower, and especially inside, be patient. A lot of crowds move in waves due to the narrow stairs, and if you’re patient, you might get that shot of the beautiful ceiling you were looking for without someone peering down at you. In 2008, two self-appointed spellcheckers and grammar police were arrested after ‘correcting’ one of the signs that had been painted by Mary Colter. They were fined and banned from National Parks from a year. If only that could happen to everyone who defaces our National Treasures. Don’t be that person. Call to action What’s your favorite vista on the East end of the park? Beer recommendations for the next visit? What artwork in the Tower struck you? Did we leave anything out? Read more about our experience at the Grand Canyon National Park’s East Rim here. Originally from Two by Tour Partners in travel and life, we are two recovering restaurant professionals who packed up and traveled westward across the United States, then journeyed to Ecuador in search of a life of exploration, culture, beauty and a place to call home.

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By Neal Singer The first step in deploying lasers on space satellites will take place Sept. 9, when NASA sends a lidar system into orbit on the space shuttle Discovery, says the UI researcher who helped design the major experiments for the mission. The lidar system, dubbed NASA LITE, is expected to be aboard the shuttle when it is launched at 4:30 p.m. EDT from Cape Canaveral, Fla., to monitor Earth's atmosphere. The shuttle is scheduled to return Sept. 18. Lidar, an acronym derived from light detection and ranging, emits laser beams rather than radio waves to obtain information. LITE derives from Lidar in Space Technology Experiment. "Through use of a pulsed laser beam as an active sensor, we can measure light back-scattered from air molecules, clouds and aerosols, or reflections from Earth's surface, and infer information about characteristics of the atmosphere," says UI electrical and computer engineer Chester S. Gardner. The system will be firing 10 times a second in the green, ultraviolet and infrared ranges. The returning light, captured by a telescope adjacent to the laser on the satellite, should yield the best information on concentrations of aerosols, movements of storm systems and heights of clouds. Later lidar systems will study atmospheric ozone depletion, the accumulation of carbon dioxide and water vapor in the atmosphere, and the expansion or shrinkage of polar ice caps. The information is expected to be much more detailed than that obtained by current methods. Satellites now use a horizon-scanning technique that measures the thinning of sunlight as it passes through the edge of Earth's atmosphere. The technique can identify chemical constituents of the atmosphere, but its resolution is relatively poor, he said. A major challenge for LITE will be to measure water reflectivity at different amounts of surface turbulence. In an attempt to accomplish this, the shuttle will pitch forward 30 degrees as it passes over specific sites and will rotate at a speed that allows it to keep the laser beam focused on specific sites. The process is expected to help calibrate water reflections of different size waves for future generations of orbiting lidar systems. Calibration stations around the globe will beam lidars upward to compare their readings with the shuttle's lidar as it passes above them. The largest such check station in terms of telescope size - 3.5 meters - will be at the Starfire Optical Range in Albuquerque, N.M., and will be staffed by UI electrical and computer engineer George Papen and several UI graduate students. Gardner, who for eight years has been part of the 12-member LITE advisory committee, will lead the day shift at the Project Science control room at the Johnson Space Center in Houston during the 45 hours of intermittent observation expected from the lidar system. He and his colleagues will advise mission controllers on science problems that may arise during the tests.

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How you begin a sentence matters. And how you end a sentence, too. What is in the middle, not so much. We know this from some studies that flushed out a couple of effects you are probably familiar with. The importance of primacy in how you begin a sentence The first one is primacy, and it refers to our tendency to remember items at the beginning of a list. For example, read the following words: Now, without looking at the list, how many of those words do you remember? Write them down if it helps. More than likely you will only remember the first word. Maybe the second. Chances are you’ll also remember two or three words at the end of the list (which is known as the recency effect). What you won’t remember are any of the words in the middle. Furthermore, studies suggest you’ll always remember more words from the end of the list than from the beginning simply because those are the last words you read. Thus, recency. In 1946, Solomon E. Asch upped the ante with studies that evaluated the impact the position of words had on people. He shared these results in the Journal of Abnormal and Social Psychology. The study we care about involves how we position adjectives to describe a person. Read the following two sentences. - “Steve is smart, diligent, critical, impulsive, and jealous.” - “Steve is jealous, impulsive, critical, diligent, and smart.” These two sentences contain the same information. However, when a group of participants were given the first sentence, they reported “Steve” in a positive light. The group given the second sentence? Yep. They reported “Steve” in a negative light. The uses for this should be obvious (Frank Luntz anyone?) Thirty years later William Crano decided to sharpen the distinction the impact order has on meaning. His studies uncovered additional effects, particularly with the use of adjectives: - Change of meaning hypothesis: Early adjectives establish an expectation, which the reader then filters all the subsequent adjectives through. - Inconsistency discounting: Adjectives presented later that don’t match earlier expectations are downgraded. - Attention decrement hypothesis: Early adjectives wield considerable influence than later ones. These conclusions are important when it comes to persuasive writing for several reasons. For instance, we often bury critical information regarding instructions in the second or third sentence of a paragraph. Most people only read the first sentence of a paragraph. And of that first sentence, because of the unbreakable law of the web, most people only read the first half before moving on. In such cases, primacy is more important. But there are times when recency is just as important. Take this long-winded sentence from Lisa Miller’s 2012 article “Listening to Xanax“: Twenty years ago, just before Kurt Cobain blew off his head with a shotgun, it was cool for Kate Moss to haunt the city from the sides of buses with a visage like an empty store and for Wurtzel to confess in print that she entertained fantasies of winding up, like Plath or Sexton, a massive talent who died too soon, “young and sad, a corpse with her head in the oven.” That it ends with “young and sad, a corpse with her head in the oven” is not an accident. Decisions had to be made when crafting that sentence. Guaranteed it did not flow from Miller’s mind in the published form. It was a piecemeal affair, an experimentation with effect. And this is the craft of writing. The creativity that can’t be rushed.

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Why Do the Boreal Forest Ecosystems of Northwestern Europe Differ from Those of Western North America? Oxford University Press The boreal forest is one of the largest terrestrial biomes on Earth. Conifers normally dominate the tree layer across the biome, but other aspects of ecosystem structure and dynamics vary geographically. The cause of the conspicuous differences in the understory vegetation and the herbivore–predator cycles between northwestern Europe and western North America presents an enigma. Ericaceous dwarf shrubs and 3– to 4-year vole–mustelid cycles characterize the European boreal forests, whereas tall deciduous shrubs and 10-year snowshoe hare–lynx cycles characterize the North American ones. We discuss plausible explanations for this difference and conclude that it is bottom-up: Winter climate is the key determinant of the dominant understory vegetation that then determines the herbivore–predator food-web interactions. The crucial unknown for the twenty-first century is how climate change and increasing instability will affect these forests, both with respect to the dynamics of individual plant and animal species and to their community interactions. Boonstra, R., H. P. Andreassen, S. Boutin, J. Hušek, R. A. Ims, C. J. Krebs, C. Skarpe, and P. Wabakken. 2016. Why Do the Boreal Forest Ecosystems of Northwestern Europe Differ from Those of Western North America? BioScience 66:722-734.

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# Project Euler Problem 46: Goldbach's other conjecture Question: It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square. For example, 9 = 7 + 2 x 12 15 = 7 + 2 x 22 21 = 3 + 2 x 32 25 = 7 + 2 x 32 27 = 19 + 2 x 22 It turns out the conjecture was false. What is the smallest odd composite that cannot be written as the sum of a prime and twice a square? Related Tags: ## Writing out the math Before we break this down into components, let's try rearranging the conjecture. n = p + 2 x s2 Where n is the number, p is our prime number, and s is the value we need to square. We then rearrange this equation to obtain the following: s = sqrt((n-p)/2) Since s must be an integer, the right hand side of the equation must equate to a whole number. If not, the conjecture does not hold for those values of n and p. Furthermore, we note how n < p since we can't take the square root of a negative number. ## Algorithm Pseudocode 1. Given a value n, obtain a list of all primes less than n. 2. For each prime p in our list, we take sqrt( (n - p) / 2 ). 3. If the result is an integer, (no decimal places) then the conjecture holds, and we can move on to the next odd n. 4. If not, move onto the next prime value, p. 5. If we have exhausted our prime values list, then we found the value of which the conjecture does not hold. ## Obtaining a list of all primes < our number To obtain a list of values less than some n, we can apply the Sieve of Eratosthenes. ## Implementation in Java Here's the implementation. The `findPrimes()` method returns an `ArrayList` of primes less than a given input. This method returns the value 5777. ``````static int disproveGoldbach() { // Start at 1 int currentNum = 1; // Our list of prime arrays ArrayList<Integer> listOfPrimes; // Boolean to exit loop when all done boolean done = false; // Keep running until we find a value that doesn't work while (true) { // Get list of prime numbers for the current number listOfPrimes = findPrimes(currentNum); // Try out all options in our list of prime numbers for (int j = 0; j < listOfPrimes.size(); j++) { int currentPrime = listOfPrimes.get(j); double eval = Math.sqrt((currentNum - currentPrime) / 2) % 1; // If there exists an int we can square and double if (eval == 0.0) { break; } // If we've exhausted our list, and no solutions are found, return! if (j == listOfPrimes.size() - 1) { return currentNum; } } // only odd numbers currentNum += 2; } } }`````` ## Full runnable code Here's the full, runnable code in case you want to test it out yourself. ``````import java.lang.Math; import java.util.HashMap; import java.util.ArrayList; public class Goldbach { public static void main(String[] args) { System.out.println(disproveGoldbach()); } static int disproveGoldbach() { // Start at 1 int currentNum = 1; // Our list of prime arrays ArrayList<Integer> listOfPrimes; // Boolean to exit loop when all done boolean done = false; // Keep running until we find a value that doesn't work while (true) { // Get list of prime numbers for the current number listOfPrimes = findPrimes(currentNum); // Try out all options in our list of prime numbers for (int j = 0; j < listOfPrimes.size(); j++) { int currentPrime = listOfPrimes.get(j); double eval = Math.sqrt((currentNum - currentPrime) / 2) % 1; // If there exists an int we can square and double if (eval == 0.0) { break; } // If we've exhausted our list, and no solutions are found, return! if (j == listOfPrimes.size() - 1) { return currentNum; } } // only odd numbers currentNum += 2; } } static ArrayList<Integer> findPrimes(int n) { // A key prime Integer will have a Boolean value of true. HashMap<Integer, Boolean> primeTable = new HashMap<>(); // Load our table with values up to and including n. for (int i = 1; i <= n; i++) { primeTable.put(i, true); } // 1 is by definition not prime. primeTable.put(1, false); // For every value up to the sqrt(n). for (int i = 2; i * i < n; i++) { // If particular value is still set as prime // (otherwise those values will have already been covered. if (primeTable.get(i)) { // Set each multiple as not a prime for (int p = i+i; p <= n; p += i) { primeTable.put(p, false); } } } // Now store all primes into a list and return ArrayList<Integer> primes = new ArrayList<>(); for (int i = 1; i <= primeTable.size(); i++) { if (primeTable.get(i)) } return primes; } }`````` ## Sources This problem is the 46th problem on Project Euler. Came up with a better solution or have a question? Comment below! Next Challenge:

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Categories # [Smart Math] Ratio Proportion Problem 31 Here’s and example of a SMART MATH problem for RATIO PROPORTION. ### Problem A certain sum of money is divided between A, B and C in the proportion of 2 : 3 : 4. If C were to give B $20, and B were to give A half of what he has now, the amounts which A and C have now would be same. What is the amount divided between the three? 1.$420 2. $480 3.$500 4. $540 5.$600 ### The Usual Method Let the shares of A, B and C be 2x, 3x and 4x respectively. (where ‘x’ is the constant of proportionality) Thus, (4x – 20) is the new share of C $\frac{3x+20}{2}$ is the new share of B and 2x + $\frac{3x+20}{2}$ is the new share of A. Also, since new shares of A and C are equal: 2x + $\frac{3x+20}{2}$ = (4x – 20) $\therefore 2x+1.5x+10=4x-20$ $\therefore 3.5x+10=4x-20$ $\therefore 0.5x=30$ $\therefore x=60$ Hence total sum = $2x+3x+4x=9x=9\times 60=$ $540 (Ans: 4) Estimated Time to arrive at the answer = 60 seconds. ### Using Technique [contentblock id=google-adsense-post] Total sum of money to be shared = $2x+3x+4x=9x$. Hence the sum should be a multiple of 9. Only option ‘4’ ($540) is a multiple of 9. This eliminates all the other options, so option ‘4’ is the answer. (Ans: 4) Estimated Time to arrive at the answer = 5 seconds. [starrater tpl=10] [contentblock id=smartmath-blockquote]

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# Quant Mock (Number Series, Simplifications, Quadratic Equations) Approved & Edited by ProProfs Editorial Team The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes. | By Quants Q Quants Community Contributor Quizzes Created: 1 | Total Attempts: 66 Questions: 15 | Attempts: 66 Settings • 1. ### In these questions, two equations are given. You have to solve both the equations and mark the appropriate answer. 225x2 -4 = 0√225y +2=0 • A. x < y • B. X > y • C. X ≤ y • D. X ≥ y • E. X = y or the relationship between x and y cannot be determined D. X ≥ y Explanation The given equations are 225x^2 - 4 = 0 and √225y + 2 = 0. To solve the first equation, we can rewrite it as 15x^2 - 2 = 0 by taking the square root of 225 and simplifying. Solving this quadratic equation, we find that x = ±√(2/15). To solve the second equation, we can rewrite it as √(225y) = -2 and then square both sides to eliminate the square root. This gives us 225y = 4, and solving for y, we find that y = 4/225. Comparing the values of x and y, we can see that x ≥ y. Therefore, the correct answer is x ≥ y. Rate this question: • 2. ### In these questions, two equations are given. You have to solve both the equations and mark the appropriate answer. x3 - 878 = 453y2 - 82 = 39 • A. x < y • B. X > y • C. X ≤ y • D. X ≥ y • E. X = y or the relationship between x and y cannot be determined D. X ≥ y Explanation The given equations are x^3 - 878 = 453y^2 - 82 = 39. By solving the equations, we can find the values of x and y. However, the relationship between x and y cannot be determined based on the given equations. Therefore, the answer is x = y or the relationship between x and y cannot be determined. Rate this question: • 3. ### In these questions, two equations are given. You have to solve both the equations and mark the appropriate answer. 9x- 15.45 = 54.55 +4x√(y + 155) - √36 = √49 • A. x < y • B. X > y • C. X ≤ y • D. X ≥ y • E. X = y or the relationship between x and y cannot be determined E. X = y or the relationship between x and y cannot be determined Explanation By solving the first equation, we can simplify it to 5x = 109. By solving the second equation, we can simplify it to √(y + 155) = 7. Since the first equation gives a unique value for x and the second equation gives a unique value for y, we can conclude that x and y are equal, i.e., x = y. Therefore, the relationship between x and y can be determined as x = y. Rate this question: • 4. ### In these questions, two equations are given. You have to solve both the equations and mark the appropriate answer.x2 + 11x+ 30 = 0y2 + 7y + 12 = 0 • A. x < y • B. X > y • C. X ≤ y • D. X ≥ y • E. X = y or the relationship between x and y cannot be determined A. x < y Explanation To find the relationship between x and y, we need to solve both equations. For the first equation, we can factorize it as (x + 5)(x + 6) = 0. This gives us two possible values for x: x = -5 or x = -6. For the second equation, we can factorize it as (y + 3)(y + 4) = 0. This gives us two possible values for y: y = -3 or y = -4. Comparing the possible values of x and y, we can see that for both cases (x = -5 or x = -6), y is always greater than x. Therefore, the correct answer is x < y. Rate this question: • 5. ### Directions: What should come in place of the question mark (?) in the following questions?√1.5625= ? • A. 125 • B. 12.5 • C. 1.5 • D. 1.25 • E. None of these D. 1.25 Explanation The square root of 1.5625 is 1.25. This can be determined by finding the number that, when multiplied by itself, equals 1.5625. In this case, 1.25 multiplied by itself equals 1.5625. Therefore, the correct answer is 1.25. Rate this question: • 6. ### Directions: What should come in place of the question mark (?) in the following questions? (103.7 × 101.3 )2 = 10? • A. 6 • B. 7 • C. 5 • D. 3 • E. None of the above E. None of the above Explanation Rate this question: • 7. ### Directions: What should come in place of the question mark (?) in the following questions?3 * ? + 30 = 0 • A. -15 • B. 15 • C. 10 • D. -30 • E. None of the above E. None of the above Explanation Rate this question: • 8. ### Directions: What should come in place of the question mark (?) in the following questions?36865+12473+21045-44102 = ? • A. 114485 • B. 66281 • C. 26281 • D. 114845 • E. None of these C. 26281 Explanation The correct answer is 26281. This can be obtained by adding the first three numbers and then subtracting the fourth number. 36865 + 12473 + 21045 - 44102 = 26281. Rate this question: • 9. ### In these questions, two equations are given. You have to solve both the equations and mark the appropriate answer. 5x2 - 18x +9 = 020y2 - 13y + 2 = 0 • A. x < y • B. X > y • C. X ≤ y • D. X ≥ y • E. X = y or the relationship between x and y cannot be determined B. X > y Explanation The given equations are quadratic equations. By solving both equations, we can determine the values of x and y. Since the answer is x > y, it means that the value of x is greater than the value of y. Rate this question: • 10. ### What approximate value should come in place of the question mark (?) in the following questions? (You are not expected to calculate the exact value.)25.675% of 1321 + 64.328% of 4001 = • A. 2912 • B. 3016 • C. 3126 • D. 6254 • E. None of these A. 2912 Explanation The approximate value that should come in place of the question mark is 2912. This can be determined by calculating 25.675% of 1321, which is approximately 339.05, and 64.328% of 4001, which is approximately 2572.95. Adding these two values together gives approximately 2911, which is closest to the given answer of 2912. Rate this question: • 11. ### 3, 9, 17, 27, 39, 53, ? • A. 64 • B. 69 • C. 74 • D. 78 • E. 81 B. 69 Explanation The pattern is +6, +8, +10, .... So answer is 53 + 16 = 69 Rate this question: • 12. ### 5042, 5187, 5334, 5483, 5634, ? • A. 5716 • B. 5748 • C. 5787 • D. 5793 • E. None of these C. 5787 Explanation The pattern is +145, +147, +151, ..... So the answer is 5634 + 153 = 5787 Rate this question: • 13. ### 8, 17, 38, 85, 186, ? • A. 318 • B. 354 • C. 397 • D. 408 • E. 427 C. 397 Explanation The pattern is *2 + 1 square, *2 + 2 square, *2 + 3 square, .... So the answer is 186 * 2 + 5 square = 372 + 25 = 397 Rate this question: • 14. ### In the following number series only one number is wrong. Find out the wrong number.9 , 5 , 6 , 10.5 , 23 , 61, 183 • A. 183 • B. 10.5 • C. 61 • D. 6 • E. 9 C. 61 Explanation The sequence in the series is: 9 x 0.5 + 0.5 = 5 5 x 1 + 1 = 6 6 x 1.5 + 1.5 = 10.5 10.5 x 2 + 2 = 23 23 x 2.5 + 2.5 = 60 ≠ 61 60 x 3 + 3 = 183 Rate this question: • 15. ### In the following number series only one number is wrong. Find out the wrong number.2, 4 , 11 , 37 , 151 , 771 , 4633 • A. 11 • B. 4633 • C. 37 • D. 151 • E. 4 D. 151 Explanation The sequence in the series is: 2 x 1 + 2 = 4 4 x 2 + 3 = 11 11 x 3 + 4 = 37 37 x 4 + 5 = 153 ≠ 151 153 x 5 + 6 = 771 771 x 6 + 7 = 4633 Rate this question: Quiz Review Timeline + Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness. • Current Version • Mar 14, 2023 Quiz Edited by ProProfs Editorial Team • Aug 25, 2017 Quiz Created by Quants Related Topics

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## Sunday, November 13, 2016 ### Laws of Motion Problems with Solutions Seven Motion is the change in the state of the body with respect to time and space. The bodies always tries to keep their state as it is and this property is called inertia. To change the state of the body, we need to apply a force on the body that is sufficient enough to overcome the existing inertia. We are here solving problems about force and momentum. As per the law of conservation of linear momentum, if no external force is acting on the system, the momentum of the system always remains constant and it is conserved. Problem It is given in the problem that a body of mass 10 kilogram is being acted upon a force that varies with time. It is also given that a opposing force is also acting on the same body and it is a constant force of 32 newton. The body is also having some initial velocity and we need to know the final velocity of the body after five seconds. The problem is as shown in the diagram below. Solution As force is variable with time, to find the work done, we shall integrate the variable force with time and it can be equated to change in momentum. The given data is substituted in the concept and the problem is solved as shown below. Problem It is given in the problem that a block of mass m is starting from the state of rest from the top of a smooth inclined plane of known inclination. It has reached the bottom of inclined plane in one part of the time and to travel further on smooth surface some more time is taken. We need to measure the difference in this momentum in the given time difference and the problem is as shown below. Solution We can identify the change in momentum and the momentum of each part with specific direction as it is a vector quantity. As the body after coming to the bottom has constant velocity in the further travel, both the momentum are in the direction as shown with the angular separation. We can find the effective value using the parallelogram law and the solution is as shown in the diagram below. The velocity can be found using equations of motion. Problem It is given in the problem that two monkeys are holding each other as shown and one monkey is climbing a rope. The mass of the monkeys are given for us and the maximum tension can be bared by upper monkey is given to us and we need to know what force it shall apply on the ope to carry the second money with it with out breaking its tail. Solution Tension in the lower part of the rope as the sum of the weight of that rope and acceleration of the money multiplied by the mass of it. We can find the acceleration of the upper monkey as shown below. Similarly the tension in the upper part also can be found as shown below. Problem A shall of mass 100 gram is moving with a speed known along straight line inclined at a know angle. It is divided into two parts and we need to measure the velocity and direction of the second part after explosion. The problem is as shown in the diagram below. Solution As there is no external force acting on the system, linear momentum is conserved. We can resolve the momentum into components and it can be solved as shown in the diagram below. Related Posts

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# Documentation Archive.Wiedijk100Theorems.Partition # Euler's Partition Theorem # This file proves Theorem 45 from the 100 Theorems List. The theorem concerns the counting of integer partitions -- ways of writing a positive integer n as a sum of positive integer parts. Specifically, Euler proved that the number of integer partitions of n into distinct parts equals the number of partitions of n into odd parts. ## Proof outline # The proof is based on the generating functions for odd and distinct partitions, which turn out to be equal: $$\prod_{i=0}^\infty \frac {1}{1-X^{2i+1}} = \prod_{i=0}^\infty (1+X^{i+1})$$ In fact, we do not take a limit: it turns out that comparing the n'th coefficients of the partial products up to m := n + 1 is sufficient. In particular, we 1. define the partial product for the generating function for odd partitions partialOddGF m := $$\prod_{i=0}^m \frac {1}{1-X^{2i+1}}$$; 2. prove oddGF_prop: if m is big enough (m * 2 > n), the partial product's coefficient counts the number of odd partitions; 3. define the partial product for the generating function for distinct partitions partialDistinctGF m := $$\prod_{i=0}^m (1+X^{i+1})$$; 4. prove distinctGF_prop: if m is big enough (m + 1 > n), the nth coefficient of the partial product counts the number of distinct partitions of n; 5. prove same_coeffs: if m is big enough (m ≥ n), the nth coefficient of the partial products are equal; 6. combine the above in partition_theorem. ## References # https://en.wikipedia.org/wiki/Partition_(number_theory)#Odd_parts_and_distinct_parts def Theorems100.partialOddGF {α : Type u_1} (m : ) [] : The partial product for the generating function for odd partitions. TODO: As m tends to infinity, this converges (in the X-adic topology). If m is sufficiently large, the ith coefficient gives the number of odd partitions of the natural number i: proved in oddGF_prop. It is stated for an arbitrary field α, though it usually suffices to use ℚ or ℝ. Instances For def Theorems100.partialDistinctGF {α : Type u_1} (m : ) [] : The partial product for the generating function for distinct partitions. TODO: As m tends to infinity, this converges (in the X-adic topology). If m is sufficiently large, the ith coefficient gives the number of distinct partitions of the natural number i: proved in distinctGF_prop. It is stated for an arbitrary commutative semiring α, though it usually suffices to use ℕ, ℚ or ℝ. Instances For def Theorems100.cut {ι : Type u_1} (s : ) (n : ) : Finset (ι) Functions defined only on s, which sum to n. In other words, a partition of n indexed by s. Every function in here is finitely supported, and the support is a subset of s. This should be thought of as a generalisation of Finset.Nat.antidiagonalTuple where antidiagonalTuple k n is the same thing as cut (s : Finset.univ (Fin k)) n. Instances For theorem Theorems100.mem_cut {ι : Type u_1} (s : ) (n : ) (f : ι) : f = n ∀ (i : ι), ¬i sf i = 0 theorem Theorems100.cut_equiv_antidiag (n : ) : ↑() (Theorems100.cut Finset.univ n) = @[simp] theorem Theorems100.cut_zero {ι : Type u_1} (s : ) : = {0} There is only one cut of 0. @[simp] theorem Theorems100.cut_empty_succ {ι : Type u_1} (n : ) : theorem Theorems100.cut_insert {ι : Type u_1} (n : ) (a : ι) (s : ) (h : ¬a s) : Theorems100.cut (insert a s) n = Finset.biUnion () fun p => Finset.map { toFun := fun f => f + fun t => if t = a then p.fst else 0, inj' := (_ : Function.Injective fun x => x + fun t => if t = a then p.fst else 0) } (Theorems100.cut s p.snd) theorem Theorems100.coeff_prod_range {α : Type u_1} [] {ι : Type u_2} (s : ) (f : ι) (n : ) : ↑() (Finset.prod s fun j => f j) = Finset.sum () fun l => Finset.prod s fun i => ↑(PowerSeries.coeff α (l i)) (f i) def Theorems100.indicatorSeries (α : Type u_1) [] (s : ) : A convenience constructor for the power series whose coefficients indicate a subset. Instances For theorem Theorems100.coeff_indicator {α : Type u_1} (s : ) [] (n : ) : ↑() () = if n s then 1 else 0 theorem Theorems100.coeff_indicator_pos {α : Type u_1} (s : ) [] (n : ) (h : n s) : ↑() () = 1 theorem Theorems100.coeff_indicator_neg {α : Type u_1} (s : ) [] (n : ) (h : ¬n s) : ↑() () = 0 theorem Theorems100.constantCoeff_indicator {α : Type u_1} (s : ) [] : = if 0 s then 1 else 0 theorem Theorems100.two_series {α : Type u_1} (i : ) [] : 1 + PowerSeries.X ^ = theorem Theorems100.num_series' {α : Type u_1} [] (i : ) : (1 - PowerSeries.X ^ (i + 1))⁻¹ = Theorems100.indicatorSeries α {k | i + 1 k} Instances For theorem Theorems100.partialGF_prop (α : Type u_1) [] (n : ) (s : ) (hs : ∀ (i : ), i s0 < i) (c : ) (hc : ∀ (i : ), ¬i s0 c i) : ↑(Finset.card (Finset.filter (fun p => (∀ (j : ), Multiset.count j p.parts c j) ∀ (j : ), j p.partsj s) Finset.univ)) = ↑() (Finset.prod s fun i => Theorems100.indicatorSeries α ((fun x => x * i) '' c i)) theorem Theorems100.partialOddGF_prop {α : Type u_1} [] (n : ) (m : ) : ↑(Finset.card (Finset.filter (fun p => ∀ (j : ), j p.parts) Finset.univ)) = ↑() () theorem Theorems100.oddGF_prop {α : Type u_1} [] (n : ) (m : ) (h : n < m * 2) : ↑() = ↑() () If m is big enough, the partial product's coefficient counts the number of odd partitions theorem Theorems100.partialDistinctGF_prop {α : Type u_1} [] (n : ) (m : ) : ↑(Finset.card (Finset.filter (fun p => Multiset.Nodup p.parts ∀ (j : ), j p.partsj Finset.map { toFun := Nat.succ, inj' := Nat.succ_injective } ()) Finset.univ)) = ↑() () theorem Theorems100.distinctGF_prop {α : Type u_1} [] (n : ) (m : ) (h : n < m + 1) : If m is big enough, the partial product's coefficient counts the number of distinct partitions theorem Theorems100.same_gf {α : Type u_1} [] (m : ) : ( * Finset.prod () fun i => 1 - PowerSeries.X ^ (m + i + 1)) = The key proof idea for the partition theorem, showing that the generating functions for both sequences are ultimately the same (since the factor converges to 0 as m tends to infinity). It's enough to not take the limit though, and just consider large enough m. theorem Theorems100.same_coeffs {α : Type u_1} [] (m : ) (n : ) (h : n m) : ↑() () = ↑() ()

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December 11, 2012 | A team of Italian astronomers performed a very difficult measurement for which it was necessary to use the most advanced instrumentation in combination with an unusual technique, so as to involve even the Moon as a natural astronomical mirror. The challenge was the observation of effect occurred during the transit of Venus across the Sun on June 6th, dubbed “Rossiter-McLaughlin effect”. This is a phenomenon that occurs when a celestial body passes in front of a star, hiding a part of its rotating surface and that produces a temporary distortion in the profiles of the spectral lines of light coming from the eclipsed star. Astronomers led by Paolo Molaro, from INAF Astronomical Observatory of Trieste succeeded in this ambitious task, observing and measurirng the magnitude of this tiny effect. Their findings are published online today in a paper of the journal Monthly Notices of the Royal Astronomical Society Letters, published by Oxford University Press. The Rossiter-McLaughlin effect has already been observed in systems composed of two stars that eclipse each other, but it becomes more and more difficult to observe when the celestial body is the size of a planet, and moreover not so great as Jupiter but rather similar in size to the Earth, just as it is during the transit of Venus. Measuring the extent of this weak effect on the light from other planetary systems through telescopes of the next generation such as E-ELT (the European Extremely Large Telescope) will be a useful tool for the search and study of exoplanets. Astronomers will be able to learn important orbital parameters in these systems and thus improve our understanding of the history of their formation. “Critical to the success of this mission was the use of the HARPS spectrograph at ESO that now, along with his ‘twin brother’ installed at the Telescopio Nazionale Galileo (TNG) operated by INAF on Canary Islands, represents the state of the art for measuring radial velocities of celestial objects and the best hunter of planetary systems around other stars. The measured magnitude of the effect is comparable to being able to track the speed of a person walking at a slow pace at a distance of 150 million kilometers, the space that separates us from the Sun. Nowadays there is no other instrument capable of recording so tiny changes, especially if you only have a few hours to measure them” said Lorenzo Monaco, an Italian astronomer working at ESO. But the mere use of HARPS would not be sufficient to achieve this result. The observations of the integrated light of the sun at high resolution are in fact extremely difficult to conduct and to overcome this problem, astronomers pointed their instruments to the Moon to capture the sunlight reflected from it. For this reason, the transit was observed by astronomers in Chile when in fact it would be impossible to do so, since in that region of the world it was night. This unusual strategy has imposed special calculations to achieve the desired results. “The transit of Venus seen from the Moon has a slightly different schedule than what has been observed on Earth,” said Simone Zaggia from INAF Astronomical Observatory of Padua, who participated in the mission. “The Moon was in fact 8 degrees ahead of the Earth and Venus reaches alignment with the Sun and the Moon about two hours later. The transit was also slightly longer than that observed on Earth because the Moon was above the plane of rotation of the Earth around the Sun”. Observations show that the partial eclipse on the solar disc produced by the transit of Venus has generated a modulation in the radial velocity of the Sun of less than one meter per second, which is just 3 km/h. “The agreement with the theoretical models is around a few centimetres per second and is an amazing result ever reached before” says Mauro Barbieri, from University of Padua, who is also a member of the team. “Among other things, this change in velocity is comparable with that due to the natural expansion and contraction of our star. However, our observations have allowed us to clearly see the Rossiter-McLaughlin effect during transit”. The results obtained from these observations – the only ones with purely scientific purposes that have been carried out on the Earth during the last transit of Venus – will be of great help to astronomers, who in the next decade will be able measure this phenomenon in extrasolar systems, unleashing the full potential of new generation of telescopes such as the E-ELT. “This measurement – says Paolo Molaro – foretells the sensational results that in a few years will be able to get thanks to the advent of the 40-meter class telescopes equipped with high-resolution spectrographs. This mammoth astronomical instruments will open for sure a new horizon in the study of orbital properties of other Earth-like planets that are found around other stars in our galaxy.”

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Many times the word ethics is used to describe “responsible” behavior. While the two terms are related, ethics are moral codes or values that go beyond formal laws and regulations. They are referred to as “unwritten laws”—the rights and wrongs that dictate proper behavior. Safety education teaches you how to be a responsible hunter by helping to lay the foundation for a personal code of ethics. A peculiar virtue in wildlife ethics is that the hunter ordinarily has no gallery to applaud or disapprove of his conduct. Whatever his acts, they are dictated by his own conscience, rather than by a mob of onlookers. Ethics are what you use to make decisions about what to do when nobody is watching, or when there are no formal rules to tell you what is right or wrong. In a nutshell, ethics are what you think is right or wrong. When you’re hunting, you must make the decisions—not your instructors, or even your friends or relatives. And just as you practice to become a good shot, you must practice ethical behavior to act consistently. Your ethical code doesn’t just happen all by itself. Thinking about what you consider right or wrong is important. Consider how you’d feel after acting on a decision—would you feel proud or ashamed? And how would it affect other people? To make ethics work for you, there are three steps to follow: - Realize that there are moral decisions to make for many of your actions, such as: “Should I shoot now and risk merely wounding the game, or should I wait for a better shot?” - Think about the consequences of those decisions and how they might affect you and others. - Do the right thing. That sounds simple; in real life, however, few answers are black and white. Your personal ethics will help you sort through the gray areas and any moral dilemmas you might encounter. Laws are everything you must and must not do; ethics are those things you should and should not do…

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Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 13.3 Answer Key Making Purchasing Decisions. Example 1. Silvie went to a local warehouse store to buy her family’s favorite sports drink. Which of the two options described below is the better buy? Step 1 Find the total amount of the sports drink in each purchase. Value Pack: 24(0.5) = 12 liters Sport pack: 18(0.75) = 13.5 liters Step 2 Find each unit price. The Value Pack is a better buy, because $0.77 <$0.88. Question 1. Financial Literacy Manny must choose between a pack of four 6.5-ounce containers of yogurt for $3.77 or three 8-ounce containers at$1.29 each. Which ¡s the better buy? Why? Find the total. amount of the yogurt in each purchase. A pack of 46.5 – ounce containers 4 × 6.5 = 26 – ounces A pack of 38- ounce containers 3 × 8 = 24 – ounces Now, find each unit price. A pack of 46.5-ounce containers $$\frac{\ 3.77}{26-\text { ounces }}$$ = $0.145 per ounce A pack of 38-ounce containers Each 8—ounce container costs$1.29. hence the price of 3 containers is 3 × $1.29 =$3.87. $$\frac{\ 3.87}{24-\text { ounces }}$$ = $0.16 per ounce Better buy is a pack of 4 6.5— ounce containers, because$0.145 < $0.16 Example 2 Nathan plans on hiking this summer and wants to buy a solar charger for his cell phone and notebook computer. He finds the charger that he wants at two stores. Which store has the lower price for the charger? Answer: Step 1 Find the discount price at each store. Kitt’s discount price = regular price – discount =$89.99 – 0.3($89.99) =$89.99 – $26,997 =$62,993 To the nearest cent, the discount price at Kitti’s is $62.99 Rec Plus discount price = regular price – discount =$79.99 – $15.00 =$64.99 The discount price at Rec Plus is $64.99. Step 2 Compare the discounted prices. Kitt’s offers the lower price, because$62.99 < $64.99. Reflect Question 2. Critical Thinking Why might Nathan choose the higher priced item? Answer: Nathan would choose the charger in Kitt’s even if it has a higher regular price. This is because the discount in Kitt’s is higher compared to the Rec Plus. Once the regular price for the charger in Kitt’s got discounted, the price is cheaper compared to the discounted price in Rec Plus. The discount is higher for the higher-priced item which made it cheaper after the discount Your Turn Question 3. Nathan finds a backpack at Kitt’s that is regularly$84.99, but is on sale for $$\frac{1}{3}$$ off. The same backpack is regularly $72.99 at Rec Plus but is on sale for 25% off. Which is a better buy? Explain. Answer: Find the discount price at each store. Kitts Discount price = Regular price – Discount To find the Discount, multiply the Regular price by the percent of discount.$84.99 × $$\frac{1}{3}$$ = $28.33 Discouut price =$84.99 – $28.33 Discount price =$56.66 The Discount price at Kitt’s is $56.66. Rec Plus Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 25% = 0.25.$72.99 × 0.25 = $18.25 Discount price =$72.99 – $18.25 Discount price =$54.74 Tue Discount price at Rec Plus is $54.74. Rec Plus offers the lower price, because$54.74 <$56.66. Example 3. Cedelia can get the same running Go shoes at two different stores. She wants to get two pairs of the same style. Which is the better buy? Go Run She pays$104 for 2 pairs. Shoe Shoppe She pays 2 × $59 =$118 for 2 pairs Go Run has the better buy because $104 <$118. Reflect Question 4. What If? Suppose the total price at Shoe Shoppe had been $103? What are some conditions of a rebate that would make it a better decision to buy the shoes at Go Run? Answer: First condition If the first pair has rebate at least$7 and you get second pair free. Proof: Regular price is $109, rebate is at least$7, hence the total price at Go Run is $109 —$7 = $102.$102 < $103 Hence, Go Run lias the better buy than Shoe Shoppe. Second condition If both pairs have a discount of 53%. Proof: The regular price is$109. Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 53% = 0.53. $109 × 0.53 =$57.77 Discount price = $109 –$57.77 Discount price = $51.23 The Discount price of one pair is$51.23, and the discount price of 2 pairs is $51.23 × 2 =$102.16 $102.46 <$103 Hence, Go Run has the better buy than Shoe Shoppe. First condition: If the first pair has rebate at least $7 and you get second pair free. Second condition: If both pairs have a discount of 53%. Your Turn Question 5. Greta wants to buy 3 jars of honey. Food Mart sells it for$8.99 with a “Buy 2, get 1 free” offer. Leona’s sells it for $8.49 with a coupon for 50% off with a limit of 2 coupons. Which store has the better deal? Answer: Food Mart Greta wants to buy 3 jars of honey, and Food Mart lias an offer if you buy 2 you get 1 free. Hence, Greta will buy 2 jars of honey and get one free, and that would be 3 jars of honey she needs. One jar costs$8.99. so Price of 2 jars = 2 × $8.99 =$17.98 Greta would pay $17.98 for 3 jars of honey at Food Mart. Leona‘s At Leon’s she can buy 2 jars with a coupon for 50% off, because there is a limit of 2 coupons. Hence, the third jar of honey she has to buy by the full price. One jar of honey costs$8.19. Let’s find the Discount price with a coupon. Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 50% = 0.5. $8.19 × 0.5 =$4.215 Discount price = $8.49 –$4.245 Discount price = $4.245 The Discount price of one jar of honey is$4.245. She would buy 2 jars of honey by the discount price and the third one by the full price. Hence Price of 3 jars = 2 × Discount price + Full price Price of 3 jars = 2 × $4.245 +$8.49 Price of 3 jars = $16.98 Greta would pay$16.98 for 3 jars of honey at Leona’s. Hence, Leon’s has the better buy, because $16.98 <$17.98. Question 1. The Corner Store sells 4 bottles of energy drink for $1 1.56. Bev’s sells 6 bottles for$17.94. Which is the better buy? (Example 1) Find the price of one energy drink in each purchase. The Corner Store 4 bottles of energy drink cost $11.56. Find the price of one bottle of energy drink. Price of one bottle = $$\frac{\ 11.56}{4}$$ =$2.89/bottle The price of one bottle at Coriier Store is $2.89 per bottle. Bev’s 6 bottles of energy drink cost$17.94. Find the price of one bottle of energy drink. Price of 0ne bottle = $$\frac{\ 17.94}{6}$$ = $2.99/bottle The price of one bottle at Bev’s is$2.99 per bottle. The Corner Store lias the better buy, because $2.89 <$2.99. The Corner Store has the better buy, because $2.89 <$2.99. Question 2. You can buy a 2-pound loaf of bread for $2.50 or a 2-pack of 1$$\frac{1}{2}$$-pound loaves for$3.30. Which is the better buy?(Example 1) Find the price of 0ne pound loaf of bread in each purchase. First purchase 2-pound loaf of bread for 82.50 Find the price of one pound loaf of bread. Price of one pound = $$\frac{\ 2.50}{2}$$ = $1.25 The price of one pound of loaf of bread is$1.25. Second purchase 2- pack of 1$$\frac{1}{2}$$– pound loaf of bread for $3.30 In this purchase we have 2-pack of 4$$\frac{1}{2}$$ = $$\frac{3}{2}$$ = 1.5- pound loaves. Hence, the whole purchase will be 2 × 1.5 =3. So, 3- pound loaf of bread costs$3.30. Find the price of one pound loaf of bread. Price of one pound = $$\frac{\ 3.30}{3}$$ = $1.1 The price of one pound of loaf of bread is$1.1. Second puchase is the better, because $1.1 <$1.25. Question 3. Marta can buy a 6-pack of 15-ounce cans of broth for $11.29 or three 32-ounce containers for$10.97. Which is the better buy? (Example 1) First purchase A 6- pack of 15- ounce cans of broth 6(15) = 90 oz Now, find unite price $$\frac{\ 11.29}{90-\mathrm{oz}}$$ = $0.125/oz Second purchase A 3-32- contains 3(32) = 96 oz Now, find unite price $$\frac{\ 10.97}{96-\text { ounces }}$$ =$0.11/oz Second purchase is the better, because $0.11 <$0.125. Question 4. Zena can get an item online for $19 that weighs 8 pounds. Shipping and handling costs$0.49 per pound. She can also buy the same item locally for $26.95, and she has a$5 off coupon. Which is the better buy? (Example 2) The item has 8 pounds and shipping and handling per pound is $0.49. Shipping and handling for item is$0.49 × 8 = $3.92 To find the whole price of item sum the online price and the cost of shipping and handling.$19 + $3.92 =$22.92 Online purchase costs $22.92. Locally purchase$5 off coupon is a Discount. Find the Discount price. Discount price = Regular price — Discount Discount price = $26.95 —$5 Discount price = $21.95 The Discount price for locally purchase is$21.95. The locally purchase is better, because $21.95 <$22.92. Question 5. A take-and-bake pizza chain has several coupons, which cannot be used together. J.D. is buying a pizza that costs $17.90. Should he use a$5 off coupon or a 35% off coupon? (Example 2) $5 off coupon$5 off coupon is a Discount. Find the Discount price. Discount price = Regular price – Discount Discount price = $17.90 –$5 Discount price = $12.90 The Discount price of a pizza with a$5 off coupon is $12.90. 35% off coupon Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 35% = 0.35.$17.90 × 0.35 = $6.26 Discount price =$17.90 – $6.26 Discount price =$11.64 The Discount price of a pizza with a 35% coupon off is $11.64. J.D. should use a 35% off coupon, because$11.61 <$12.90. Question 6. The King family buys an HDTV selling for$825 at PanView with a 20% off coupon and a rebate of $125. They later see the TV on sale at Rey’s TVs for$555. Did they get the better deal? (Example 3) Determine the cost of the HDTV the King fami[y purchased at PanView. Show the 20% off coupon as decimaL 825 × 0.20 = 165 Determine the discount for the HDTV 825 – 165 = 660 Subtract the discount from the original price 660 – 125 = 535 Subtract the rebate from the discounted price The King family get the better deal. purchasing the HDTV at PanView instead at Rey’s TVs Yes Question 7. Credit card A has an annual fee of $50 but gives you a rebate at the end of the year of 2% of your total purchases. Credit card B has no annual fee or rebate. If you spend about$150 a month, which card is better for you? (Example 3) Credit card A If you spend $150 a month, it means that you spend 12 ×$150 = $1,800 a year. Credit card A has an annual fee of$50, hence, we have to add fee to the amount you spend a year. $1,800 +$50 = $1,850 At the end of the year you get a rebate of 2% of your total purchase, hence we have to subtract 2% from the whole amount$1,850. Write percent as decimal, ie 2% = 0.02. Find 2% of $1,850.$1,850 × 0.02 = $37 Now subtract.$1,850 – $37 =$1,813 If you use Credit card A, you will spend $1,813 a year. Credit card B Credit card B has no annual or rebate, hence, yearly you will spend 12 ×$150 = $1,800 If you use Credit card B, you will spend$1,800 a year. Hence, the Credit card B is better, because $1,800 <$1,813. Essential Question Check-In Question 8. Is the lower unit price always the best buy? No, it is not always. Sometimes there is an offer like, “Buy 2, get 1 free” of items with higher unit price. Also, there is some discount on quantity on items with higher unit price, which could be better buy than buy of unit with lower unit price without discount. The quality of the product when you buy it, regardless of the price, should not be neglected. Question 9. Store 1 has a price of $99 on an MP3 player. Store 2 is offering the same MP3 player at a sale price of 25% off their regular price of$125. Jerusha wants to buy an MP3 player. From which store should she buy it? Explain. Store 2 Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 25% = 0.25. Discount = $125 × 0.25 =$31.25 Discount price $125 –$31.25 Discount price = $93.75 The Discount price of an MP3 player in Store 2 is$93.75. The price of an MP3 player in Store 1 is $99. He should buy an MP3 player in Store 2, because$93.75 < $99. Question 10. Multistep Randy wants trail mix for his hiking trip. The ready-made trail mix costs$8.95 for 1.5 pounds. The costs of the bulk ingredients to make one pound of trail mix are as follows: salted peanuts—$1.25, raisins—$1.70, sunflower seeds—$0.50, cashews—$0.87, and almonds—$0.65. If Randy plans to take 6 pounds of trail mix, which option is cheaper? How much does he save by choosing the cheaper option? Answer: The ready-made trail mix A pack of 1.5 pounds costs$8.95. and Randy wants to buy 6 pounds of it. Hence, he needs to buy 1 packs of 1.5 pounds of trail mix. 4 × $8.95 =$35.8 6 pounds of ready-made trail mix will cost $35.8. Self—made trail mix To find the cost of one pound of trail mix. prices of all ingredients should be summed up. One pound of self-made trail mix =$1.25 + $1.70 +$0.50 + $0.87 +$0.65 = $4.97 To find the cost of 6 pounds of self-made trail mix multiply by 6 the cost of one pound. 6 ×$4.97 = $29.82 The cost of 6 pounds of self-made trail mix will be$29.82. The self-made trail mix is cheaper option than the ready—made trail mix, because $29.82 <$35.8. Question 11. Tyron and Penelope both bought 4-wheelers. Tyron paid $199 upfront, and will pay the remainder in 12 payments of$50 each. Penelope paid nothing up front, and will make 18 payments of $49. Who got the better buy? Explain. Answer: Tyron To find how much Tyron paid 4—wheeler, sum the amount he paid up front and the total remainder. First, find the total remainder. To find the total remainder multiply the number of payments by the amount of each payment. The total remainder = 12 ×$50 = $600 Now, find the total cost. The total cost of 4—wheeler =$199 + $600 =$799 Tyron paid $799 for 4—wheeler. PeneloPe Unlike Tyron Penelope will pay the price in 18 payments of$49. To find the total cost multiply the number of payments by the amount of each palyment. The total cost of 4—wheeler = 18 × $19 =$882 Penelope paid $882 for 4—wheeler. Tyron lias the better buy that Penelope, because$799 < $882. Question 12. Financial Literacy T’Shonda is buying a laptop computer. She will pay 8% sales tax on the price before ány rebates. Where will she get a better buy? Explain. Answer: XYZ-Tronic First, find the sales tax on the price(Subtotal). Write the tax rate as decimal, ie 8% = 0.08 Tax = Subtotal × Tax rate Tax =$629 × 0.08 = $50.32 Now, add the subtotal and the tax to find the total price. Total price =$629 + $50.32 =$679.32 The Total price before rebate is $679.32 To find the price after rebate, subtract mail—in—rebate from the Total price. The price after rebate =$679.32 – $150 =$529.32 In XYZ-Tronic she would pay $529.32 for a laptop. Tec U—Comp First, find the sales tax on the price(Subtotal). Write the tax rate as decimal. ie 8% = 0.08 Tax = Subtotal × Tax rate Tax =$649 × 0.08 = $51.92 Now, add the subtotal and the tax to find the total price. Total price =$649 + $51.92 =$700.92 The total price before rebate is $700.92 To find the price after rebate(The Discount price), subtract the Discount of 25% from the Total price(Regular price). Discount price = Regular price — Discount To find the Discount multiply the Regular price by the percent of discount. Write percent as decimal, ie 25% = 0.25. Discount =$700.92 × 0.25 = $175.23 Discount price =$700.92 – $175.23 Discount price =$525.69 The Discount price of a laptop is $525.69. T’Shonda will get the better buy in Tec—U-Comp, because$525.69 < $529.32. Question 13. Critical Thinking What single discount is equal to a discount of $$\frac{1}{4}$$ off followed by an additional 10% off the sale price? Answer: We want to know what single discount is equal to these discounts together. First, there is a discount of 25%. Write a fraction as decimal, ie $$\frac{1}{4}$$ = 0.25 Now, write the decimal as percent, ie 0.25 = 25% Hence, when some item has discount of $$\frac{1}{4}$$, it means that item has discount of 25%. After the discount of 25%, the total cost of that item is actually 75% of the regular price(the regular price represents 100% of the item) of that item, because 100% – 25% = 75%. After the discount of 25%, there is an additional. discount of 10%. An additional discount of 10% we can not compute on 100% of item price, because now the actual cost of the item is 75% of the first regular price(because first we had a discount of 25%). So, now we have to find 10% of 75% and subtract from it Write percent as decimal, ie 10% = 0.1 To find 10% of 75%, multiply 75% by the percent written in decimal. 75% × 0.1 = 7.5% Now, subtract. 75% – 7.5% = 67.5% Finally, the total cost of the item with first discount of 25% and then an additional 10% is 67.5% of the reguLar price of that item. As the cost of an item is now 67.5%, this means that these two discounts together represent a 32.5% discount, because 100% – 67.5% = 32.5%. Hence, the single discount that is equal to a discount of $$\frac{1}{4}$$ off followed by an additional 10% off is 32.5% off. The single discount that is equal to a discount of $$\frac{1}{4}$$ off followed by an additional 10% off is 32.5% off. Question 14. Make a Conjecture John is comparing the prices of two bags of the same cereal. He notices that the larger bag holds 10 more ounces and costs$1.50 more. How can he use the unit price of the smaller bag to decide the better buy? Explain. John can use the unit price of the smaller bag by multiplying it by 10 since the larger bag contains 10 more ounces. If the result of this is more than $1.50, then it is better to buy the larger bag instead of the smaller bag. But if the result is less than$1.50, it is still better to buy the smaller bag. Multiply the unit price of the smaller bag by 10. Texas Go Math Grade 7 Lesson 13.3 H.O.T. Focus on Higher Order Thinking Answer Key Question 15. Draw Conclusions Mr. Jaros has the following options for buying a digital video recorder and access to the recording service for 2 years. DiV: $49.99 digital video recorder, 2-year subscription at$16.98 a month TVU: Free digital video recorder, 2-year commitment at $19.95 a month a. Which is the better deal? Explain. Answer: DiV To find the total cost. of a digital video recorder and access to the recording service for 2 years we have to sum the cost of digital video recorder and the total cost of 2—year subscription. To find the total cost of subscription multiply the number of months by monthly fee for subscription. One year have 12 months, and 2 years have 2 × 12 = 24 months. The total cost of subscription = 24 ×$16.98 = $407.52 Now find the total cost of a digital video recorder and access to the recording service for 2 years.$49.99 + $407.52 =$457.51 The offer at DiV would cost $457.51. TVU At TVU Mr.Jaros can get free digital video recorder and only would pay 2- year commitment at$19.93. So, the total cost of a digital video recorder and access to the recording service for 2 years is actually the cost of total 2—years commitment. To find the total cost of commitment multiply the number of months by monthly fee. One year has 12 months, and 2 years have 2 × 12 = 24 months. The total cost of commitment = 24 × $19.95 =$478.8 The offer at TVU would cost $478.8. The better deal is at DiV, because$457.51 < $478.8. b. What If? Suppose each offer were for 1 year. Would that change your answer? Explain. Answer: Div To find the total cost of a digital video recorder and access to the recording service for 1 years we have to sum the cost of digital video recorder and the total cost of 1-year subscription. To find the total cost of subscription multiply the number of months by monthly fee for subscription. One year has 12 months. The total cost of subscription = 12 ×$16.98 = $203.76 Now find the total cost of a digital video recorder and access to the recording service for 1 years.$49.99 + $203.76 =$253.75 The offer at DiV would cost $253.75. TVU At TVU Mr.Jaros can get free digital video recorder and only would pay 1-year commitment at$19.95. So, the total cost of a digital video recorder and access to the recording service for 1 years is actually the cost of total 1-years commitment, To find the total cost of commitment multiply the number of months by monthly fee. One year has 12 months. The total cost of commitment = 12 × $19.95 =$239.4 The offer at TVU would cost $239.4. If the offer were for 1 year, the better deal would be at TVU, because$239.4 < $253.75. c. Make a Conjecture Find the difference in monthly rates. Divide the cost of the DiV digital video recorder by the difference and round up to the nearest whole number. What does this quotient represent? Answer: The difference in monthly rates =$19.95 = $16.98 =$2.97 Now, divide the cost of the DiV digital video recorder by the difference we calculated. $$\frac{49.99}{2.97}$$ = 16.83 ≈ 17 This quotient respresent the number of months. If the offer were for this number of months, both offers would cost almost the same(because we round up the quotient to the nearest whole number). Proof: DiV The total cost of subscription = 17 × $16.98 =$288.66 To find the total cost of a digital video recorder and access to the recording service for 17 months we have to sum the cost of digital video recorder and the total cost of 17 months subscription. $49.99 +$288.66 = $338.65 TVU To find the total cost of commitment multiply the number of months by monthly fee. The total cost of commitment = 17 ×$19.95 = $339.15$338.65 ≈ $339.15 This quotient respresent the number of months. If the offer were for this number of months. Both offers would cost almost the same. Question 16. Analyze Relationships Sandy wants to buy 5 pounds of apples. She has a coupon for$1.00 off for every 3 pounds of apples. She gets to the store and discovers that apples are on sale for $0.75 a pound. Is it cheaper for her to buy 5 pounds or 6 pounds? Explain. Answer: If Sandy buys 5 pounds of apples. she can use only one coupon for$1 off, because the coupon is valid for every 3 pounds. The cost of 011e pound of apples is $0.75. Hence, 5 pounds of apples. without coupon, will cost 5 ×$0.75 = $3.75 Now, to find the cost of 5 pounds of apples with a coupon. subtract$1 from $3.75.$3.75 – $1 =$2.75 Hence, 5 pounds of apples will cost $2.75 If Sandy buys 6 pounds of apples. she can use only two coupon for$1 off, because the coupon is valid for every 3 pounds. The cost of 0ne pound of apples is $0.75. Hence, 6 pounds of apples, without coupon, will cost 6 ×$0.75 = $4.5 Now, to find the cost of 6 pounds of apples with two coupon, subtract$2(because she can use 2 coupons) from $4.5.$4.5 – $2 =$2.5 Hence, 6 pounds of apples will cost $2.5 It is cheaper for Sandy to buy 6 pounds of apples. because$2.5 <$2.75. Question 17. Draw Conclusions Two stores have a sale on T-shirts originally priced at$8.50. Yeager’s has a “Buy 2, get 1 free” sale. Gample’s has a 30% off sale. Dirk wants to buy only 2 T-shirts. Which is the better buy for him? Explain your reasoning. Yeager ‘s Yeager’s offer is “3 T-shirts for the price of 2”, ie “buy 2, get 1 free”. Dirk wants to buy only 2 T-shirts, but buying 2 T-shirts will definitely get a third one. Let ‘s see how much those 3 shirts would cost. The price of 1 T-shirt is $8.50, so Dirk would pay for 2 T-shirts, and get a third one for free. The price of 3 T-shirts = 2 ×$8.50 = $17 3 T-shirts would cost$17, but we want to know what is the value of 2 T-shirts. To find that, divide $17 by 3. The value of one T-shirt, = $$\frac{\ 17}{3}$$ =$5.67 Time value of 2 T-shirts = 2 × $5.67 =$11.34 The value of 2 T-shirts at Yeager’s is $11.34. Gample’s Gamples offer is a discount of 30% on each T—shirt. Let’s find how much one T-shirt would cost, ie the Discount price. Discount price = Regular price – Discount To find the Discount multiply the Regular price by the percent of discount. The regular price of 1 T-shirt is$8.50. Write percent as dechnal, ie 30% = 0.30. Discount = $8.50 × 0.30 =$2.55 [)iscount price = $8.50 –$2.55 Discount price = $5.95 The Discount price of one T-shirt is$5.95. The Discount price(the value) of 2 T-shirts at Cample’s is 2 × $5.95 =$11.9. Hence, the better buy for Dirk is at Yeager’s, because the value of 2 T-shirts is less than the value at Gample’s, ie $11.34 <$11.9. The better buy for Dirk is at Yeager’s, because $11.34 <$11.9. Question 18. Represent Real-World Problems Suppose you are buying books from an online store, and the total price of your books is $39. Orders of$50 or more for eligible items qualify for free shipping. Would you buy more to qualify for free shipping? Or would you check out with only the books you have in your shopping cart? Explain your answer. The first question that would come into your mind is, how much is the shipping fee for the books with a total price of $39. If the shipping fee is more than$11, it is better to buy another book which will make the total price at $50. But if the shipping fee is less than$11, lets say $5 and you really don’t have any book to purchase, then you could just pay the shipping fee and your total price will still be less than$50.

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Learning about angles has never been easier. This PowerPoint offers 25 slides. First, it shows students the great importance of angles in our world. Then it instructs students about acute, obtuse and right angles in a comic book like manner that uses both visual and auditory memory strategies. Next, students get to practice their new knowledge by uncovering the many angles we can make using our bodies. Moreover, complementary and supplementary angles are taught using more fun memory strategies. The PowerPoint ends with a classroom activity! It's an enjoyable and memorable lesson that your students will love. What's more - there is a link to a free video by Dr. Warren on angles!

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Chapter 6, Problem 33RE ### Calculus (MindTap Course List) 11th Edition Ron Larson + 1 other ISBN: 9781337275347 Chapter Section ### Calculus (MindTap Course List) 11th Edition Ron Larson + 1 other ISBN: 9781337275347 Textbook Problem # Sales The sales S (in thousands of units) of a new product after it has been on the market for t years is given by S = C e k / t .(a) Find S as a function of t when 5000 units have been sold after 1 year and the saturation point for the market is 30,000 units (that is, lim t → ∞ S = 30 ).(b) How many units will have been sold after 5 years? (a) To determine To calculate: The sales(in thousands of units) of a new product as a function of time tS=Cekt if for t=1,S=5 and saturation point of the market is 30000limtS=30000 Explanation Given: t=1,S=5 and limt→∞S=30000 Formula used: The sales model S=Cekt Here S is the sales,t is time in years and C is the sales at t=∞. Calculation: Consider the expression S=Cekt …… (1) Now, it is given that when t=1 then S=5 So, put the above values in equation 1: S=Cekt5=Cek1C=5ek                                                                                           (b) To determine To calculate: The no. of units that will have been sold after 5 years ### Still sussing out bartleby? Check out a sample textbook solution. See a sample solution #### The Solution to Your Study Problems Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees! Get Started

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Author: Vitaliy Herasymiv Tester: Tasnim Imran Sunny Editorialist: Tuan Anh Data Structures: Trie, Dynamic Programming, Bitwise operation Given a tree, with each edge being assigned a non-negative weight. The weight of the path from u to v is the XOR-sum of all the edges along the path. We need to find the path with the maximal weight. Before we proceed to the problem let us define the xor-sum. XOR operation is a bitwise “Exclusive OR” operation performed on two integers in binary representation. First, the shorter number is prepended with leading zeroes until the numbers have equal size in binary. Then the resulting number (also in binary) contains 0 in all positions where the corresponding bits coincide, and 1 on the rest of the positions. For example, 3 XOR 5 = 0112 XOR 1012 = 1102 = 6. And as explained in the problem statement, XOR-sum of a list of numbers is the result of XOR-ing all of them. XOR-sum of (A1 XOR A2 XOR … XOR A[N]) is defined as A1 XOR (A2 XOR (A3 XOR ( … XOR A[N]))). Now, coming at the problem: Using a simple dynamic programming technique, we can calculate that S[u] is the weight of the path from 1 to u. The weight of the path from u to v is S[u] xor S[v]. It’s not hard to prove this observation. Let c be the lowest common ancestor of u and v. S[u] = S[c] xor weight(c, u), and S[v] = S[c] xor weight(c, v) where, weight(x, y) is the weight of the path from x to y. S[u] xor S[v] = S[c] xor weight(c, u) xor S[c] xor weight(c, v) = weight(u, v). After the S array is prepared, our problem reduces to finding two numbers in the S array that give the maximal xor-sum. We will use a data structure called Trie which will help use manage the numbers when we treated them as the binary strings. If you are not familiar with Trie, you must read about it here and try to do some simple problems at the following links The pseudo code is given below: Make an empty Trie T FOR all number v in S Find the maximal xor-sum of v with an numbers in the T. Update the result Insert v into the T. ENDFOR The heart of our solution is at the third line of the pseudo code. Suppose, that we represent each number by a 20-character binary string. Let v = a1a2…a20 where a1 represents the most significant bit and a20 represents the least significant bit. To make the xor-sum u xor v as large as possible (u is a number in the Trie), our strategy is try finding each bit of u starting from the first bit to the last bit. With each ith bit, we check whether the ith bit of u can be 1 - ai or not. If it can be, then the ith bit of u is 1 - ai since this makes the ith bit of the xor-sum become 1. Otherwise the ith bit of u is ai because we don’t have a better choice. After each step, we know one more bit of u and that is why Trie can help us in this process. We just need to store the current node of the Trie which corresponds to the current prefix of u. From this node we can easily check whether the next bit of u can be 0 or 1 and make the decision from that. The complexity of this solutions will be O(Nlog(Maximal weight)). AUTHOR’S AND TESTER’S SOLUTIONS: Author’s solution can be found here. Tester’s solution can be found here. In their solutions, there is a slight modification. They insert all numbers in S into the trie first and then find the maximal xor-sum of each S[i] with an numbers in the Trie. It works because S[i] xor S[i] = 0 so inserting all the numbers in the Trie at the beginning do not affect our result. Equivalent Suffix Tries (On CodeChef) Phone List (On SPOJ)

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The most commonly reported measure of the consumer price levels in the United States is the Consumer Price Index (CPI). Published by the U.S. Department of Labor 's Bureau of Labor Statistics, the CPI is a fixed-weight price index using a fixed basket of goods that are representative of what a typical consumer purchases each month. There are many different CPI's calculated by region, types of products, types of consumers, etc. The most commonly reported CPI is the CPI-U, which is the CPI for all urban consumers. Increases in the CPI level serve as a measure of the consumer inflation rate. The rate of inflation over a period of time is simply the percentage increase in the CPI over the period, often reported on an annualized basis. Uses of the CPI The CPI has many important uses, including the following: Economic indicator - the CPI is the most commonly reported measure of consumer prices. Reference for escalation agreements - labor contracts and other payment agreements that are indexed to inflation rely on the CPI. Deflator for economic series - when a series of data is to be adjusted so that it is reported in constant dollars, the CPI often is used as the deflator. Because of the widespread use of the CPI, especially for adjusting payments to inflation, its accuracy can have a significant impact on the economy. In recent years, the accuracy of the CPI has been questioned due to a number of biases that cause it to overstate the effective rate of inflation. The CPI tends to overstate inflation because of the following biases: Substitution bias - when the price of a product in the consumer basket increases substantially, consumers tend to substitute lower-priced alternatives. For example, if a freeze in Florida causes the price of oranges to skyrocket, consumers may substitute Texas grapefruits for Florida oranges. Since the CPI is a fixed-weight price index, it would not accurately predict the impact of the price increase on the consumer's budget. Quality bias - over time, technological advances increase the life and usefulness of products. For example, the useful life of automobile tires increased substantially over the past few decades, decreasing the tire cost on a per mile basis, but the CPI does not reflect such improvements. New product bias - new products are not introduced into the index until they become commonplace, so the dramatic price decreases often associated with new technology products are not reflected in the index. Outlet bias - the consumer shift to new outlets such as wholesale clubs and online retailers is not well-represented by the CPI. Some economists estimate that such biases overstate the CPI by about 1% per year. The U.S. Department of Labor has responded to these biases by more frequently changing the base period when the items in the index and their weights are adjusted. Also, the government now is quicker to add new products to the CPI basket and has made quality adjustments to the index. Economics (Barron's Business Review Series) The articles on this website are copyrighted material and may not be reproduced, stored on a computer disk, republished on another website, or distributed in any form without the prior express written permission of QuickMBA.com.

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De moivre formula Question 1. Nov 22, 2005 Bob19 Hi I have a question regarding the use of de moivre formula: I'm presented with a complex number $$z = (cos(v) + i sin(v))^n = 1$$ I'm suppose to show that $$z^n = 1$$ is a root of unity. Is there a procedure on how to show this? If n = 6 and $$v = \frac{4 \pi}{6}$$ Sincerely and Best Regards Bob 2. Nov 22, 2005 HallsofIvy Staff Emeritus Are you sure you've copied this correctly? You are saying that you are told that z= 1 ?? And you want to prove that 1 is a "root of unity"?? I very much doubt that! Please copy the problem carefully. Perhaps you are given that z= cos v+ i sin(v) and want to show that (cos v+ i sin(v))n= zn= 1, thus showing that z is a "root of unity". Furthermore, you then say "if n= 6 and $v= \frac{4\pi}{6}$". Is that a separate problem or is the original problem to show that $$\left(cos\left(\frac{4\pi}{6})+ i sin(\frac{4\pi}{6}\right)\right)^6= 1$$? If it is the latter, since YOU titled this "DeMoivre's Formula Question", what does DeMoivre's formula tell you $\left(\(cos\left(\frac{4\pi}{6})+ i sin(\frac{4\pi}{6}\right)\right)^6$ is? Last edited: Nov 23, 2005 3. Nov 23, 2005 Bob19 Hello I have been looking through my textbook which gives the following procedure on how to show if $$(cos(\frac{4 \pi}{6}) + i sin(\frac{4 \pi}{6}))$$ Is the six root of unity for $$z^{6} = 1$$ Its know that $$1 = cos(2 k \pi) + i sin(2 k \pi)$$ where k = 1,2,3,.....m According to De Moivre's formula the n'th root unity can be expressed as $$(cos(\frac{2 k \pi}{n}) + i sin(\frac{2 k \pi}{n}))$$ My case k = 2 and n = 6 If I insert these into De Moivre's formula I get $$z = (cos(\frac{4 \pi}{6}) + i sin(\frac{4 \pi}{6}))$$ I insert z into the initial equation and get $$(cos(\frac{4 \pi}{6}) + i sin(\frac{4 \pi}{6}))^6 = (cos(\frac{24 \pi}{6}) + i sin(\frac{24 \pi}{6})) = 1$$ Therefore $$(cos(\frac{4 \pi}{6}) + i sin(\frac{4 \pi}{6}))$$ is the 6'th root of unity for $$z^6 = 1$$ I have hand it in tomorrow so therefore am I on the right track? Sincerely and Best Regards, Bob Last edited: Nov 23, 2005 4. Nov 23, 2005 HallsofIvy Staff Emeritus Yes, you can do that but it would be easier, since you are already given $$z = (cos(\frac{4 \pi}{6}) + i sin(\frac{4 \pi}{6}))$$, to just take the 6 th power of that and show that it is 1.

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Introspection is the self-observation and reporting of conscious inner thoughts, desires and sensations. It is a conscious and purposive process relying on thinking, reasoning, and examining one's own thoughts, feelings, and, in more spiritual cases, one's soul. It can also be called contemplation of one's self, and is contrasted with extrospection, the observation of things external to one's self. Introspection may be used synonymously with and in a similar way to human self-reflection. It is used greatly as a spiritual examination. Introspection is like the activity described by Plato when he asked, "…why should we not calmly and patiently review our own thoughts, and thoroughly examine and see what these appearances in us really are?" As a method in science Behaviorists claimed that introspection was unreliable and that the subject matter of scientific psychology should be strictly operationalized in an objective and measurable way. This then led psychology to focus on measurable behavior rather than consciousness or sensation. Cognitive psychology accepts the use of the scientific method, but often rejects introspection as a valid method of investigation for this reason, especially concerning the causes of behavior and choice. Herbert Simon and Allen Newell identified the 'think aloud protocol', in which investigators view a subject engaged in a task, and who speaks his thoughts aloud, thus allowing study of his thought process without forcing the subject to comment on his thinking. On the other hand, introspection can be considered a valid tool for the development of scientific hypotheses and theoretical models, in particular in cognitive sciences and engineering. In practice, functional (goal-oriented) computational modeling and computer simulation design of meta-reasoning and metacognition are closely connected with the introspective experiences of researchers and engineers. Introspection was used by German physiologist Wilhelm Wundt in the experimental psychology laboratory he had founded in Leipzig in 1879. Wundt believed that by using introspection in his experiments he would gather information into how the subjects' minds were working, thus he wanted to examine the mind into its basic elements. Wundt did not invent this way of looking into an individual's mind through their experiences; rather, it can date to Socrates. Wundt's distinctive contribution was to take this method into the experimental arena and thus into the newly formed field of psychology. Inaccessible mental processes and confabulation Psychological research on cognition and attribution has asked people to report on their mental processes, for instance to say why they made a particular choice or how they arrived at a judgement. In some situations, these reports are clearly confabulated. For example, people justify choices they have not in fact made. Such results undermine the idea that those verbal reports are based on direct introspective access to mental content. Instead, judgements about one's own mind seem to be inferences from overt behavior, similar to judgements made about another person. However, it is hard to assess whether these results only apply to unusual experimental situations, or if they reveal something about everyday introspection. The theory of the adaptive unconscious suggests that a very large proportion of mental processes, even "high-level" processes like goal-setting and decision-making, are inaccessible to introspection. Even when their introspections are uninformative, people still give confident descriptions of their mental processes, being "unaware of their unawareness". This phenomenon has been termed the introspection illusion and has been used to explain some cognitive biases and belief in some paranormal phenomena. When making judgements about themselves, subjects treat their own introspections as reliable, whereas they judge other people based on their behavior. This can lead to illusions of superiority. For example, people generally see themselves as less conformist than others, and this seems to be because they do not introspect any urge to conform. Another reliable finding is that people generally see themselves as less biased than everyone else, because they do not introspect any biased thought processes. These introspections are misleading, however, because biases work sub-consciously. One experiment tried to give their subjects access to others' introspections. They made audio recordings of subjects who had been told to say whatever came into their heads as they answered a question about their own bias. Although subjects persuaded themselves they were unlikely to be biased, their introspective reports did not sway the assessments of observers. When subjects were explicitly told to avoid relying on introspection, their assessments of their own bias became more realistic. In Eastern Christianity, some of the concepts critical to addressing the needs of man such as sober introspection, called nepsis, are specific to watchfulness of the human heart and address the conflicts of the human nous, heart or mind. Also noetic understanding can not be circumvented nor satisfied by rationalizing or discursive thought (i.e. systemization). Introspections (also referred to as internal dialogue, interior monologue, self-talk) is the fiction-writing mode used to convey a character's thoughts. As explained by Renni Browne and Dave King, "One of the great gifts of literature is that it allows for the expression of unexpressed thoughts…" (Browne and King 2004, p. 117). According to Nancy Kress, a character's thoughts can greatly enhance a story: deepening characterization, increasing tension, and widening the scope of a story (Kress 2003, p. 38). As outlined by Jack M. Bickham, thought plays a critical role in both scene and sequel (Bickham 1993, pp. 12–22, 50–58). - Phenomenology (psychology) - Rumination (psychology) - Style (fiction) - Mode (literature) - Conceptual proliferation - Boring, Edwin G. (1953). "A history of introspection". Psychological Bulletin 50 (3): 169–189. doi:10.1037/h0090793. PMID 13056096. http://www-psych.stanford.edu/~knutson/aaa/boring53.pdf. Retrieved 2009-07-17. - Anthony Jack, Andreas Roepstorff, ed (2003). Trusting the subject?: the use of introspective evidence in cognitive science. Imprint Academic. ISBN 9780907845560. - Wilson, Timothy (2002). Strangers to Ourselves: Discovering the Adaptive Unconscious. Cambridge: Belknap Press. ISBN 0-674-00936-3. - Wilson, Timothy D. Wilson; Sara D. Hodges (1992). "Attitudes as Temporary Constructions". In Leonard L. Martin, Abraham Tesser. The Construction of social judgments. Lawrence Erlbaum Associates. ISBN 9780805811490. - Theaetetus, 155 - J Perner et al (2007). "Introspection & remembering". Synthese. Springer. - Wilson, Robert Andrew; Keil, Frank C. (Eds.) (2001). The MIT Encyclopedia of the Cognitive Sciences (MITECS). Cambridge, Massachusetts: The MIT Press. ISBN 0-262-73144-7. http://books.google.com/?id=-wt1aZrGXLYC&printsec=frontcover. Cf. p.xx - Nisbett, Richard E.; Timothy D. Wilson (1977). "Telling more than we can know: Verbal reports on mental processes". Psychological Review 8: 231–259. , reprinted in David Lewis Hamilton, ed (2005). Social cognition: key readings. Psychology Press. ISBN 9780863775918. - Johansson, Petter; Lars Hall, Sverker Sikström, Betty Tärning, Andreas Lind (2006). "How something can be said about telling more than we can know: On choice blindness and introspection". Consciousness and Cognition (Elsevier) 15 (4): 673–692. doi:10.1016/j.concog.2006.09.004. PMID 17049881. - White, Peter A. (1988). "Knowing more about what we can tell: 'Introspective access' and causal report accuracy 10 years later". British Journal of Psychology (British Psychological Society) 79 (1): 13–45. - Wilson, Timothy D.; Elizabeth W. Dunn (2004). "Self-Knowledge: Its Limits, Value, and Potential for Improvement". Annual Review of Psychology 55: 493–518. doi:10.1146/annurev.psych.55.090902.141954. PMID 14744224. - Wilson, Timothy D.; Yoav Bar-Anan (August 22, 2008). "The Unseen Mind". Science (American Association for the Advancement of Science) 321 (5892): 1046–1047. doi:10.1126/science.1163029. PMID 18719269. - Pronin, Emily (January 2007). "Perception and misperception of bias in human judgment". Trends in Cognitive Sciences (Elsevier) 11 (1): 37–43. doi:10.1016/j.tics.2006.11.001. ISSN 1364-6613. PMID 17129749. - Wegner, Daniel M. (2008). "Self is Magic". In John Baer, James C. Kaufman, Roy F. Baumeister. Are we free?: psychology and free will. New York: Oxford University Press. ISBN 9780195189636. http://isites.harvard.edu/fs/docs/icb.topic67047.files/2_13_07_Wegner.pdf. Retrieved 2008-07-02. - Pronin, Emily; Matthew B. Kugler (July 2007). "Valuing thoughts, ignoring behavior: The introspection illusion as a source of the bias blind spot". Journal of Experimental Social Psychology (Elsevier) 43 (4): 565–578. doi:10.1016/j.jesp.2006.05.011. ISSN 0022-1031. - Pronin, Emily; Jonah Berger, Sarah Molouki (2007). "Alone in a Crowd of Sheep: Asymmetric Perceptions of Conformity and Their Roots in an Introspection Illusion". Journal of Personality and Social Psychology (American Psychological Association) 92 (4): 585–595. doi:10.1037/0022-35126.96.36.1995. ISSN 022-3514. PMID 17469946. - Schultz, D. P. & Schultz, S. E. (2004). A history of modern psychology (8th ed.). Belmont, CA: Wadsworth/Thomson Learning. - Bickham, Jack M. (1993). Scene & Structure. Writer's Digest Books. ISBN 0-89879-551-6. - Browne & King (2004). Self-Editing for Fiction Writers: How to Edit Yourself into Print. New York: Harper Resource. ISBN 0-06-054569-0 - Gillespie, A. (2006). Descartes’ demon: A dialogical analysis of ‘Meditations on First Philosophy.’ Theory & Psychology, 16, 761-781. - Gillespie, A. (2007). The social basis of self-reflection . In Jaan Valsiner and Alberto Rosa (Eds), The Cambridge Handbook of Socio-Cultural Psychology. Cambridge: Cambridge University Press. - Kress, Nancy (August 2003), Writer's Digest. |Look up introspection in Wiktionary, the free dictionary.| - Introspection entry by Eric Schwitzgebel in the Stanford Encyclopedia of Philosophy - Introspection in the Internet Encyclopedia of Philosophy

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Transplanting body parts is now a growth industry, and in a relatively short period of time since the first heart transplant of around 40 years ago. However while transplanting hearts, livers and so on is common, helping people see again using transplant technology has until recently been difficult, if not impossible. That may be about to change, as scientists have grown part of an eyeball in a laboratory. The part of the eyeball which is perhaps the most important is the retina. It seems that Japanese medical scientists have managed to grow this from scratch. They began with blank embryonic stem cells which are able to be turned into any cells in the body, in turn becoming any particular organ that’s needed. Once the required cells were created, the scientists added proteins and other chemicals to entice the stems cells to produce a retina. The creation was roughly at the stage of an unborn baby. Speaking with the Daily Mail, Robin Ali, professor at University College London said: “It is a major landmark. To see that beautiful structure in a dish as if it had just been taken from an animal is absolutely astounding.” Echoing his thoughts, a fellow scientist from Oxford University Robert MacLaren told reporters: “The thought of generating the cells in large numbers from patients’ own skin is very exciting.” If Mr. MacLaren is right, this new breakthrough could help millions of people who suffer blindness from diseases such as age-related macular degeneration, a common cause of blindness in elderly people. The experiments were carried out on mice, so extrapolation onto humans is stretching it a bit at the moment. Nevertheless, it is something that the medical profession and blind people will welcome.

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# Algebra Pick a number. Multiply by 2. Subtract 8. Divide by 2. Add 4. What is the result? Use algebra to show why the tricks work. asked by Cheyenne 1. Try first with a number... say 7 first multiply by 2, that is 7x2=14 subtract 8, that is 14-8=6 divide by 2, that is 6/2= 3 add 4, that is 3 + 4 = 7 So what happened to your original number?? posted by MsPi_3.14159265 2. x = your number ( x * 2 - 8 ) / 2 + 4 = x * 2 / 2 - 8 / 2 + 4 = x - 4 + 4 = x posted by Bosnian 3. (7×2)-8÷2+4=7 posted by Cheyenne First Name Your Answer ## Similar Questions 1. ### Algebra Pick a number. Double it. Multiply the result by 3. Add 24. Divide by 6. Subtract your original number. Is the result always the same? Write a convincing argument for what happens. HELP! 2. ### ALGEBRA can you help me with this. d don't get it at all :( let n be the number used for the given number puzzle. use algebra to show how the puzzle works. 1. pick a number 2. subtract 9 3. multiply by 6 4. divide by 3 5. add 18 6. 3. ### Math Pick what age you would like to be (may be your actual age if you like). Add 10. Multiply the result by 4. Add 200. Divide by 4. Subtract your original number. The final result is 60. Explain how I knew that. 4. ### math for elementry school teacher Mr. Mathemagician asks you to pick any whole number. Add 10. Multiply the result by 4. Add 200. Divide by 4. Subtract your original number. Mr. Mathemagician says, “You’re final result is 60!” Explain Mr. Mathemagician’s 5. ### hheeelp Mr. Mathemagician asks you to pick any whole number. Add 10. Multiply the result by 4. Add 200. Divide by 4. Subtract your original number. Mr. Mathemagician says, “You’re final result is 60!” Explain Mr. Mathemagician’s 6. ### Algebra Jill asks each of her classmates to choose a number, then multiply the number by -3, add 2 to the product, multiply the result by -2, and then subtract 14. Finally, each student is asked to divide the result by 6 and record the 7. ### Algebra Hello all! I had a quick homework question: I have to prove that the output of this always ends up as 1, regardless of the starting number: *Think of a number between 1 and 10. Add 1; double the result; add 3; subtract 4; add 5; 8. ### algebra multiply by 3, add 4, divide by 5, subtract 6, result :1 whatis the n 9. ### Algebra How do I express this in algebraic form? And could you please explain how you came up with the expression? "Come up with a number. Add 3 to it. Muliply by 1 more than the original number. Subtract 3. Divide by the original number. 10. ### INTRODUCTORY ALGEBRA FOR HOMEWORK I HAVE TO DO A NUMBER TRICK BY PICKING A NUMBER ADD 5 DOUBLE THE RESULT SUBTRACT 4 THEN DIVIDE THE RESULT BY 2 AND THE RESULT SHOULD BE THREE.THEN I HAVE TO EPLAIN WHY THE RESULT IS ALWAYS 3. I DON'T GET IT CAN YOU More Similar Questions

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The Olfactory Nerve, or First Cranial Nerve, is the pathway taken by Olfactory impulses from the Nasal mucosa to the Brain. The Olfactory Tract connects the Olfactory Bulb with the Olfactory Tubercle, where it divides into a Medial and Lateral Olfactory Tract. The Optic Nerve, or Second Cranial Nerve, lies just Posterior and Inferior to the Medial Olfactory Tract. It carries information from the Eye for Vision and Ocular Reflexes. The Third Cranial Nerve, or Oculomotor Nerve arises at the Ventral aspect of the MesenCephalon and transverses through the Cavernous Sinus to the Orbit. It supplies all the Intrinsic Ocular Muscles and all Extrinsic Ocular Muscles except for the Lateral Rectus and Superior Oblque. The ParaSympathetic Fibers from this Nerve innervate the Ciliary Muscle of the Lens and the Sphincter Muscle of the Pupil. The Fourth Cranial Nerve, or Trochlear Nerve, supplies only the Superior Oblique Muscle of the Eye, and it arises just below the Inferior Quadrigeminal Bodies of the BrainStem. It emerges from the Posterior aspect of the BrainStem and passes around the Lateral side of the Cerebellar Peduncle into the Margin of the Tentorium and into the Cavernous Sinus, where it goes to the Orbit. The Fifth Cranial Nerve, or Trigeminal Nerve, is the Largest Cranial Nerve, and it carries Fibers that give Sensation to the Face and Motor Fibers to the Muscles of Mastication. It exits from the BrainStem through the AnteroLateral surface of the Pons. The Sixth Cranial Nerve, or Abducent Nerve, supplies the Lateral Rectus Muscle of the Eyeball and issues from the Brain at the Inferior border of the Pons, just above the Pyramid of the Medulla Oblongata. The Seventh Cranial, or Facial Nerve, consists of two parts: The Auditory Nerve, or Eighth Cranial Nerve, is entirely Sensory, and consists of Vestibular and Cochlear divisions. The Glossopharyngeal, or Ninth Cranial Nerve is a Mixed Nerve consisting of an Afferent part, which supplies the Pharynx and Tongue and the Carotid Sinus and Body. The Vagus, or Tenth Cranial Nerve is also a Mixed Nerve, which contains a large number of ParaSympathetic Fibers and passes through the Neck and Thorax into the Abdomen. It supplies Afferent Fibers chiefly to the Pharynx, Esophagus, Stomach, Larynx, Trachea, and Lungs. It's attached by numerous Rootlets to the side of the Medulla Oblongata, in series with the Accessory Nerve below and the Glossopharyngeal Nerve above. The Rootlets unite to form a Single Tract, which exits from the Cranial Cavity through the Jugular Foramen. The Accessory Nerve, or Eleventh Cranial Nerve, consists of Bulbar and Spinal portions. It arises in series with the Vagus and Glossopharyngeal Nerve and controls Motor Function of the Sternomastoid and the Trapezius Muscles. The Twelfth Cranial Nerve, or Hypoglossal Nerve, is a predominantly Efferent Nerve that supplies all the Muscles of the Tongue, both Intrinsic and Extrinsic, except the Palatoglossus Muscle. It arises from numerous Rootlets from the Anterior portion of the Medulla Oblongata. The Rootlets are arranged in double bundles and unite in the Anterior Condylar Canal, where they emerge from the Cranial Cavity. The John Hopkins Atlas Of Human Functional Anatomy 2nd Edition 1977 Donlin M. Long, M.D.

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This storyboard does not have a description. Germany, in 1971, had been ruled by a Communist Government. Erich Honecker ruled this Communist Party and used Stasi, a form of secret police, to rule Germany. To Honecker's dismay, in 1989, many East Germans fled their country and mass demonstrations against his harsh regime began in the fall. On November 9, the Communist Government surrendered by opening its border to the West. East Germans swarmed across the border, reuniting with friends and family. People on both sides of the Berlin wall began tearing it down. The government, with no other option, ordered to have the rest of the wall torn down. During East Germany's first free election, the Christian Democrats won almost 50% of the vote. The Christian Democrats supported political union with West Germany. The reunification of both East and West occurred on October 3, 1989. Despite the earlier problems in the year of 1989, by the end of 1990 the countries of West and East Germany had fully reunited to form one Germany. East Germany's first free election: March 1990 Explore Our Articles and Examples Try Our Other Websites! Photos for Class – Search for School-Safe, Creative Commons Photos (It Even Cites for You! – Easily Make and Share Great-Looking Rubrics – Create Custom Nursery Art

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COPD (Chronic Obstructive Pulmonary Disease) What is chronic obstructive pulmonary disease (COPD)? COPD is a lung disease that makes it hard to breathe. It is caused by damage to the lungs over many years, usually from smoking. COPD is often a mix of two diseases: - Chronic bronchitis (say "bron-KY-tus"). In chronic bronchitis, the airways that carry air to the lungs (bronchial tubes) get inflamed and make a lot of mucus. This can narrow or block the airways, making it hard for you to breathe. - Emphysema (say "em-fuh-ZEE-muh"). In a healthy person, the tiny air sacs in the lungs are like balloons. As you breathe in and out, they get bigger and smaller to move air through your lungs. But with emphysema, these air sacs are damaged and lose their stretch. Less air gets in and out of the lungs, which makes you feel short of breath. COPD gets worse over time. You can't undo the damage to your lungs. But you can take steps to prevent more damage and to feel better. What causes COPD? COPD is almost always caused by smoking. Over time, breathing tobacco smoke irritates the airways and destroys the stretchy fibres in the lungs. Other things that may put you at risk include breathing chemical fumes, dust, or air pollution over a long period of time. Second-hand smoke also may damage the lungs. It usually takes many years for the lung damage to start causing symptoms, so COPD is most common in people who are older than 60. You may be more likely to get COPD if you had a lot of serious lung infections when you were a child. People who get emphysema in their 30s or 40s may have a disorder that runs in families, called alpha-1 antitrypsin deficiency. But this is rare. What are the symptoms? The main symptoms are: - A long-lasting (chronic) cough. - Mucus that comes up when you cough. - Shortness of breath that gets worse when you exercise. As COPD gets worse, you may be short of breath even when you do simple things like get dressed or fix a meal. It gets harder to eat or exercise, and breathing takes much more energy. People often lose weight and get weaker. At times, your symptoms may suddenly flare up and get much worse. This is called a COPD exacerbation (say "egg-ZASS-er-BAY-shun"). An exacerbation can range from mild to life-threatening. The longer you have COPD, the more severe these flare-ups will be. How is COPD diagnosed? To find out if you have COPD, a doctor will: - Do a physical examination and listen to your lungs. - Ask you questions about your past health and whether you smoke or have been exposed to other things that can irritate your lungs. - Have you do breathing tests, including spirometry, to find out how well your lungs work. - Do chest X-rays and other tests to help rule out other problems that could be causing your symptoms. If there is a chance you could have COPD, it is very important to find out as soon as you can. This gives you time to take steps to slow the damage to your lungs. How is it treated? The best way to slow COPD is to quit smoking. This is the most important thing you can do. It is never too late to quit. No matter how long you have smoked or how serious your COPD is, quitting smoking can help stop the damage to your lungs. Your doctor can prescribe treatments that may help you manage your symptoms and feel better. - Medicines can help you breathe easier. Most of them are inhaled so they go straight to your lungs. If you get an inhaler, it is very important to use it just the way your doctor shows you. - A lung (pulmonary) rehab program can help you learn to manage your disease. A team of health professionals can provide counselling and teach you how to breathe easier, exercise, and eat well. - In time, you may need to use oxygen some or most of the time. People who have COPD are more likely to get lung infections, so you will need to get a flu vaccine every year. You should also get a pneumococcal shot. It may not keep you from getting pneumonia. But if you do get pneumonia, you probably won't be as sick. How can you live well with COPD? There are many things you can do at home to stay as healthy as you can. - Avoid things that can irritate your lungs, such as smoke and air pollution. - Use an air filter in your home. - Get regular exercise to stay as strong as you can. - Eat well so you can keep up your strength. If you are losing weight, ask your doctor or dietitian about ways to make it easier to get the calories you need. Dealing with flare-ups: As COPD gets worse, you may have flare-ups when your symptoms quickly get worse and stay worse. It is important to know what to do if this happens. Your doctor may give you an action plan and medicines to help you breathe if you have a flare-up. But if the attack is severe, you may need to go to the emergency room or call 911. Managing depression and anxiety: Knowing that you have a disease that gets worse over time can be hard. It's common to feel sad or hopeless sometimes. Having trouble breathing can also make you feel very anxious. If these feelings last, be sure to tell your doctor. Counselling, medicine, and support groups can help you cope. Health Tools help you make wise health decisions or take action to improve your health. - Breathing Exercises: Using a Manual Incentive Spirometer - Breathing Problems: Using a Dry Powder Inhaler - Breathing Problems: Using a Metered-Dose Inhaler - COPD: Avoiding Weight Loss - COPD: Avoiding Your Triggers - COPD: Clearing Your Lungs - COPD: Keeping Your Diet Healthy - COPD: Learning to Breathe Easier - COPD: Using Exercise to Feel Better - Oxygen Therapy: Using Oxygen at Home Frequently Asked Questions Learning about chronic obstructive pulmonary disease (COPD): Living with COPD: COPD is most often caused by smoking. Most people with COPD are long-term smokers, and research shows that smoking cigarettes increases the risk of getting COPD. COPD is often a mix of two diseases: chronic bronchitis and emphysema. Both of these diseases are caused by smoking. Although you can have either chronic bronchitis or emphysema, people more often have a mixture of both diseases. Other possible causes of COPD include: - Long-term exposure to lung irritants such as industrial dust and chemical fumes. - Preterm birth that leads to lung damage (neonatal chronic lung disease). - Inherited factors (genes), including alpha-1 antitrypsin deficiency. This is a rare condition in which your body may not be able to make enough of a protein (alpha-1 antitrypsin) that helps protect the lungs from damage. People who have this disorder and who smoke generally start to have symptoms of emphysema in their 30s or 40s. Those who have this disorder but don't smoke generally start to have symptoms in their 80s. When you have COPD: - You have a cough that won't go away. - You often cough up mucus. - You are often short of breath, especially when you exercise. - You may feel tightness in your chest. Many people with COPD have attacks called flare-ups or exacerbations (say "egg-ZASS-er-BAY-shuns"). This is when your usual symptoms quickly get worse and stay worse. A COPD flare-up can be dangerous, and you may have to go to the hospital. - Coughing up more mucus than usual. - A change in the colour or thickness of that mucus. - More shortness of breath than usual. - Greater tightness in your chest. Work with your doctor to make a plan for dealing with a COPD flare-up. If you are prepared, you may be able to get it under control. Try not to panic if you start to have a flare-up. Quick treatment at home may help you manage serious breathing problems. What Increases Your Risk Tobacco smoking is the most important risk factor for COPD. Compared to smoking, other risks are minor. - Pipe and cigar smokers have less risk of getting COPD than cigarette smokers. But they still have more risk than non-smokers. - The risk for COPD increases with both the amount of tobacco you smoke each day and the number of years you have smoked. To learn more, see the topic Quitting Smoking. Some people may be more at risk than others for getting the disease, especially if they have low levels of the protein alpha-1 antitrypsin (alpha-1 antitrypsin deficiency), a disorder that runs in families. Preterm babies usually need to have long-term oxygen therapy because their lungs are not fully developed. This therapy can cause lung damage (neonatal chronic lung disease) that can increase the risk for COPD later in life. Asthma and COPD are different diseases, even though both of them involve breathing problems. People with asthma may have a greater risk for getting COPD, but the reasons for this are not fully understood. Risks in the environment - Outside air pollution. Air pollution may make COPD worse. It may increase the risk of a flare-up, or COPD exacerbation, when your symptoms quickly get worse and stay worse. Try not to be outside when air pollution levels are high. - Indoor air pollution. Have good ventilation in your home to avoid indoor air pollution. - Second-hand smoke. It is not yet known whether second-hand smoke can lead to COPD. But a large study showed that children who were exposed to second-hand smoke were more likely to get emphysema than children who weren't exposed.footnote 2 And people who are exposed to second-hand smoke for a long time are more likely to have breathing problems and respiratory diseases. - Occupational hazards. If your work exposes you to chemical fumes or dust, use safety equipment to reduce the amount of fumes and dust you breathe. When to Call a Doctor Call 911 or other emergency services now if: - Breathing stops. - Moderate to severe difficulty breathing occurs. This means a person may have trouble talking in full sentences or breathing during activity. - Severe chest pain occurs, or chest pain is quickly getting worse. - You cough up large amounts of bright red blood. Call your doctor immediately or go to the emergency room if you have been diagnosed with COPD and you: - Cough up a couple of tablespoons of blood. - Have shortness of breath or wheezing that is quickly getting worse. - Start having new chest pain. - Are coughing more deeply or more often, especially if you notice an increase in mucus (sputum) or a change in the colour of the mucus you cough up. - Have increased swelling in your legs or belly. - Have a high fever [over 38.5°C (101°F)]. - Develop flu-like symptoms. If your symptoms (cough, mucus, and/or shortness of breath) suddenly get worse and stay worse, you may be having a COPD flare-up, or exacerbation. Quick treatment for a flare-up may help keep you out of the hospital. Call your doctor soon for an appointment if: - Your medicine is not working as well as it had been. - Your symptoms are slowly getting worse, and you have not seen a doctor recently. - You have a cold and: - Your fever lasts longer than 2 to 3 days. - Breathlessness occurs or becomes noticeably worse. - Your cough gets worse. - You have not been diagnosed with COPD but are having symptoms. A history of smoking (even in the past) greatly increases the likelihood that symptoms are from COPD. - You cough up any amount of blood. Talk to your doctor If you have been diagnosed with COPD, talk with your doctor at your next regular appointment about: - Help to stop smoking. To review tips on how to stop smoking, see the topic Quitting Smoking. - A yearly flu vaccine. - A pneumococcal vaccine. Children usually get a pneumococcal shot before age 2. Doctors also recommend a pneumococcal shot for everyone age 65 and older even if they got the shot as a child. - An exercise program or pulmonary rehabilitation. - Any updates of your medicines or treatment that you may need. Who to see You may need to see a specialist in lung disease, called a respirologist, if: - Your diagnosis of COPD is uncertain or hard to make because you have diseases with similar symptoms. - You have unusual symptoms that are not usually seen in people with COPD. - You are younger than 50 and/or have no history or a short history of cigarette smoking. - You have to go to the hospital often because of sudden increases in shortness of breath. - You need long-term oxygen therapy or corticosteroid therapy. - You and your doctor are considering surgery, such as a lung transplant or lung volume reduction. Examinations and Tests To diagnose COPD, your doctor will probably do the following tests: - Medical history and physical examination. These will give your doctor important information about your health. - Lung function tests, including an FEV1 test. These tests measure the amount of air in your lungs and the speed at which air moves in and out. Spirometry is the most important of these tests. - Chest X-ray. This helps rule out other conditions with similar symptoms, such as lung cancer. Tests done as needed - Arterial blood gas test. This test measures how much oxygen, carbon dioxide, and acid is in your blood. It helps your doctor decide whether you need oxygen treatment. - Oximetry. This test measures the oxygen saturation in the blood. It can be useful in finding out whether oxygen treatment is needed, but it provides less information than the arterial blood gas test. - Electrocardiogram (ECG, EKG) or echocardiogram. These tests may find certain heart problems that can cause shortness of breath. - Transfer factor for carbon monoxide. This test looks at whether your lungs have been damaged, and if so, how much damage there is and how bad your COPD might be. Tests rarely done - Alpha-1 antitrypsin (AAT) test. AAT is a protein your body makes that helps protect the lungs. People whose bodies don't make enough AAT are more likely to get emphysema. - A CT scan. This gives doctors a detailed picture of the lungs. Because COPD is a disease that keeps getting worse, it is important to schedule regular checkups with your doctor. Checkups may include: Tell your doctor about any changes in your symptoms and whether you have had any flare-ups. Your doctor may change your medicines based on your symptoms. The sooner COPD is diagnosed, the sooner you can take steps to slow down the disease and keep your quality of life for as long as possible. Screening tests help your doctor diagnose COPD early, before you have any symptoms. Talk to your doctor about COPD screening if you: - Are a smoker or an ex-smoker. - Have had serious asthma symptoms for a long time, and they have not improved with treatment. - Have a family history of emphysema. - Have a job where you are exposed to a lot of chemicals or dust. The U.S. Preventive Services Task Force (USPSTF) doesn't recommend COPD screening for adults who are not at high risk for COPD.footnote 3 And some experts recommend that screening be done only for people who have symptoms of a lung problem.footnote 4 The Canadian Thoracic Society (CTS) does not recommend screening smokers who do not have symptoms of COPD. But screening is recommended for smokers and ex-smokers age 40 and older who have any of the following symptoms:footnote 1 - A regular cough and/or production of mucus (sputum) - Frequent respiratory tract infections, such as colds - Reports of regular and worsening activity-related wheezing or shortness of breath The goals of treatment for COPD are to: - Slow down the disease by quitting smoking and avoiding triggers, such as air pollution. - Limit your symptoms, such as shortness of breath, with medicines. - Increase your overall health with regular activity. - Prevent and treat flare-ups with medicines and other treatment. Pulmonary rehab can help you meet these goals. It helps train your mind, muscles, and heart to get the most out of damaged lungs. The program involves a team of health professionals who help prevent or manage the problems caused by COPD. It typically combines exercise, breathing therapy, advice for eating well, and other education. Much of the treatment for COPD includes things you can do for yourself. Quitting smoking is the most important thing you can do to slow the disease and improve your quality of life. Other things you can do that really make a difference including eating well, staying active, and avoiding triggers. To learn more, see Living With COPD. The medicines used to treat COPD can be long-acting to help prevent symptoms or short-acting to help relieve them. To learn more, see Medications. Other treatment you may need If COPD gets worse, you may need other treatment, such as: - Oxygen treatment. This involves getting extra oxygen through a face mask or through a small tube that fits just inside your nose. It can be done in the hospital or at home. - Treatment for muscle weakness and weight loss. Many people with severe COPD have trouble keeping their weight up and their bodies strong. This can be treated by paying attention to eating regularly and well. - Help with depression. COPD can affect more than your lungs. It can cause stress, anxiety, and depression. These things take energy and can make your COPD symptoms worse. But they can be treated. If you feel very sad or anxious, call your doctor. - Surgery. Surgery is rarely used for COPD. It's only considered for people who have severe COPD that has not improved with other treatment. Dealing with flare-ups COPD flare-ups, or exacerbations, are when your symptoms—shortness of breath, cough, and mucus production—quickly get worse and stay worse. Work with your doctor to make a plan for dealing with a COPD flare-up. If you are prepared, you may be able to get it under control. Don't panic if you start to have one. Quick treatment at home may help you prevent serious breathing problems. A flare-up can be life-threatening, and you may need to go to your doctor's office or to a hospital. Treatment for flare-ups includes: - Quick-relief medicines to help you breathe. - Anticholinergics (such as ipratropium or tiotropium) - Oral corticosteroids (such as methylprednisolone or prednisone) - Beta2-agonists (such as salbutamol or terbutaline) - Machines to help you breathe. The use of a machine to help with breathing is called mechanical ventilation. Ventilation is used only if medicine isn't helping you and your breathing is getting very difficult. - Non-invasive positive pressure ventilation (NPPV) forces air into your lungs through a face mask. - With invasive ventilation, a breathing tube is inserted into your windpipe, and a machine forces air into your lungs. - Oxygen to help you breathe. Oxygen treatment can be done in the hospital or at home. - Antibiotics. These medicines are used when a bacterial lung infection is considered likely. People with COPD have a higher risk of pneumonia and frequent lung infections. These infections often lead to COPD exacerbations, or flare-ups, so it's important to try to avoid them. The best way to keep COPD from starting or from getting worse is to not smoke. There are clear benefits to quitting, even after years of smoking. When you stop smoking, you slow down the damage to your lungs. For most people who quit, loss of lung function is slowed to the same rate as a non-smoker's. Stopping smoking is especially important if you have low levels of the protein alpha-1 antitrypsin. People who have an alpha-1 antitrypsin deficiency may lower their risk for severe COPD if they get regular shots of alpha-1 antitrypsin. Family members of someone with alpha-1 antitrypsin deficiency should be tested for the condition. Avoid bad air Other airway irritants (such as air pollution, chemical fumes, and dust) also can make COPD worse, but they are far less important than smoking in causing the disease. If you have COPD, you need to get a flu vaccine every year. When people with COPD get the flu, it often turns into something more serious, like pneumonia. A flu vaccine can help prevent this from happening. Also, getting regular flu vaccines may lower your chances of having COPD flare-ups. People with COPD often get pneumonia. Getting a shot can help keep you from getting very ill with pneumonia. Children usually get a pneumococcal shot before age 2. Doctors also recommend a pneumococcal shot for everyone age 65 and older even if they got the shot as a child. Talk with your doctor about whether you need a second shot. Pertussis (also called whooping cough) can increase the risk of having a COPD flare-up. So making sure you are current on your pertussis vaccinations may help control COPD. COPD gradually gets worse over time. Shortness of breath gets worse as COPD gets worse. - If you are diagnosed early, before you have a lot of lung damage, you may have very mild symptoms, even when you are active. - If you are diagnosed later, you may have already lost much of your lung function. - If you are active, you may be short of breath during activities that didn't used to cause this problem. - If you are not very active, you may not notice how much shortness of breath you have until your COPD gets worse. - If you have had COPD for many years, you may be short of breath even when you are at rest. Even simple activities may cause very bad shortness of breath. It's very important to stop smoking. If you keep smoking after being diagnosed with COPD, the disease will get worse faster, your symptoms will be worse, and you will have a greater risk of having other serious health problems. The lung damage that causes symptoms of COPD doesn't heal and cannot be repaired. But if you have mild to moderate COPD and you stop smoking, you can slow the rate at which breathing becomes more difficult. You will never be able to breathe as well as you would have if you had never smoked, but you may be able to postpone or avoid more serious problems with breathing. Other health problems from COPD may include: - More frequent lung infections, such as pneumonia. - An increased risk of thinning bones (osteoporosis), especially if you use oral corticosteroids. - Problems with weight. If chronic bronchitis is the main part of your COPD, you may need to lose weight. If emphysema is your main problem, you may need to gain weight and muscle mass. - Heart failure affecting the right side of the heart (cor pulmonale). - A collapsed lung (pneumothorax). COPD can damage the lung's structure and allow air to leak into the chest cavity. - Sleep problems because you are not getting enough oxygen into your lungs. Hospice palliative care Treatment for COPD is getting better and better at helping people live longer. But COPD is a disease that keeps getting worse, and it can be fatal. Hospice palliative care is a kind of care for people who have diseases that don't go away and that often get worse over time. It's different from care to cure your illness. Its goal is to improve your quality of life—not just in your body but also in your mind and spirit. You can have this care along with treatment to cure your illness. A time may come when treatment for your illness no longer seems like a good choice. This can be because the side effects, time, and costs of treatment are greater than the promise of cure or relief. But you can still get treatment to make you as comfortable as possible during the time you have left. Hospice palliative care providers will work to help manage shortness of breath and other symptoms or side effects. They may help you decide what treatment you want or don't want. And they can help your loved ones understand how to support you. You and your doctor can decide when you may be ready for hospice palliative care. For more information, see the topics: Living With COPD When you manage COPD, you: - Quit smoking. - Take steps to improve your ability to breathe. - Eat well and stay active. - Learn all you can about COPD. - Get support from your family and friends. It's never too late to quit smoking. No matter how long you have had COPD or how serious it is, quitting smoking will help slow down the disease and improve your quality of life. Although lung damage that already has occurred doesn't reverse, quitting smoking can slow down how quickly your COPD symptoms get worse. One Man's Story: "I tried to quit cold turkey, but after just a few days I could tell that wasn't going to work. I realized that I needed to try something else. So I tried the patch, and that made a big difference. I can feel a difference in my breathing. And I feel hopeful that quitting will give me a few more years on my feet."—Ned You may think that nothing can help you quit. But today there are several treatments shown to be very good at helping people stop smoking. They include: - Nicotine replacement therapy. - The medicines bupropion (Zyban) and varenicline (Champix). - Support groups. Today's medicines offer lots of help for people who want to quit. You will double your chances of quitting even if medicine is the only treatment you use to quit, but your odds get even better when you combine medicine and other quit strategies, such as counselling. For more information, see the topic Quitting Smoking. Make breathing easier Do all you can to make breathing easier. - Avoid conditions that may irritate your lungs, such as indoor and outdoor air pollution, smog, cold dry air, hot humid air, and high altitudes. - Conserve your energy. You may get more tasks done and feel better if you learn to save energy while doing chores and other activities. Take rest breaks and sit down whenever you can while you fold laundry, cook, and do other household tasks. An occupational therapist or physiotherapist can help you find ways to do everyday activities with less effort. - Stay as active as possible, and get regular exercise. Try to do activities and exercises that build muscle strength and help your cardiovascular system. If you get out of breath, wait until your breathing returns to normal before continuing. - Learn breath training techniques to improve airflow in and out of your lungs. - Learn ways to clear your lungs that can help you save energy and oxygen. - Discuss pulmonary rehabilitation with your doctor. - Take the medicines prescribed by your doctor. If you use an inhaler, be sure you know how to use it properly. One Man's Story: "There was a time when I couldn't take 10 steps without running out of breath. Now I walk an hour around my neighbourhood every day—without needing my oxygen. I feel better than I have in years."—Cal Good nutrition is important to keep up your strength and health. Problems with muscle weakness and weight loss are common in people with severe COPD. It's dangerous to become very underweight. Seek education and support Treating more than the disease and its symptoms is very important. You also need: - Education. Educating yourself and your family about COPD and your treatment program helps you and your family cope with your lung disease. - Counselling and support. Shortness of breath may reduce your activity level and make you feel socially isolated because you cannot enjoy activities with your family and friends. You should be able to lead a full life and be sexually active. Counselling and support groups can help you learn to live with COPD. - A support network of family, friends, and health professionals. Learning that you have a disease that may shorten your life can trigger depression or grieving. Anxiety can make your symptoms worse and can trigger flare-ups or make them last longer. Support from family and friends can reduce anxiety and stress and make it easier to live with COPD. - Your treatment plan. Following a treatment plan will make you feel better and less likely to become depressed. A self-reward system—such as a night out to eat after staying on your medicine and exercise schedule for a week—can help keep you motivated. One Woman's Story: "Not being the person I used to be—it makes me really sad sometimes. There are lots of days I don't want to even get up, but then I think about taking my walk or seeing my friends, and I want get out there. COPD may slow me down, but it isn't going to stop me."—Sarah Medicine for COPD is used to: - Reduce shortness of breath. - Control coughing and wheezing. - Prevent COPD flare-ups, also called exacerbations, or keep the flare-ups you do have from being life-threatening. Most people with COPD find that medicines make breathing easier. Some COPD medicines are used with devices called inhalers or nebulizers. It's important to learn how to use these devices correctly. Many people don't, so they don't get the full benefit from the medicine. - Bronchodilators are used to open or relax your airways and help your shortness of breath. - Short-acting bronchodilators ease your symptoms. They are considered a good first choice for treating stable COPD in a person whose symptoms come and go (intermittent symptoms). They include: - Anticholinergics (such as ipratropium). - Beta2-agonists (such as salbutamol or terbutaline). - A combination of the two (such as a combination of salbutamol and ipratropium). - Long-acting bronchodilators help prevent breathing problems. They help people whose symptoms do not go away (persistent symptoms). They include: - Anticholinergics (such as aclidinium, tiotropium, or umeclidinium). - Beta2-agonists (such as formoterol or salmeterol). - A combination of the two, or a combination of a beta2-agonist and a corticosteroid medicine. - Short-acting bronchodilators ease your symptoms. They are considered a good first choice for treating stable COPD in a person whose symptoms come and go (intermittent symptoms). They include: - Phosphodiesterase-4 (PDE4) inhibitors are taken every day to help prevent COPD exacerbations. The only PDE4 inhibitor available is roflumilast (Daxas). - Corticosteroids (such as prednisone) may be used in pill form to treat a COPD flare-up or in an inhaled form to prevent flare-ups. They are often used if you also have asthma. - Other medicines include methylxanthines, which generally are used for severe cases of COPD. They may have serious side effects, so they are not usually recommended. Tips for using inhalers The first time you use a bronchodilator, you may not notice much improvement in your symptoms. This doesn't always mean that the medicine won't help. Try the medicine for a while before you decide if it is working. Many people don't use their inhalers right, so they don't get the right amount of medicine. Ask your health care provider to show you what to do. Read the instructions on the package carefully. Most doctors recommend using spacers with metered-dose inhalers. But you should not use a spacer with a dry powder inhaler. Lung surgery is rarely used to treat COPD. Surgery is never the first treatment choice and is only considered for people who have severe COPD that has not improved with other treatment. - Lung volume reduction surgery removes part of one or both lungs, making room for the rest of the lung to work better. It is used only for some types of severe emphysema. - Lung transplant replaces a sick lung with a healthy lung from a person who has just died. - Bullectomy removes the part of the lung that has been damaged by the formation of large, air-filled sacs called bullae. This surgery is rarely done. Other treatment for COPD includes: - Oxygen treatment. This treatment involves breathing extra oxygen through a face mask or through a tube inserted just inside your nose. It may ease shortness of breath. And it can help people with very bad COPD and low oxygen levels live longer. - Ventilation devices. These are machines that help you breathe better or breathe for you. They are used most often in the hospital during COPD flare-ups. - Alpha-1 antitrypsin injections (such as Prolastin). These medicines can help people who have alpha-1 antitrypsin deficiency. Other Places To Get Help - O'Donnell DE, et al. (2008). Canadian Thoracic Society recommendations for the management of chronic obstructive pulmonary disease—2008 update—highlights for primary care. Canadian Respiratory Journal, 15(Suppl A): 1A–8A. Available online: http://www.lung.ca/cts-sct/pdf/COPD-Highlights.pdf. - Lovasi GS, et al. (2010). Association of environmental tobacco smoke exposure in childhood with early emphysema in adulthood among nonsmokers. American Journal of Epidemiology, 171(1): 54–62. - U.S. Preventive Services Task Force (2008). Screening for chronic obstructive pulmonary disease using spirometry: U.S. Preventive Services Task Force recommendation statement. Annals of Internal Medicine, 148(7): 529–534. - Qaseem A, et al. (2011). Diagnosis and management of stable chronic obstructive pulmonary disease: A clinical practice guideline update from the American College of Physicians, American College of Chest Physicians, American Thoracic Society, and European Respiratory Society. Annals of Internal Medicine, 155(3): 179–191. Other Works Consulted - Criner GJ, Sternberg AL (2008). A clinician's guide to the use of lung volume reduction surgery. Proceedings of the American Thoracic Society, 5(4): 461–467. - Diaz PT, et al. (2008). Optimizing bronchodilator therapy in emphysema. Proceedings of the American Thoracic Society, 5(4): 501–505. - Falk JA, et al. (2008). Inhaled and systemic corticosteroids in chronic obstructive pulmonary disease. Proceedings of the American Thoracic Society, 5(4): 506–512. - Global Initiative for Chronic Obstructive Lung Disease (2014). Global Strategy for the Diagnosis, Management, and Prevention of Chronic Obstructive Pulmonary Disease. http://www.goldcopd.org/guidelines-global-strategy-for-diagnosis-management.html. Accessed May 21, 2014. - King DA, et al. (2008). Nutritional aspects of chronic obstructive pulmonary disease. Proceedings of the American Thoracic Society, 5(4): 519–523. - Maclay JD, et al. (2009). Update in chronic obstructive pulmonary disease 2008. American Journal of Respiratory and Critical Care Medicine, 179(7): 533–541. - Qaseem A, et al. (2011). Diagnosis and management of stable chronic obstructive pulmonary disease: A clinical practice guideline update from the American College of Physicians, American College of Chest Physicians, American Thoracic Society, and European Respiratory Society. Annals of Internal Medicine, 155(3): 179–191. Primary Medical Reviewer E. Gregory Thompson, MD - Internal Medicine Adam Husney, MD - Family Medicine Specialist Medical Reviewer Ken Y. Yoneda, MD - Pulmonology Current as ofMay 23, 2016 Current as of: May 23, 2016 To learn more about Healthwise, visit Healthwise.org. © 1995-2017 Healthwise, Incorporated. Healthwise, Healthwise for every health decision, and the Healthwise logo are trademarks of Healthwise, Incorporated.

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This week, Willow Class had a science-based Forest School session and they learnt more about vertebrates and invertebrates! Before going to the forest, the children classified some animals and began to quickly identify whether an animal was an invertebrate or vertebrate. Then, we focused on the kinds of animals we would find in our woodland. The children then went on a bug hunt all over the forest to see which types of invertebrates they could find and used a classification key to find more features of their animals. They worked really well as small groups and were really considerate to their environment. After they had finished, they had a great time creating skeletons of vertebrates with sticks and anything else they could find in the forest! Edward, Chloe and Jesse made an amazing crocodile one that stood up by itself! Finley, Helbert, Tommy and George made a fantastic eagle one – complete with a beak and tail! Next week, we are hoping to light a fire and cook some marshmallows so, if any other adults are free to come and help us, we would really appreciate it!

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第一次诸侯战争（First Barons' War）was an armed military conflict that was fought in the Kingdom of England from 1215 to 1217. Like several other wars throughout history, it was another theater of the endless conflict between the Assassins and Templars. In this war, the group of rebellious English barons were supported by the French Army to instigate a civil war against King John after the monarch refused to accept the terms of the newly-crafted Magna Carta agreement. However, the war quickly evolved into an attempt by the French prince Louis VIII to gain English lands. The Assassins, led by Robert Fitzwalter, fought for the French-aligned Barons while the Templars used their influence to help the King. Additionally, operating idependently from the Assassins, Master Assassin William of Cassingham chose to fight for King John and his son, Prince Henry. Although Louis managed to seize several English towns during the war, his barons eventually defected back to the English side after King John's death, leaving Louis without support and unable to secure his hold on England. On 11 September 1217, Louis relinquished the ground he had won during the war and returned to France, with the conflict ending in a stalemate.

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The importance of music, and how it has made us evolve. In one way or another, music is present in almost every sphere of our lives. It can be, for example, inserted into a scene from a horror movie to increase tension and anguish, or it can be used during a fitness class so that your attendees follow the right pace. On the other hand, in any social event worth its salt, a melody cannot be missing, even in the background. From Richard Wagner’s famous bridal march at a wedding to the bands and singer-songwriters that set nighttime bars, musicality is always present. Individuals in all human societies can perceive musicality and be emotionally sensitive to sound (Amodeo, 2014). It is easy for anyone to know when a song pleases them, causes them sadness or even euphoria. And, like many other things in our lives, we accept the existence of music as something natural. However, when analyzed from a scientific point of view, the ability to create and enjoy music is quite complex and has attracted the attention of researchers from many different fields. - Recommended Article: “What Music Do Smart People Listen to?” Music could favor survival For a few decades, evolutionary scientists have set out to find the origin of music in the biological history of the human being. This perspective starts from the theory of natural selection, affirming that it is the needs imposed by the environment that shape the design of all species, since the individuals with the best adaptations (physiological or psychological) at all times will survive. These beneficial traits arise from various genetic mutations, which if positive for survival will have a greater chance of being transmitted from generation to generation. In the case of humans, the pressure of natural selection has affected the structure and functions of the brain over thousands of years , surviving the design that allowed carrying out more functional behaviors. However, our species is much more complex. Although natural selection has shaped the biological design of the organism, it is culture and what we learn throughout life that ends up defining who we are. With these ideas in mind, many ethologists, neuroscientists, musicologists, and biologists agree that there was a moment in history when music helped our ancestors survive in a harsh and hostile environment. In a review of the subject, Martín Amodeo (2014) affirms that the ability to appreciate sound art could even have an essential role in the emergence of the human species. These statements may be surprising since, currently, the use that is given to music is apparently playful and does not involve a matter of life and death, fortunately. When did music emerge? Musicality would be prior to the appearance of art and language, the latter two being the almost exclusive property of Homo sapiens. The hominids before the human being would not have the necessary mental capacity to elaborate a complex language, having to stick to a pre-linguistic communication system based on sounds that changed rhythm and melody. In turn, they accompanied these sounds with gestures and movements, representing as a whole simple meanings about the emotions that they wanted to convey to their classmates (Mithen, 2005). Although there was still a long way to go in history to reach the current level, music and verbal language would have their primitive starting point here. However, although music and verbal language have a common origin, there is a great difference between the two. The sounds we assign to words have nothing to do with their meaning in real life. For example, the word “dog” is an abstract concept that has been attributed to this mammal randomly through culture. The advantage of language would be that certain sounds can refer to very precise propositions. On the contrary, the sounds of music would be in a certain way natural and it could be said that: “music seems to mean what it sounds like” (Cross, 2010) although the meaning of this is usually ambiguous and cannot be expressed with exact words. In this regard, researchers from the University of Sussex (Fritz et. Al, 2009) conducted a cross-cultural study in support of this thesis. In their research, they studied the recognition of three basic emotions (happiness, sadness and fear) present in various Western songs by members of the African Mafa tribe, who had never had contact with other cultures and, of course, had never heard the songs that were presented to them. The Mafas recognized the songs as happy, sad, or scary, so it seems that these basic emotions can also be recognized and expressed through music. In summary, one of the main functions of music, in its origins, could be the induction of moods in other people (Cross, 2010), which can serve to try to modify the behavior of others based on certain objectives . We carry music inside since we are born Another of the pillars of today’s music may be in the mother-child relationship. Ian Cross, professor of Music and Science and researcher at the University of Cambridge, has studied the age of acquisition, by babies, of all the faculties that allow musical perception, concluding that before the first year of life they already they have developed these capacities to the level of an adult. The development of verbal language, on the other hand, will be more time consuming. To cope with this, the child’s parents resort to a peculiar form of communication. As Amodeo (2014) describes, when a mother or father speaks to a baby, they do so differently than when they establish an adult conversation. When speaking to the newborn while being rocked rhythmically, a higher-than-normal voice is used, using repetitive patterns, somewhat exaggerated intonations, and very marked melodic curves. This way of expressing themselves, which would be an innate language between the son and the mother, would help to establish a very deep emotional connection between them. Parents who had this capacity in hostile times would see their descendants care easier since, for example, they could calm the cry of a child, preventing it from attracting predators. Therefore, those with this pre-musical ability would be more likely that their genes and characteristics would survive and be spread over time. Martín Amodeo maintains that the rhythmic movements and the singular vocalizations that the father performed would give rise to the song and music. In addition, the ability of babies to capture this would be maintained throughout life and would allow, in adulthood, they could feel emotions when listening to a certain combination of sounds, for example, in the form of musical composition. This mechanism of mother-child interaction is common to all cultures, which is why it is considered universal and innate. Music makes us feel more united There are also theories based on the social function of music, since this would favor the cohesion of the group. For ancient humans, cooperation and solidarity in a hostile environment was key to survival. A pleasant group activity such as the production and enjoyment of music would cause the individual to secrete a high amount of endorphins, something that would occur together if the melody is heard by several people at the same time. This coordination, by allowing music to transmit basic feelings and emotions, would allow obtaining a “generalized emotional state in all members of a group” (Amodeo, 2014). Various studies affirm that group interaction through music favors empathy, consolidates the identity of the community, facilitates integration in it and, as a consequence, maintains its stability (Amodeo, 2014). A cohesive group through activities such as music would therefore facilitate its survival as it would promote cooperation between large groups of people. Applying it to our days as well, the beauty of music when enjoyed in a group is based on two factors. On the one hand, there is a biological factor that allows us to elicit shared emotions before, for example, the same song. This favors the feeling of mutual affiliation (Cross, 2010). The second factor is based on the ambiguity of the music. Thanks to our complex cognitive abilities, human beings have the ability to attribute meanings to what they hear based on their personal experience. Due to this, in addition to promoting basic emotions, music allows each person to give a personal interpretation to what she hears, adjusting it to her current state. Musical practice improves our cognitive abilities The last factor that seems to have helped the development of music as such a complex cultural factor is its ability to influence other cognitive abilities. Like almost any skill that is learned, music training modifies the brain in its functions and structure. In addition, there is a solid basis that indicates that musical training has a positive influence on other domains such as spatial reasoning, mathematics or linguistics (Amodeo, 2014). Similar in other species Finally, it should be mentioned that animals such as belugas and many birds have followed similar evolutionary processes. Although the main function of song in many birds (and in some marine mammals) is to communicate states or to try to influence other animals (for example, in courtship through song or to mark territory), it seems that sometimes they sing only for fun. In addition, some birds keep an aesthetic sense and try to make compositions that, when analyzed musically, follow certain rules. In conclusion, since music seems to be something as natural as life itself, knowledge of it should be encouraged from childhood, despite the fact that it has unfortunately lost weight in the current educational system. It stimulates our senses, relaxes us, makes us vibrate and unites us as a species, so those who classify it as the greatest heritage that we have are not very far from reality. - Amodeo, MR (2014). Origin of Music as an Adaptive Trait in the Human. Argentine Journal of Behavioral Sciences, 6 (1), 49-59. - Cross, I. (2010). Music in culture and evolution. Epistemus, 1 (1), 9-19. - Fritz, T., Jentschke, S., Gosselin, N., Sammler, D., Peretz, I., Turner, R., Friederici, A. & Koelsch, S. (2009). Universal recognition of three basic emotions in music. Current biology, 19 (7), 573-576. - Mithen, SJ (2005). The singing Neanderthals: The origins of music, language, mind and body. Cambridge: Harvard University Press.

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How can I study effectively? The best way to find the most effective study method for you is to test various tips, such as the ones listed below. - Thwart the “Curve of Forgetting” - Use Active Recall. - Use the Leitner System. - Take the Practice Tests. - Make Connections. - Try the Feynman Notebook Method. - Take on the Role of Teacher. - Think About Your Thinking. How do you write aims and objectives? When writing your objectives try to use strong positive statements. Achievable – Don’t attempt too much – a less ambitious but completed objective is better than an over-ambitious one that you cannot possible achieve. Realistic – do you have the necessary resources to achieve the objective – time, money, skills, etc. What is an example of an objective question? Objective questions are those based in fact, where a respondent’s answer can be determined as right, wrong, true or false. An example of an objective question would be to ask where someone lives or what they bought from your store. What are general objectives in teaching? 2. specific than “aims” and are also more action oriented. This is to say that, while aims tend to describe a philosophy of education, objectives specify what is intended as observable and measurable, action- oriented statement of intention of an educational programme. What is a well written objective? A well-written learning objective outlines the knowledge, skills and/or attitude the learners will gain from the educational activity and does so in a measurable way. An effective learning objective should include the following 5 elements: who, will do, how much or how well, of what, by when. How should you study with your notes? How to write good study notes - Structure your notes by the syllabus dot points. - Include examples in your notes. - Write notes in your own words. - Write yourself exam tips as you go. - Visualise complicated information. - Always go over your notes and work on condensing them. What is a good objective? Objectives should be clear, well defined and unambiguous. Each objective should be focussed on one key outcome. Measurable: Objectives should be measurable so that you can demonstrate it has been achieved. What are the two main types of objective? Objectives are the specific measurable results of the initiative….There are three basic types of objectives. - Process objectives. These are the objectives that provide the groundwork or implementation necessary to achieve your other objectives. - Behavioral objectives. - Community-level outcome objectives. How can I get highest marks in exam? Student-to-student: Tips for scoring high on your exams - Know the test format. Don’t forget to ask your professor what you can expect for the layout of the exam. - Create a study schedule. - Utilize materials from the professor. - Eat breakfast. - Chew gum. - Get a good night’s sleep. - Manage your time. - Answer the questions you know first. What called objective test? From Wikipedia, the free encyclopedia. Objective tests are measures in which responses maximize objectivity, in the sense that response options are structured such that examinees have only a limited set of options (e.g. Likert scale, true or false). How do you write a study objective question? Answering MCQ exam questions - Know the rules: Read your instructions carefully. - Be precise: Most marks are lost in MCQ exams through the misreading of questions. - Read the entire question carefully, don’t just glance at the question and select the most logical answer. - Answer the easy questions. How do you start a research objective? Objectives can be general or specific….Writing your research objectives clearly helps to: - Define the focus of your study. - Clearly identify variables to be measured. - Indicate the various steps to be involved. - Establish the limits of the study. - Avoid collection of any data that is not strictly necessary. What is an example of an objective personality test? There are many different objective personality tests, but The Minnesota Multiphasic Personality Inventory (MMPI-2) and Myers-Briggs Type Indicator (MBTI) are two most common examples. The MMPI-2 and MBTI are made of multiple sections containing multiple questions. Each section examines a separate personality trait. What is the most important objective of education? Intellectual Achievement: To provide students with academic knowledge and skills in order to prepare them for post-secondary education or the workforce. This has been the most agreed upon aim of education. Most parents want their children to reach high standards in math, English, history, and science. What are the 3 parts of an objective? A well-constructed learning objective describes an intended learning outcome and contains three parts: 1) conditions under which the resulting behavior is to be performed, 2) an observable student behavior (such as a capability) that is attained, described in concrete terms, and 3) a criterion that shows how well the …

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Signup to receive updates from Gina Cascone & Bree Sheppard Activities for learning about our world and time! AROUND THE GLOBE Our planet is a beautiful sphere traveling through space on its yearlong journey around the sun. We have 5 oceans, 7 seas, 7 continents, and 196 countries, all vibrant with life. Over 7 billion people, speaking more than 6,500 different languages inhabit this world. We live in different time zones, with different climates, in different kinds of houses. We eat different meals and practice different traditions. We celebrate our differences, as one family, sharing one home…Earth. Traveling the world and learning about other cultures - Each country and its people have made wondrous contributions to the quality of life on this planet. Exploring other cultures helps our children understand the importance of our differences as well as the value of our universal similarities. - Using a globe or a map, find your own home first. Then mark off the places visited in this book. After learning about your community, travel along with the book, discovering all you can about each location and the remarkable and unique qualities they all have to offer. Compare each country’s way of life to life in your hometown. Spend some time at your local library or online, gathering information before you move on through the pages. And, of course, feel free to make other stops all around the world. AROUND THE CLOCK For thousands of years, human beings have been keeping track of time. It was important to know how many hours of daylight they had to hunt and gather food. Back in 1500 B.C., the first clocks were not run by batteries or electricity. Time was calculated by watching the movement of shadows created by the sun. The sundial is so accurate a tool that it was exclusively used until 1400 A.D. While they are rarely seen today, they are the model for our modern clocks. Making a Sundial (with directions from the National Wildlife Federation) - Poke a hole through the center of a paper plate. Write the number 12 on the edge of the plate. Using a ruler, draw a straight line from the number 12 to the hole. - Poke a straw through the hole and carefully slant it toward the line. - At noon on a sunny day, take the plate outside. On the ground, turn the plate so that the shadow of the straw falls along the line to the number 12. Fasten the plate to the ground so that it does not move. - One hour later, check the position of the shadow along the edge of the plate and write the number 1 on that spot. Continue each hour, predicting the position while checking and marking the actual position. This activity will help with observation, communication, and prediction skills while having fun learning to tell time the way our earliest ancestors.

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The increasing prevalence of obesity is happening not only in the United States but also worldwide. According to WHO data, the prevalence of obesity has doubled since 1980. Almost 65% of the world's population lives in countries where overweight and obesity kills more people than underweight. Today, obesity affects not only adults but also children; 15-20% of children and adolescents are obese in the United States. Obesity is a serious h ealth problem worldwide. The primary cause of obesity is an energy imbalance. When energy intake is more than energy expenditure, the excess energy could be stored as triacylglycerol in the adipocytes. This excess energy can increase the number and size of adipocytes, eventually expanding the adipose tissue. Adipose tissue can be deposited under the skin and in the intra-abdominal area. More and more research has shown that adipose tissue is an endocrine organ that can regulate the whole-body energy homeostasis through the secretion of various adipose-derived hormones or adipokines and affects the function of other organs, such as the brain, liver, pancreas, and skeletal muscle. Therefore, obesity plays a key role in metabolic syndromes and is highly related to diabetes, cardiovascular disease, and cancer. The National Institutes of Health has developed some strategic plans for obesity research, including the discovery of biological mechanisms regulated to energy balance; understanding of the correlates, determinants, and consequences of obesity; the design and testing of interventions to promote healthy weight; the dissemination and implementation of research; and improvements in measurement tools, technology, and methods. Their ultimate goal is to prevent and treat obesity efficiently. Recently, researchers have been more interested in the role of natural compounds such as epigallocatechin-3-gallate from green tea, raspberry ketones from raspberries, and synephrine from orange in regulating lipid metabolism to decrease adipogenesis in vivo or in vitro.Our proposed research is seeking novel compounds from fruits and vegetables which have anti-adipogenic and anti-obesity activity and study their mode of actions. |Effective start/end date||10/20/15 → 9/30/20| - National Institute of Food and Agriculture (National Institute of Food and Agriculture (NIFA)) Explore the research topics touched on by this project. These labels are generated based on the underlying awards/grants. Together they form a unique fingerprint.

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As of the 20th of May, 2019, a fundamental constant of the universe has redefined the kilogram. But do not fret, the average person will not see a change in their day-to-day lives; your food portions and scales will still be as they always were. Nonetheless, this is a huge leap for human advancement because, for the past 129 years, the kilogram has been defined by a physical hunk of platinum and iridium stored in one of the most secure locations in the world. “Le Grand K” as it is called, is held in Paris, with multiple other copies scattered throughout the world, and has been avoiding a unit altering scratch for too long now. The past years of waiting for the redefinition have been especially crucial, as the conditions for precision had to meet a certain level of quality to be deemed worthy of pursuing. The very clean and over simplified plan of action; use a constant (rather than an actual weight) to define mass. And so, scientists voted to use something called the Planck constant as a more precise measurement system. Seems pretty easy right, but what is the Planck constant? As Richard Brown, of the National Physical Laboratory (NPL) explains: “The Planck Constant is a physical constant which relates the energy carried by a photon, or light or electromagnetic radiation, and relates the energy of that to its frequency.” Despite its name, the value of the constant has been fluctuating ever so slightly over the last century. The idea of a changing constant should not settle well in the mind, and it has not in the science community. Thus, the Avogadro Project was created to rid the world of the troublesome oxymoron. The project aimed to redefine the avogadro constant, or the number of atoms in 12 grams of carbon-12, to a resolution less than 2*10^-8. The reason being that the avogadro constant has a direct relationship with Planck’s constant. The project spent millions of dollars to create the roundest ball of silicon-28 isotopes in the world, weighing in at one kilogram. In 2015, the project was able to define the new avogadro’s constant. The near atomic precision of the sphere allowed scientists to redefine the value to a much higher level of precision which, in turn, makes Planck’s constant more precise. We now know what Planck’s constant is, and that it is precise enough to use, but how can there be a relationship between the energy in a photon and mass? “The relationship is quite a complex one and I think in order to explain that we have to think about the experiment that’s being used to redefine the kilogram. And that experiment is something called the The Kibble Balance, named after Brian Kibble, who invented the experiment in the 1970s at NPL. The Kibble balance is an experiment which balances mechanical power, from a mass, with electrical power, from an electromagnetic. We calculate the electrical power from that electromagnet using quantum electrical effects, and those equations are governed by fundamental constants. One of which is the planck constant.” says Richard The final measurements produced a final value of h with an uncertainty of 10 parts per billion. Rearrange the equation for Planck’s constant and one is able to define a kilogram, a definition that can be understood by any intelligent, interstellar species. “One of the best analogies I’ve heard about the revision of the SI is it’s a bit like strengthening the foundations of your house; you don’t notice any difference immediately, but what it means is that your house will last a lot longer and you’re going to be able to do more things to it in the future.” That foundation is supporting human ingenuity, and we have now set one that is incredibly strong to fuel our future endeavors. “…(A)s technology advances and we see things like 5G communication, quantum computing, sensor networks, it’s the better measurements we can make with the revised SI that will make that technology be implemented all the faster.” .(tagsToTranslate)kilogram(t)redefining kilogram(t)Planck constant(t)Richard Brown(t)National Physical Laboratory This is a syndicated post. Read the original post at Source link .

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# 3.6: Basic Counting Rules Difficulty Level: At Grade Created by: CK-12 ## Learning Objectives • Understand the definition of random sampling. • Calculate ordered arrangements using factorials. • Calculate combinations and permutations. • Calculate probabilities with factorials. Inferential Statistics is a method of statistics that consists of drawing conclusions about a population based on information obtained from a subset or sample of the population. The main reason a sample of the population is only taken rather than the entire population (a census) is because it is less costly and it can be done more quickly than a census. In addition, because of the inability to actually reach everyone in a census, a sample can actually be more accurate than a census. Once a statistician decides that a sampling is appropriate, the next step is to decide how to select the sample. That is, what procedure should we use to select the sample from the population? The most important characteristic of any sample is that it must be a very good representation of the population. It would not make sense to use the average height of basketball players to make an inference about the average height of the entire US population. It would not be also reasonable to estimate the average income of the entire state of California by sampling the average income of the wealthy residents of Beverly Hills. Therefore, the goal of sampling is to obtain a representative sample. For now, we will only study one powerful way of taking a sample from a population. It is called random sampling. ## Random Sampling A random sampling is a procedure in which each sample of a given size is equally likely to be the one selected. Any sample that is obtained by random sampling is called a random sample. In other words, if \begin{align*}n\end{align*} elements are selected from a population in such a way that every set of \begin{align*}n\end{align*} elements in the population has an equal probability of being selected, then the \begin{align*}n\end{align*} elements form a random sample. Example: Suppose you randomly select \begin{align*}4\;\mathrm{cards}\end{align*} from an ordinary deck of \begin{align*}52\;\mathrm{cards}\end{align*} and all the cards selected are kings. Would you conclude that the deck is still an ordinary deck or do you conclude that the deck is not an ordinary one and probably contains more than \begin{align*}4\end{align*} kings? Solution: The answer depends on how the cards were drawn. It is possible that the \begin{align*}4\end{align*} kings were intentionally put on top of the deck and hence drawing \begin{align*}4\end{align*} kings is not unusual, it is actually certain. However, if the deck was shuffled well, getting \begin{align*}4\end{align*} kings is highly improbable. The point of this example is that if you want to select a random sample of \begin{align*}4\;\mathrm{cards}\end{align*} to draw an inference about a population, the \begin{align*}52\;\mathrm{cards}\end{align*} deck, it is important that you know how the sample was selected from the deck. Example: Suppose a lottery consists of \begin{align*}100\end{align*} tickets and one winning ticket is to be chosen. What would be a fair method of selecting a winning ticket? Solution: First we must require that each ticket has an equal chance of winning. That is, each ticket must have a probability of \begin{align*}1/100\end{align*} of being selected. One fair way of doing that is mixing all the tickets in a container and blindly picking one ticket. This is an example of random sampling. However, this method would not be too practical if we were dealing with a very large population, say a million tickets, and we were asked to select \begin{align*}5\end{align*} winning tickets. There are several standard procedures for obtaining random samples using a computer or a calculator. Sometimes experiments have so many simple events that it is impractical to list them. However, in some experiments we can develop a counting rule, with the use of tree diagrams that can aid us to do that. The following examples show how that is done. Example: Suppose there are six balls in a box. They are identical except in color. Two balls are red, three are blue, and one is yellow. We will draw one ball, record its color, and set it aside. Then we will draw another one, record its color. With the aid of a tree diagram, calculate the probability of each outcome of the experiment. Solution: We first draw a tree diagram to aid us see all the possible outcomes of this experiment. The tree diagram shows us the two stages of drawing two balls without replacing them back into the box. In the first stage, we pick a ball blindly. Since there are \begin{align*}2\end{align*} red, \begin{align*}3\end{align*} blue, and \begin{align*}1\end{align*} yellow, then the probability of getting a red is \begin{align*}2/6.\end{align*} The probability of getting a blue is \begin{align*}3/6\end{align*} and the probability of getting a yellow is \begin{align*}1/6.\end{align*} Remember that the probability associated with the second ball depends on the color of the first ball. Therefore, the two stages are not independent. To calculate the probabilities of getting the second ball, we look back at the tree diagram and observe the followings. There are eight possible outcomes for the experiment: RR: red on the \begin{align*}1^{st}\end{align*} and red on the \begin{align*}2^{nd}\end{align*} RB: red on the \begin{align*}1^{st}\end{align*} and blue on the \begin{align*}2^{st}\end{align*} And so on. Here are the rest, \begin{align*}RY, BR, BB, BY, YR, YB.\end{align*} Next, we want to calculate the probabilities of each outcome. \begin{align*}P(R\ 1^{st}\ \text{and}\ R\ 2^{st} ) & = P(RR) = 2/6 \cdot 1/5 = 2/30\\ P(R\ 1^{st}\ \text{and}\ B\ 2^{st} ) & = P(RB) = 2/6 \cdot 3/5 = 6/30\\ P(RY) & = 2/6 \cdot 1/5 = 2/30\\ P(BR) & = 3/6 \cdot 2/5 = 6/30\\ P(YB) & = 3/6 \cdot 2/5 = 6/30\\ P(YB) & = 3/6 \cdot 1/5 = 3/30\\ P(YB) & = 1/6 \cdot 2/5 = 2/30\\ P(YB) & = 1/6 \cdot 3/5 = 3/30\end{align*} Notice that all the probabilities must add up to \begin{align*}1\end{align*}, as they should. The method used to solve the example above can be generalized to any number of stages. This method is called the Multiplicative Rule of Counting. ## The Multiplicative Rule of Counting (I) If there are \begin{align*}n\end{align*} possible outcomes for event \begin{align*}A\end{align*} and \begin{align*}m\end{align*} possible outcomes for event \begin{align*}B\end{align*}, then there are a total of \begin{align*}nm\end{align*} possible outcomes for the series of events \begin{align*}A\end{align*} followed by \begin{align*}B\end{align*}. Another way of stating it: (II) You have \begin{align*}k\end{align*} sets of elements, \begin{align*}n_1\end{align*} in the first set, \begin{align*}n_2\end{align*} in the second set,..., and \begin{align*}n_k\end{align*} in the \begin{align*}k\end{align*}th set. Suppose you want to take one sample from each of the \begin{align*}k\end{align*} sets. The number of different samples that can be formed is the product \begin{align*}n_1 n_2 n_3 \ldots n_k\end{align*} Example: A restaurant offers a special dinner menu every day. There are three entrées to choose from, five appetizers, and four desserts. A costumer can only select one item from each category. How many different meals can be ordered from the special dinner menu? Solution: Let’s summarize what we have. Entrees:3 Appetizer: 5 Dessert: 4 We use the multiplicative rule above to calculate the number of different dinner meals that can be selected. We simply multiply all the number of choices per item together: \begin{align*}(3)(5)(4) = 60\end{align*} There are \begin{align*}60\end{align*} different dinners that can be ordered by the customers. Example: Here is a classic example. In how many different ways can you seat \begin{align*}8\end{align*} people at a dinner table? Solution: For the first seat, there are eight choices. For the second, there are seven remaining choices, since one person has already been seated. For the third seat, there are \begin{align*}6\end{align*} choices, since two people are already seated. By the time we get to the last seat, there is only one seat left. Therefore, using the multiplicative rule above, we get \begin{align*}(8)(7)(6)(5)(4)(3)(2)(1) = 40,320\end{align*} The multiplication pattern above appears so often in statistics that it has its own name and its own symbol. So we say “eight factorial,” and we write \begin{align*}8!\end{align*}. ## Factorial Notation \begin{align*}n! = n(n - 1)(n - 2) \ldots 1\end{align*} Example: Suppose there are \begin{align*}30\end{align*} candidates that are competing for three executive positions. How many different ways can you fill the three positions? Solution: This is a more difficult problem than the examples above and we will use the second version of the Multiplicative Rule of Counting. We need to analyze it in the following way: The executive positions can be denoted by \begin{align*}k = 3\end{align*} sets of elements that correspond to \begin{align*}n_1 =\end{align*} The number of candidates that are available to fill the first position \begin{align*}n_2 =\end{align*} The number of candidates remaining to fill the second position \begin{align*}n_3 =\end{align*} The number of candidates remaining to fill the third position Hence, \begin{align*} n_1 = 30\\ n_2 = 29\\ n_3 = 28\end{align*} The number of different ways to fill the three positions is \begin{align*}n_1 n_2 n_3 = (30)(29)(28) = 24,360\ \text{possible positions.}\end{align*} The arrangement of elements in distinct order, as the example above shows, is called the permutation. Thus, from the example above there are \begin{align*}24,360\end{align*} possible permutations of three positions drawn from a set of \begin{align*}30\end{align*} elements. ## Counting Rule for Permutations The number of ways to arrange in order \begin{align*}n\end{align*} different objects within \begin{align*}r\end{align*} positions is \begin{align*}P^n_r = \frac{n!} {(n- r)!}\end{align*} Example: Let’s go back to the previous example but this time we want to compute the number of ordered seating arrangements we have for \begin{align*}8\end{align*} people for only \begin{align*}5\end{align*} seats. Solution: In this case, we are considering a total of \begin{align*}n = 8\end{align*} people and we wish to arrange \begin{align*}r = 5\end{align*} of these people to be seated. Substituting into the permutation equation, \begin{align*}P^n_r & = \frac{n!} {(n - r)!} = \frac{8!} {(8 -5)!} \\ & = \frac{8!} {3!} \\ & = \frac{40,320} {6} \\ & =6720\end{align*} Another way of solving this problem is to use the Multiplicative Rule of Counting, Since there are only \begin{align*}5\end{align*} seats available for \begin{align*}8\end{align*} people, then for the first seat, there are eight people. For the second seat, there are seven remaining people, since one person has already been seated. For the third seat, there are \begin{align*}6\end{align*} people, since two people are already seated. For the fifth seat, there are \begin{align*}4\end{align*} people. After that we run out of seats. Thus \begin{align*}(8)(7)(6)(5)(4) = 6720.\end{align*} Of course, the permutation rule is more powerful since it has the advantage of using the factorial. Most scientific calculators can do factorials permutations, so make sure to know how to do them on your calculator. Example: The board of directors at The Orion Foundation has \begin{align*}13\end{align*} members. Three officers will be elected from the \begin{align*}13\end{align*} members to hold the positions of a provost, a general director and a treasure. How many different slates of three candidates are there, if each candidate must specify which office he or she wishes to run for? Solution: Each slate is a list of one person for each of three positions, the provost, the general director and the treasure. If, for example, Mr. Smith, Mr. Hale, and Ms. Osborn wish to be on a slate together, there are several different slates possible, depending on which one will run for provost, general director and treasurer. So we are not just asking for the number of different groups of three names on a slate but we are also asking for a specific order, since it makes a difference which name is listed in which position. So, \begin{align*}n = 13\\ r = 3 \end{align*} Using the permutation formula, \begin{align*}P^n_r = \frac{n!} {(n - r)!} = \frac{13!} {(13 - 3)!} = 1716\end{align*} There are \begin{align*}1716\end{align*} different slates of officers. Notice that in our previous examples, the order of people or objects was taken into account. What if the order is not important? For example, in the previous example for electing three officers, what if we wish to choose \begin{align*}3\end{align*} members of the \begin{align*}13-\end{align*}member board to attend a convention. Here, we are more interested in the group of three but we are not interested in their order. In other words, we are only concerned with different combinations of \begin{align*}13\end{align*} people taken \begin{align*}3\end{align*} at a time. The permutation rule will not work here since order is not important. We have a new formula that will compute different combinations. ## Counting Rule for Combinations The number of combinations of \begin{align*}n\end{align*} objects taken \begin{align*}r\end{align*} at a time is \begin{align*}C^n_r = \frac{n!} {r!(n - r)!}\end{align*} It is important to notice the difference between permutations and combinations. When we consider grouping and order, we use permutations. But when we consider grouping with no particular order, we use combinations. Example: Back to our example above. How many different groups of three are there, taken out of \begin{align*}13\end{align*} people? Solution: As explained in the previous paragraph, we are interested in combinations rather than permutations of \begin{align*}13\end{align*} people taken \begin{align*}3\end{align*} at a time. We use the combination formula \begin{align*}C^n_r & = \frac{n!} {r!(n - r)!} \\ C^{13}_3 & = \frac{13!} {3!(13 - 3)!} = \frac{13!} {3!10!} = 286\end{align*} There are \begin{align*}286\end{align*} different groups of \begin{align*}3\end{align*} to go to the convention. In the above computation you can see that the difference between the formulas for \begin{align*}nCr\end{align*} and \begin{align*}nPr\end{align*} is in the factor \begin{align*}r!\end{align*} in the denominator of the fraction. Since \begin{align*}r!\end{align*} is the number of different orders of \begin{align*}r\end{align*} things, and combinations ignore order, then we divide by the number of different orders. Example: You are taking a philosophy course that requires you to read \begin{align*}5\end{align*} books out of a list of \begin{align*}10\end{align*} books. You are free to select any five books and read them in whichever order that pleases you. How many different combinations of \begin{align*}5\end{align*} books are available from a list of \begin{align*}10\end{align*}? Solution: Since considerations of order in which the books are selected are not important, we compute the number of combinations of \begin{align*}10\end{align*} books taken \begin{align*}5\end{align*} at a time. We use the combination formula \begin{align*}C^n_r & = \frac{n!} {r!(n - r)!}\\ C^{10}_5 & = \frac{10!} {5!(10 - 5)!} = 256\end{align*} There are \begin{align*}252\end{align*} different groups of \begin{align*}5\end{align*} books that can be selected from a list of \begin{align*}10\end{align*} books. ## Technology Note The TI-83/84 calculators and the EXCEL spreadsheet have commands for factorials, permutations, and combinations. Using the TI-83/84 Calculators Press [MATH] and then choose PRB (Probability). You will see the following choices, among others: \begin{align*}nPr, nCr,\end{align*} and ! The screens show the menu and the proper uses of these commands. Using EXCEL In Excel the above commands are entered as follows: • \begin{align*}=\end{align*} PERMUT (10,2) • \begin{align*}=\end{align*} COMBIN (10,2) • \begin{align*}=\end{align*} FACT (10) ## Lesson Summary 1. Inferential Statistics is a method of statistics that consists of drawing conclusions about a population based on information obtained from a subset or sample of the population. 2. A random sampling is a procedure in which each sample of a given size is equally likely to be the one selected. 3. The Multiplicative Rule of Counting states: if there are \begin{align*}n\end{align*} possible outcomes for event \begin{align*}A\end{align*} and \begin{align*}m\end{align*} possible outcomes for event \begin{align*}B\end{align*}, then there are a total of \begin{align*}nm\end{align*} possible outcomes for the series of events \begin{align*}A\end{align*} followed by \begin{align*}B\end{align*}. 4. The factorial, ' ! ', means \begin{align*}n! = n(n - 1)(n - 2) \ldots 1.\end{align*} 5. The number of permutations (ordered arrangements) of \begin{align*}n\end{align*} different objects within \begin{align*}r\end{align*} positions is \begin{align*}P^n_r = \frac{n!} {(n r)!} \end{align*} 6. The number of combinations (unordered arrangements) of \begin{align*}n\end{align*} objects taken \begin{align*}r\end{align*} at a time is \begin{align*}C^n_r = \frac{n!} {r!(n - r)!}\end{align*} ## Review Questions 1. Determine the number of simple events when you toss a coin the following number of times: (Hint: as the numbers get higher, you will need to develop a systematic method of counting all the outcomes) 1. Twice 2. Three times 3. Five times 4. Look for a pattern in the results of a) through c) and try to figure out the number of outcomes for tossing a coin \begin{align*}n\end{align*} times. 2. Flying into Los Angeles from Washington DC, you can choose one of three airlines and can choose either first class or economy. How many travel options do you have? 3. How many different \begin{align*}5-\end{align*}card hands can be chosen from a \begin{align*}52-\end{align*}card deck? 4. Suppose an automobile license plate is designed to show a letter of the English alphabet, followed by a five-digit number. How many different license plates can be issued? 1. \begin{align*}4\end{align*} 2. \begin{align*}8\end{align*} 3. \begin{align*}32\end{align*} 4. \begin{align*}2^n\end{align*} 1. \begin{align*}6\end{align*} 2. \begin{align*}2,598,960\end{align*} 3. \begin{align*}2,600,000\end{align*} ### Notes/Highlights Having trouble? Report an issue. Color Highlighted Text Notes Show Hide Details Description Tags: Subjects:

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Girls of the past — and, tragically, in the present — hear it all the time. Because of their gender, they just can’t do math. And if they can, well, they will never be as good as the boys. To put it very kindly, this attitude is not accurate, nor is it healthy. Negative stereotypes perpetuate a dreadful cycle. When bombarded with messages of their own (allegedly genetic, realistically false) failings, girls internalize them. Thus discouraged, they ultimately do not perform to the fullest extent of their intellectual capabilities. Which then gives teachers, parents, and other authority figures “proof” that they should not expect much of their female math students. That this attitude persists may directly correlate with the sluggish and troubled growth of female students majoring in mathematics. In reality, girls’ talents and capacity for academic achievement are no different than boys’. Studies prove that they perform equally well when receiving the exact same praise and support as their male counterparts. Destroy the stereotypes, and we’ll raise the numbers and status of women in mathematics. And equitable exposure and education remains the greatest strategy for improving this traditionally marginalized demographic’s profile. Some Notable Trailblazers It would be a fallacy to say that women mathematicians today benefit from the passionate efforts and contributions from their predecessors. They do, of course, but that declaration only peers into one facet of these great thinkers’ successes. The truth is, everyone owes a debt of gratitude to pioneering women in the mathematics. Devoting themselves to the discipline, even if they faced (or continue facing) discrimination and dismissal, can inspire anyone of any gender and career path. Their research has also propelled mathematics forward, which in turn, has propelled humanity forward. So while the following trailblazers did help diversify mathematics and open up new opportunities for their successors, it is important to recognize that their influence stretches well beyond fostering gender equality. Hypatia of Alexandria (D. 415 CE) probably wasn’t the first female mathematician; she is acknowledged as the first known one. The daughter of legendary thinker Theon, Hypatia studied mathematics and Neoplatonist philosophy under her father’s guidance, eventually acquiring astronomy, philosophy, and mathematics students of her very own. Most of her contributions to the mathematics involved furthering Appolonius’ conic sections. As the editor of On the Conics of Appolonius, Hypatia helped bring parabolas, ellipses, and hyperbolas into mainstream study. She simplified the concepts in order to make them more accessible to her students and readers, thereby spreading knowledge mathematicians now consider standard today. Historians recognize Elena Lucrezia Cornaro Piscopia (1646-1684) as the first woman to ever receive a college degree — and a doctorate at that. She excelled at music, philosophy, astronomy, theology, languages and, of course, mathematics. While known primarily as an interdisciplinary prodigy, Piscopia’s most groundbreaking accomplishment opened up new opportunities for not only women in mathematics, but academia in general. Some accounts state she enjoyed a lectureship at University of Padua starting in 1678. Because her prodigious intellect earned her accolades and respect from scholars across Europe, Piscopia almost singlehandedly busted up the myth that women contribute nothing to the academic world. Much of Marie Crous‘ personal life , including her date of birth and death , is unknown, though her mathematical influence continues significantly impacting daily life. She did not invent the decimal point, but she created its current form separating the different parts of a number. In addition, she also innovated and popularized the concept of using zeroes to indicate a blank decimal place. These seventeenth century constructions survive and thrive today, most notably as the basis for the metric system and some currencies. Inspired by her confidant and possible lover Voltaire, Emilie du Chatelet (1706-1749) pursued a life of physics and mathematics not even marriage and motherhood could curtail. Institutions du physique, published in 1740, was originally intended as a textbook for her son’s mathematics and physics lessons; it eventually wound up considered her masterpiece. The book blended the research of her contemporary Willem ‘s Gravesande with that of Gottfried Leibniz to note that a moving object’s energy is proportionate to the square of its velocity, rather than just the velocity. Chatelet also translated Isaac Newton’s Principia Mathematica into French, adding her own notes and corrections. Today, francophone mathematicians still consider her work the definitive French-language version of the hugely influential text. The prolific Maria Gaetana Agnesi (1718-1799) produced multiple volumes of mathematical significance in her lifetime, and received a groundbreaking offer to serve as the Chair of Mathematics at University of Bologna. Nobody knows if she ultimately accepted Pope Benedict XIV’s great honor, though the brilliant academic did serve in a readership role at the school. She gave the witch of Agnesi its name in her seminal Instituzioni analitiche ad uso della gioventu italiana. Some consider this the very first book ever published covering two different styles of calculus, integral and differential. When the two volumes first hit academia, her fellow mathematicians celebrated her writing and often used her references as textbooks. This led to an invitation to join the Bologna Academy of Sciences. Sophie Germain (1776-1831) dabbled in multiple mathematical disciplines (and even the social sciences), but is best known as one of the masterminds behind elasticity theory , which just happened to earn her a prestigious prize from the Paris Academy of Sciences. Because women were unable to receive much of an education at the time, she corresponded with mentors (most notably the renowned Carl Friedrich Gauss and Adrien-Marie Legendre) via letter instead. However, she hid behind a masculine nom de plume because she feared stigmatization from the scientific community. Number theory eventually proved her strongest subject. Germain’s most triumphant moment came when she proposed several different approaches to Fermat’s Last Theorem; one of these is now known as Sophie Germain’s Theorem. The Academy of Sciences’ Sophie Germain Prize annually honors the most innovative minds in fundamental mathematics. Modern computer science exists because of Ada Byron, Countess of Lovelace (1815-1852). She wrote what historians and technicians consider the very first computer program for Charles Babbage’s analytical engine. It consisted of an algorithm calculating Bernoulli numbers, though remains untested even now. Because she almost singlehandedly established an entirely new scientific discipline, Byron (more popularly known as Ada Lovelace) enjoys considerably more praise and attention from contemporary audiences than any other female mathematician. The Ada Initiative promotes women furthering the cause of open source software. The United States Department of Defense developed a programming language named “Ada.” Ada Lovelace Day is a nascent holiday celebrated in mid-October drawing attention to successful women in the STEM fields. Mathematician and astronomer Mary Somerville (1780-1872) calculated the probability of a planet whose orbit disturbs Uranus’ in the sixth edition of On the Connexion of the Physical Sciences, published in 1842. Thanks to her mathematical speculations, John Couch Adams discovered Neptune. Even before that, however, 1835 saw her and Caroline Herschel sharing the historical honor of being the first women named to the Royal Astronomical Society. Somerville’s translation of Mecanique Celeste by Pierre-Simon Laplace absolutely thrilled English-speaking scientists. They appreciated how concrete and easy-to-understand she presented the material. The succinct and simple writing style she employed led Somerville to receive The Royal Geographic Society’s first Victoria Medal for making complex science more accessible. Although Sonia Kovalevsky (or Kovalevskaya) (1850-1891) was not the first woman to edit a scientific journal, her work with Acta Mathematica set her among the most significant. She also holds the honor of being the first woman in the Russian Academy of Sciences and the first European woman to earn a Ph.D. in mathematics. A calculus whiz, one of her most notable contributions to mathematics is the Kovalevskaya top. Only Joseph Louis Lagrange and Leonard Euler had devised a fully integrable system for rigid body motion. This distinguished discovery, which furthered the study and application of classical mechanics, earned her the French Academy of Science’s prestigious Prix Bordin in 1888. The name Florence Nightingale (1820-1910) conjures up images of nurses, but she accomplished much more than advancing medical science. She also happened to be quite the crackerjack statistician. Although she did not create data visualizations such as graphs and pie charts, Nightingale adopted them very early. Incorporating statistical graphics into her discussions of sanitation reform and other healthcare topics helped popularize the medium; today, they remain crisp, clean, and clear options for anyone trying to relay statistical research. Nightingale herself even created her own style of pie chart, known as the polar area diagram. No less than Albert Einstein himself considered Amalie Emmy Noether (1882-1935) an inspiration. In a 1935 piece for The New York Times, he referred to her as “the most creative mathematical genius thus far produced since the higher education of women began.” Her early work, especially the landmark paper Idealtheorie in Ringbereichen, eventually birthed the term “Noetherian ring” and provided an abstract algebra foundation used in theoretical physics. As a topologist, she focused her prolific output on non-communicative algebra, rings, linear transformations, and invariants while also delving into physics. She did not found the practice of algebraic topology, but her research , especially regarding homology groups , constructed the foundation. In terms of historical impact, however, her Noether’s Theorem is now considered one of the most essential cornerstones of theoretical physics. Mary Cartwright (1900-1998) claimed many firsts throughout her prestigious career — first female mathematician elected as a fellow at The Royal Society, first woman to win the Sylvester Medal, and the first woman to serve as the President of the London Mathematical Society and as a councilmember of The Royal Society. Collaborations with John Edensor Littlewood yielded major inquiries into chaos and its relationship with differential equations. While they did not establish chaos theory (more commonly known as “the butterfly effect”), their work refined and better defined it. Cartwright’s theorem is probably her best-known contribution to analytic functions. Ada Byron was the world’s first computer scientist, and Grace Hopper (1906-1992) followed her illustrious influence as one of the world’s first computer engineers. She contributed heavily to the development of COBOL, the first programming language independent of any particular machine, and programmed the Harvard Mark I while serving in the US Navy during World War II. COBOL was not her only creation; Hopper also developed FLOW-MATIC, MATH-MATIC, and ARITH-MATIC under UNIVAC, but COBOL remains her most continuously popular innovation since its 1959 inception. The widely-used term “debugging” also hails from an incident where a moth trapped in a computer disrupted her calculations. For nearly three decades, Julia Robinson (1919-1985) and her team of mathematicians , Yuri Matiyasevich, Martin Davis, and Hilary Putnam , wrestled against the notorious Hilbert’s tenth problem. They ultimately concluded that no algorithm could resolve the Diophantine equation. For most of her career, Robinson exclusively focused on decision problems. But she dabbled in game theory, even solving a problem worth $200 at RAND. The United States National Academy of Sciences elected her the very first female mathematician member in 1975, and she broke further ground in 1983 when she was elected the first woman president of the American Mathematical Society. Resources for Women in Mathematics Although women remain underrepresented in the mathematics and related industries, they do not waiver when supporting one another. They form organizations and initiatives to network, provide opportunities, celebrate the most notable names, and encourage more women to reject stereotypes and embrace number nerdery. The Association for Women in Mathematics (AWM) remains one of the cornerstones furthering the eponymous cause. It hosts a plethora of events, lectures, awards, scholarships, and seminars uniting participants and nurturing a love of all things mathematical. Members also mobilize on college campuses and participate in educational advocacy programs. Above all, they seek to increase representation and appreciation of women mathematicians. For any female professionals and students — or aspiring students — this organization serves as an essential gathering place for mentorships, advice, and sharing new opportunities for personal, professional, and societal growth. For women currently enrolled in a mathematics undergraduate or graduate program, The Institute for Advance Study, National Science Foundation, and Princeton University offer an 11-day mentorship program. Qualified applicants receive opportunities to meet with industry professionals, academics, and their fellow students through seminars, roundtables, panels, and lectures. Emphasis lay on mentoring up-and-coming women in mathematics. Discussions also center around resolving issues of underrepresentation and attracting more female students to the profession. Women in Mathematics Education largely reaches out to girls in kindergarten through high school. However, they do provide plenty of opportunities for female mathematics educators to learn and grow as well. Members organize events and trade ideas on how to best address classroom stereotypes and make more female students enthusiastic about math. Undergraduate and graduate students are encouraged to contact WME to open their own campus chapters. Doing so helps them best address any unique needs local learners have , not to mention gaining valuable resume fodder. Perhaps unsurprisingly, Ada Byron inspired many a mathematically-inclined undertaking celebrating women in mathematics. The Ada Initiative does not exclusively cater to female open source professionals, though it was founded by two women pursuing equal standing in a male-dominated industry. Every October, Ada Lovelace Day is celebrated in cities around the world. Organize put together fun and educational local events lauding the accomplishments of female mathematicians and scientists as well as teaching young girls to pursue the STEM disciplines. Reading up on the lives of influential and inspiring female mathematicians can kick-start motivation and creativity. Both Agnes Scott University and University of Oregon produce and collect biographies of groundbreaking women in mathematics. Getting lost in their archives makes for a lovely educational treat for fans of both math and history. Prizes, Awards, and Honors Watching women mathematicians receive accolades for their achievements inspires others to press forward with their studies, no matter their age, level of schooling, or their gender. Anyone can watch these accomplished academics accept validation and recognition and hope to emulate their example. The highest achievements women may earn in mathematics are the very same ones men do well. No Nobel Prize in Mathematics exists, but the International Mathematical Union’s International Medal for Outstanding Discoveries in Mathematics (better known as the Fields Medal) and the Norwegian Academy of Science and Letters’ Abel Prize are often cited as the equivalents. Unfortunately, just because women are eligible does not mean any have won. Mathematics’ upper echelons cower behind a thick barricade begging to be smashed open. American Mathematical Society devotes numerous prizes to the development of mathematics, one of which exclusively recognizes women; the others are, of course, open to qualified individuals of all genders and gender identities. The Ruth Lyttle Satter Prize in Mathematics rewards $5000 every two years, celebrating the contributions of one female mathematician. Eligible research must have been released within the past six years. Obviously, AWM provides the most awards and honors furthering the cause of women in mathematics. With four grants, three distinguished lectures, and six prizes and awards available, female mathematicians do not want for peer recognition. The Ruth I. Michler Memorial Prize bestows upon the recipient $47,000 and a coveted semester-long fellowship at Cornell University, making it one of the most prestigious mathematical honors unavailable to men. Other awards honor educational achievements, mentorships, and promising undergraduate students. There’s even an essay contest for inspiring middle school, high school, and college girls to keep with their mathematics lessons. With any luck, they’ll continue nursing a passion for the subject. With the decline in women majoring in mathematics, the demographic’s future may appear to be in danger. But “danger” does not necessarily indicate “disaster.” So many professors and professionals devote themselves to the cause that there is no real danger of the female mathematician species going extinct. Programs like the Carnegie Science Center’s Girls, Math and Science Partnership (GMSP), Girls Inc.’s Operation Smart, and numerous camps target the pre-college crowd. All of them provide nurturing environments, activities, and mentorships conducive to mathematical exploration. They actively combat the negative stereotypes about women in math. Encouraging girls to succeed at an early age rather than ramming them into rigid dictates builds the confidence and drive to follow their passions. Rather than stepping into a male-dominated industry, deeming it a lost cause, and switching over to something more “feminine,” participating kids learn how to stand up and stay put. Colleges themselves also serve as valuable staging grounds in the fight for equal representation of women in math-related fields. Many campuses , such as Carleton College, Massachusetts Institute of Technology, and George Washington University, among others , offer resources, throw events, and organize mentorships specifically for math-loving ladies. Smith College’s renowned Center for Women in Mathematics is often cited as the most attentive, progressive, and inspiring program of the type. Female students majoring in math should check if their schools already have outreach available. If not, they might want to organize their own show of solidarity. Doing so will keep them and their peers focused on their studies, and maybe even encourage more women to embrace mathematics and revolutionize the practice. And, maybe someday, even win a Fields Medal and an Abel Prize.

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Constructivism is a philosophical viewpoint about the nature of knowledge. Specifically Papert, inspired by constructivist and experiential learning ideas of Piaget. .. Some parents and mathematicians protested the design of textbooks that omitted or de-emphasized instruction of standard mathematical methods. What is the difference between Piaget’s constructivism and Papert’s ” constructionism”? Beyond the El constructivismo y el construccionismo. PDF | Seymour Papert’s vision for early childhood education involves using Logo, a child-friendly computer Data were taken for 2 years in a kindergarten. |Published (Last):||2 July 2005| |PDF File Size:||1.94 Mb| |ePub File Size:||19.1 Mb| |Price:||Free* [*Free Regsitration Required]| The teacher acts as little as possible. It is argued that constructivist theories are misleading or contradict known findings. Jonassen also suggested that novices be taught with “well-structured” learning environments. A further dd of the role of the facilitator in the social constructivist viewpoint, is that the instructor and construvtivismo learners are equally involved in learning from each other as well. Logo is the best known of them. Research and theory insights about instruction for complex learning. The math wars controversy in the United States construcrivismo an example pappert the type of heated debate that sometimes follows the implementation constuctivismo constructivist-inspired curricula in schools. Jong Suk Kim found that using constructivist teaching methods for 6th graders resulted in better student achievement than traditional teaching methods. Journal constructviismo Educational Psychology. Constructivism has also informed the design of interactive machine learning systems. Accommodation can be understood as the mechanism by which failure leads to learning: Constructivism does not refer to a specific pedagogyalthough it is often confused with constructionisman educational theory developed by Seymour Papertinspired by constructivist and experiential learning ideas of Piaget. This is also named after cnstructivismo Harkness table and involves students seated in a circle, motivating and controlling their own discussion. In their initial test of student performance immediately following the lessons, they found no significant difference between traditional and constructivist methods. Learn how and when to remove these template messages. Current trends in higher education push for more “active learning” teaching approaches which are often based on constructivist views. Inhe began a long and productive collaboration with the LEGO company, one of the first and largest corporate sponsors of the Media Lab. Wikipedia articles needing page number citations from January Articles with incomplete citations from January All articles with incomplete citations Articles with incomplete citations from February Wikipedia articles needing page number citations from February Articles with incomplete citations from March Articles with too few wikilinks from January All articles with too few wikilinks Articles covered by WikiProject Wikify from January All articles covered by WikiProject Wikify Wikipedia articles with style issues from January All articles with style issues Articles with multiple constructivism issues All articles with unsourced statements Articles with unsourced statements from October Articles with unsourced statements from November This continuum of faded guidance has been tested empirically to produce a series of learning effects: Not only is unguided instruction normally less effective; there cnostructivismo also evidence that it may have negative results when students acquire misconceptions or incomplete or disorganized knowledge. Professor Emeritus Seymour Papert, pioneer of constructionist learning, dies at 88 construvtivismo These languages have been dynamically typedand reflective. The primary differentiation from the traditional approach being that the engagement of the students in dde learning makes them more receptive to learning things at an appropriate time, rather than on a preset schedule. See the preceding two sections of this article. Constructivism and the Technology of Instruction: January Learn how and when to remove this template message. Thus, assessment and learning are seen as inextricably linked and not separate processes. Please help improve it by rewriting it in an encyclopedic style. Professor Emeritus Seymour Papert, pioneer of constructionist learning, dies at 88 | MIT News The Journal of Experimental Education. Where the sequencing of subject matter is concerned, it is the constructivist viewpoint that the foundations of any subject may be taught to anybody at any stage in some form. However, constructivism is often associated with pedagogic approaches that promote active learningor learning by doing. In so constructivis,o as there is any evidence from controlled studies, it almost uniformly supports direct, strong instructional guidance rather constructivist-based minimal guidance during the instruction of novice to intermediate learners. Students Solving Authentic Corporate Problems”. A Belated review of the “Constructivist Bible ” “. The concept of constructivism has influenced a number of disciplines, including psychologysociologyeducation and the history of science. Learners look for meaning and will try to find regularity and order in the events of the world even in the absence of full or complete information. Inwhile in Vietnam for a conference constructivusmo mathematics education, he suffered a serious brain injury when struck by a motor scooter construtcivismo Hanoi. Holt and Willard-Holt emphasize the concept of dynamic assessment, which is a way of assessing the true potential of learners that differs significantly from conventional tests. The emphasis thus turns away from the instructor and the content, and towards the learner. Library resources about Constructivism philosophy of education. Cognitive load theory was applied in several contexts. Learners compare their version of the truth with that of the instructor and fellow learners to get to a new, socially tested version of truth Kukla constructiismo Other constructivist scholars agree with this and emphasize that individuals make meanings through the interactions with each other and with the environment they live in. Then it awakens and rouses to life an entire set of functions in the stage of maturing, which lie in the zone of proximal development. In the late s, at a time when computers still cost hundreds of thousands of dollars, Papert came up with the idea for Logothe first programming language for children. Implications and applications to education. Cognitive Psychology and Instruction 3rd ed.

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## Number syetem tricks by5 Division rule by 5 A last digit of a number must be 0 or 5 then the whole number must be devided Ex:- 81637985÷5 Ans) 5÷5=1 So 81637985 must be devided by 5 Practice 1)26562970 2)6441875 3)816572980 You probably already know what a number system is - ever hear of binary numbers or hexadecimal numbers? Simply put, a number system is a way to represent numbers. We are used to using the base-10 number system, which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary). Before we get started, let's try a little activity for fun. There are many different ways to represent a color, but one of the most common is the RGB color model. Using this model, every color is made up of a combination of different amounts of red, green, and blue. You may be wondering how colors relate to number systems. In short, on a computer, any color is stored as a large number: a combination of red, green, and blue. (We'll go into more detail on this later.) Because it's just a number, it can be represented in multiple ways using different number systems. Your job is to guess how much red, green, and blue is in the background color of the activity below. The values for red, green, and blue can range from 0 to 255. Feel free to use the various hints provided to help you out. If you don't understand the numerical hints yet, no problem! You can see what your guess looks like using the View Guess button. Right now, it may seem tricky, but hopefully by the end of the article, it will seem easy. ## Number systems tricks Division rule by 8 2^3=8 Soif the last three numbers is devided by 8 then the whole number is devisible by 8 Ex:- 2825832 Ans) 832÷8 =104 So 2825832 is devisible by 8 Practice questions 1)7447875 2)8275277 3)8167288 4)9277385 For more subscribe You probably already know what a number system is - ever hear of binary numbers or hexadecimal numbers? Simply put, a number system is a way to represent numbers. We are used to using the base-10 number system, which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary). Before we get started, let's try a little activity for fun. There are many different ways to represent a color, but one of the most common is the RGB color model. Using this model, every color is made up of a combination of different amounts of red, green, and blue. You may be wondering how colors relate to number systems. In short, on a computer, any color is stored as a large number: a combination of red, green, and blue. (We'll go into more detail on this later.) Because it's just a number, it can be represented in multiple ways using different number systems. Your job is to guess how much red, green, and blue is in the background color of the activity below. The values for red, green, and blue can range from 0 to 255. Feel free to use the various hints provided to help you out. If you don't understand the numerical hints yet, no problem! You can see what your guess looks like using the View Guess button. Right now, it may seem tricky, but hopefully by the end of the article, it will seem easy. ## Number system tricks 2017 You probably already know what a number system is - ever hear of binary numbers or hexadecimal numbers? Simply put, a number system is a way to represent numbers. We are used to using the base-10 number system, which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary). Before we get started, let's try a little activity for fun. There are many different ways to represent a color, but one of the most common is the RGB color model. Using this model, every color is made up of a combination of different amounts of red, green, and blue. You may be wondering how colors relate to number systems. In short, on a computer, any color is stored as a large number: a combination of red, green, and blue. (We'll go into more detail on this later.) Because it's just a number, it can be represented in multiple ways using different number systems. Your job is to guess how much red, green, and blue is in the background color of the activity below. The values for red, green, and blue can range from 0 to 255. Feel free to use the various hints provided to help you out. If you don't understand the numerical hints yet, no problem! You can see what your guess looks like using the View Guess button. Right now, it may seem tricky, but hopefully by the end of the article, it will seem easy. Divisability by 4 2^2=4 So if the last two digits is devisible by4 then the whole number will be devisible by 4 Ex:- 1736636÷4 Ans)(36÷4)=9 So 1736636 will be devisible by 4 Q)try these 1)2764782 2)7355618 3)7365517 4)8266171 5)72755177 For more comment pls ## Number system tricks for solving fast You probably already know what a number system is - ever hear of binary numbers or hexadecimal numbers? Simply put, a number system is a way to represent numbers. We are used to using the base-10 number system, which is also called decimal. Other common number systems include base-16 (hexadecimal), base-8 (octal), and base-2 (binary). Before we get started, let's try a little activity for fun. There are many different ways to represent a color, but one of the most common is the RGB color model. Using this model, every color is made up of a combination of different amounts of red, green, and blue. You may be wondering how colors relate to number systems. In short, on a computer, any color is stored as a large number: a combination of red, green, and blue. (We'll go into more detail on this later.) Because it's just a number, it can be represented in multiple ways using different number systems. Your job is to guess how much red, green, and blue is in the background color of the activity below. The values for red, green, and blue can range from 0 to 255. Feel free to use the various hints provided to help you out. If you don't understand the numerical hints yet, no problem! You can see what your guess looks like using the View Guess button. Right now, it may seem tricky, but hopefully by the end of the article, it will seem easy. Number system Division rule by 2 2^1=2 Soif  the first digit of the number devisible by 2 then the total number will be divided Ex:- 165794÷2 Ans) 4÷2=2 So 165794 will be divisable by 2 Qu) 1) 18734898 2)6482528 3)88597674 4)93772 Comment ans ## Cute photos Central Bank of India Recruitment 2017 – Faculty Posts: Central Bank of India Samajik Utthan Avam Prashikshan Sansthan (CBI-SUAPS) has published notification for the recruitment of vacancies Faculty for RSETIs (Rural Self Employment Training Institutes) Kota on contract basis for the Year 2017-18. Eligible candidates may apply in prescribed application format on or before 10-06-2017. Other details like age limit, educational qualification, selection process & how to apply are given below…. Central Bank of India Vacancy Details: Name of the Post: Faculty Age Limit: Candidates age limit should be less than 65 years. Educational Qualification: Candidates should possess Post Graduation viz. 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The Battle of Saratoga was the turning point of the Revolutionary War. The scope of the victory is made clear by a few key facts: On October 17, 1777, 5,895 British and Hessian troops surrendered their arms. General John Burgoyne had lost 86 percent of his expeditionary force that had triumphantly marched into New York from Canada in the early summer of 1777. The divide-and-conquer strategy that Burgoyne presented to British ministers in London was to invade America from Canada by advancing down the Hudson Valley to Albany. There, he would be joined by other British troops under the command of Sir William Howe. Howe would be bringing his troops north from New Jersey and New York City. Burgoyne believed that this bold stroke would not only isolate New England from the other American colonies, but achieve command of the Hudson River and demoralize Americans and their would-be allies, such as the French. In June 1777, Burgoyne's army of over 7,000 men (half of whom were British troops and the other half Hessian troops from Brunswick and Hesse-Hanau) departed from St. Johns on Lake Champlain, bound for Fort Ticonderoga, at the southern end of the lake. As the army proceeded southward, Burgoyne drafted and had his men distribute a proclamation that, among other things, included the statement "I have but to give stretch to the Indian forces under my direction, and they amount to thousands," which implied that Britain's enemies would suffer attacks from Native Americans allied to the British. More than any other act during the campaign, this threat and subsequent widely reported atrocities such as the scalping of Jane McCrea stiffened the resolve of the Americans to do whatever it took to assure that the threat did not become reality. The American forces at Fort Ticonderoga recognized that once the British mounted artillery on high ground near the fort, Ticonderoga would be indefensible. A retreat from the Fort was ordered, and the Americans floated troops, cannon, and supplies across Lake Champlain to Mount Independence. From there the army set out for Hubbardton where the British and German troops caught up with them and gave battle. Round one to the British. Burgoyne continued his march towards Albany, but miles to the south a disturbing event occurred. Sir William Howe decided to attack the Rebel capital at Philadelphia rather than deploying his army to meet up with Burgoyne and cut off New England from the other Colonies. Meanwhile, as Burgoyne marched south, his supply lines from Canada were becoming longer and less reliable. I have the honor to inform your Lordship that the enemy [were] dislodged from Ticonderoga and Mount Independent, on the 6th instant, and were driven on the same day, beyond Skenesborough on the right, and the Humerton [Hubbardton] on the left with the loss of 128 pieces of cannon, all their armed vessels and bateaux, the greatest part of their baggage and ammunition, provision and military stores ... – General John Burgoyne, letter to Lord George Germain (1777) In early August, word came that a substantial supply depot at Bennington, Vermont, was alleged to be lightly guarded, and Burgoyne dispatched German troops to take the depot and return with the supplies. This time, however, stiff resistance was encountered, and American general John Stark surrounded and captured almost 500 German soldiers. One observer reported Bennington as "the compleatest Victory gain'd this War." Burgoyne now realized, too late, that the Loyalists (Tories) who were supposed to have come to his aid by the hundreds had not appeared, and that his Native American allies were also undependable. American general Schuyler proceed to burn supplies and crops in the line of Burgoyne's advance so that the British were forced to rely on their ever-longer and more and more unreliable supply line to Canada. On the American side, General Horatio Gates arrived in New York to take command of the American forces. By mid-September, with the fall weather reminding Burgoyne that he could not winter where he was and needed to proceed rapidly toward Albany, the British army crossed the Hudson and headed for Saratoga. On September 19 the two forces met at Freeman's Farm north of Albany. While the British were left as "masters of the field," they sustained heavy human losses. Years later, American Henry Dearborn expressed the sentiment that "we had something more at stake than fighting for six Pence pr Day." In late September and during the first week of October 1777, Gate's American army was positioned between Burgoyne's army and Albany. On October 7, Burgoyne took the offensive. The troops crashed together south of the town of Saratoga, and Burgoyne's army was broken. In mop-up operations 86 percent of Burgoyne's command was captured. The victory gave new life to the American cause at a critical time. Americans had just suffered a major setback the Battle of the Brandywine along with news of the fall of Philadelphia to the British. One American soldier declared, "It was a glorious sight to see the haughty Brittons march out & surrender their arms to an army which but a little before they despised and called paltroons." A stupendous American victory in October 1777, the success at Saratoga gave France the confidence in the American cause to enter the war as an American ally. Later American successes owed a great deal to French aid in the form of financial and military assistance. Spies worked for both British and American armies. Secret messages and battle plans were passed in a variety of creative ways, including being sewn into buttons. Patriots and loyalists penned these secret letters either in code, with invisible ink, or as mask letters. Here is an example of Loyalist Sir Henry Clinton's mask letter. The letter on the left is the mask letter with the secret message decoded; to the right is an excerpt of the full letter. Benedict Arnold is best remembered as a traitor; an American patriot who spied for the British during the American Revolution. But there is more to his story than this sad event. Arnold was a fierce patriot during the Stamp Act crisis and the early years of the American Revolution. During the battles of Lexington and Concord, Arnold worked with Ethan Allen to capture Fort Ticonderoga and was named a colonel. As a member of George Washington's Continental Army, he led a failed attack on Quebec, but was nonetheless named brigadier general in 1776. His next big moment came at the Battle of Saratoga. Here, Benedict Arnold was instrumental in stopping the advance of the British and in obtaining the surrender of British General John Burgoyne. During the Battle of Freeman's Farm, Arnold's leg was severely wounded when pinned beneath his horse. (Both Arnold and his leg survived, there is a monument to his leg at Saratoga National Historic Park.) Over the next two years, Benedict Arnold remained a patriot, but was upset and embittered at what he felt was a lack of his recognition and contribution to the war. In 1778, following British evacuation of Philadelphia, George Washington appointed Arnold military commander of the city. This is where the story gets interesting. In Philadelphia, Benedict Arnold was introduced to and fell in love with Margaret (Peggy) Shippen, a young, well-to-do loyalist who was half his age. Ms. Shippen had previously been friendly with John André, a British spy who had been in Philadelphia during the occupation as the adjutant to the British commander in chief, Sir Henry Clinton. It is believed that Peggy introduced Arnold to André. Meanwhile, Benedict Arnold's reputation while in Philadelphia was beginning to tarnish. He was accused of using public wagons for private profit and of being friendly to Loyalists. Faced with a court-martial for corruption, he resigned his post on March 19, 1779. Following his resignation, Arnold began a correspondence with John André, now chief of British intelligence services. But Arnold had also maintained his close relationship with George Washington and still had access to important information. Over the next few months Benedict Arnold continued his talks with André and agreed to hand over key information to the British. Specifically, Arnold offered to hand over the most strategic fortress in America: West Point. Arnold and André finally met in person, and Arnold handed over information to the British spy. But, unfortunately for both men, André was caught and Arnold's letter was found. Arnold's friend, George Washington, was heartbroken over the news, but was forced to deal with the treacherous act. While Benedict Arnold escaped to British-occupied New York, where he was protected from punishment. John André was executed for spying. Benedict Arnold was named brigadier general by the British government and sent on raids to Virginia. Following Cornwallis's surrender at Yorktown in 1781, Arnold and his family sailed to Britain with his family. He died in London in 1801.

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Screens show the literature of today's students whether it's a movie, a television program, or even a video game. Today's English Language Arts curriculum originated in past centuries to teach people about the popular culture of their time, written stories. But today's literature no longer relies on print alone; instead it has expanded to include stories told on screens. Most of the reasons to teach the structure and devices of fiction apply with equal force to screened stories. In fact, the need to teach about screened fiction becomes more urgent every day as today's youth increasingly shift their attention toward screens and away from the written word. For these reasons, TWM contends that ELA teachers who desire to impart lifetime lessons about the wonder of stories will give students the tools to analyze screened fiction. Since the best filmed stories use many of the elements and devices of written fiction, ELA educators are well qualified to provide instruction on how the elements and devices of fiction are used in screened stories. However, there are obstacles to teaching film as literature in ELA classes. The Common Core Curriculum Standards give minimal attention to the need to teach screened fiction and teachers are bound by their contracts to teach to the standards. In addition, class time is extremely limited. Some teachers have pointed out that today's students are often so unused to reading that teaching the elements and devices of written literature by showing appropriate film clips assists students in applying those concepts to written texts. Reading in the Dark: Using Film As a Tool in the English Classroom (2001) written by John Golden, published by the National Council of Teachers of English Publications. While this is a valuable insight, it doesn't teach students that the entirety of a filmed work of fiction can be subjected to literary analysis. Moreover, just as reading an entire book in class is by necessity an infrequent occurrence, showing a movie and leading the class through an in-depth literary analysis of the film is something that can be done only once or twice a semester. Part of the solution to this conundrum is TWM's Movies as Literature Homework Project which requires students to watch movies at home and prepare an analysis of the film based on TWM's Film Study Worksheet INSTRUCTIONS FOR USING THE ASSIGNMENT The assignment consists of the following documents: (1) The Movies as Literature Homework Project and (2) a list of films. Click here for TWM's suggested list . Keep a large number of TWM's Film Study Worksheets for students to take them home when necessary. Make sure that students understand each term used in TWM's Film Study Worksheet . For classes below the tenth grade, go through the questions and demonstrate how they can be answered. In the alternative, have students respond to the prompts in the worksheet (or a shortened worksheet) after seeing a movie in class. After students have had time to write short responses to the prompts, discuss the responses in class. This project can be used directly as presented by TeachWithMovies or it can be adapted to enhance its benefits. For example, teachers can have students make presentations to the class about literary elements or devices that they have seen in the movies they have watched for the assignment. If the class has been focusing on a group of literary devices, question #10 of the Film Study Worksheet can be modified to refer to them. Teachers can, over the semester, require students to view a popular and easily accessible movie outside of class that can then be analyzed during school. In this case, teachers should also show the movie once or twice after school for those who can't get access to the film. Other variations include the following: Students can be required to watch three or four movies. Students can also be separated into groups of four or fewer with each group being asked to give an oral presentation in response to a question on the Worksheet. For middle school or junior high school classes, the Worksheet can be simplified by eliminating some of the questions or by requiring that fewer examples be given. For students who are not familiar with archetypes, delete question #10 or substitute another question. For example, the following question can replace #10 "Describe three images or scenes that stand out in your mind when you think about this movie." Questions relating to topics that have been studied in class can be substituted for some of the questions in the Worksheet. Students can be given time in class to peer review each other's Worksheets. The possibilities are endless. TWM has developed a list of films to attach to the assignment. This list is based on movies for which a Learning Guide or Lesson Plan is available on TWM. Teachers should add movies that they feel would be appropriate. Review the instructions on the assignment with students after handing out the project. For a film study worksheet for historical fiction shown in a social studies class For a film study worksheet for ELA classes, click here Spread the GOOD NEWS about

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The Animal Kingdom is the entire fauna which exists in the nature. The animal kingdom includes all types of animals and there is a specific hierarchy with the help of which they are classified. It is according to their physical traits, habits and habitats. Given below is the Animal Kingdom Hierarchy which helps us to classify the Animals according to different categories so that identifying them becomes easier. This hierarchy is according to the development and evolution of species on earth. The main categories of animals are: - Unicellular (Protozoa): The animals which have only one cell are unicellular animals. They are microorganisms whose body is just a single cell. Example: Sarcodina andAmoebozoa. - Multicellular (Metazoa): The animals whose body is made up of multiple cells are known as multicellular. They include all the other animals except for protozoa. - Multicellular animals are further classified into: - Invertebrates: Invertebrates are the animals who do not have bones in their bodies. They are further classified into: - Worms: Worms are small invertebrates that usually live in the moisture and help in the contribution to degradation of substances. - Sponges: Sponges are multicellular animals which have pores on their bodies, allowing water to pass directly through it. The examples of sponges include Yellow Tube Sponge, Purple Vase Sponge etc. - Coelenterates: They are marine species encompassing two animal Phyla. The bodies of these species are hollow and hence, they do not have stability and keep moving with the water flow. - Arthropods: Arthropods are animals which have an external skeleton covering their body. They have a segmented body and joint appendages. These animals include butterflies, crabs, lobsters etc. - Molluscs:Molluscs are marine species. They include Octopus, Snails and Squids. They are slimy in texture. - Echinoderms: Echinoderms are another name for species like Starfish and Sea Cucumber, who have a brittle-like body. Vertebrates: Vertebrates are the animals who have a backbone and a skeleton to support their body structure. Invertebrate animals include: - Fish: Fish are marine species who live in water. They have scales and breathe through their gills. They can be carnivorous as well as herbivorous. - Amphibians: Amphibians are species who can live in the water as well as outside water. They include Frogs, Caecilians and Salamanders. - Reptiles: Reptiles are cold blooded animals. They include snakes, turtles and lizards. They are cold blooded and hence, their bodies react fast to temperatures and hence, they need to stay in the shade when it is too hot and in warmth when it’s too cold. - Birds: Birds are endothermic species which are classified with feathers, wings and beak without teeth. They commute by flying in the air but there are a few exceptions to it. Birds include Parrot, Crow, Sparrow, etc. - Mammals: Mammals are warm blooded animal species who walk on four limbs. They do not lay eggs and procreate directly. Mammals include Tigers, Bears, Lions, Elephants etc. The human is the only mammal who walks on two limbs. Mammals are considered to be the most progressive species of all animals. Know about Animal Intelligence Hierarchy.

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# SOLUTION: Use rapid sketching techniques to graph r = 4 sin theta. Be sure to show how you arrived at your graph. Only use your calculator to check. Thanks! Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: Use rapid sketching techniques to graph r = 4 sin theta. Be sure to show how you arrived at your graph. Only use your calculator to check. Thanks!      Log On Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Algebra: Exponent and logarithm as functions of power Solvers Lessons Answers archive Quiz In Depth Question 631548: Use rapid sketching techniques to graph r = 4 sin theta. Be sure to show how you arrived at your graph. Only use your calculator to check. Thanks!Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!```r = 4·sin That is a circle of diameter 4. Since it is sine the very bottom of the circle is at the pole (origin). If it were cosine the pole (origin) would be at the far left side of the circle. That one is easy to change to rectangular form Replace sin@ by r = 4() Multiply both sides by r r² = 4y Change r² to x² + y² x² + y² = 4y x² + y² - 4y = 0 Complete the square by adding 4 to both sides: x² + y² - 4y + 4 = 4 x² + (y - 2)² = 4 Write x as (x - 0) (x - 0)² + (y - 2)² = 2² which is a circle with center (0,2) with radius 2. Edwin```

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- Author(s):Anita Straker - Available from: February 1995 Develops pupils' mental skills in a variety of inventive ways. Send a Query× This resource book for teachers is intended to help children aged 9 to 11 (Y5 and Y6, P5 and P6 in Scotland) to think about numbers and carry out mental calculations. The first part contains suggestions on ways of working, and classroom organisation. The second part has a series of ideas for oral work, some most suitable for small group work, others for the whole class. The third part contains 32 pages of photocopy masters of games and puzzles that will give children enjoyable practice of mental calculation. Solutions to the puzzles are included at the end of the book, along with the answers to the two pupils’ books that are published separately. - 1 Ways of working - 2 Oral work - 3 Puzzles and games - 4 Answers to Mental maths 1 and 2. Latest newsAll news 13 November 2019 Three approaches to differentiation in primary science Try these out in your class wherever you are in the curriculum. Thank you for your feedback which will help us improve our service. If you requested a response, we will make sure to get back to you shortly.×

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The discovery of a 12,000-year-old skeleton has helped clear up a problem that has long puzzled scientists – the origins of the first Americans. Differences between the skeletons of the earliest and modern native Americans have led researchers to suggest the older humans had their roots in Europe, Asia or Australia. But now a study published in Science has found the earliest Americans could have come from the same place as native Americans – Beringia, an area around the Bering Strait that connected Asia and North America in ancient times – despite the differences in appearances. Divers chanced upon the skeleton – that of small teenage girl who is thought to have fallen to her death in an underground cave system in Mexico 12,000 years ago – in 2007: “The Hoyo Negro girl was related to living Native Americans and has ancestry from the same Beringian population,” says Deborah Bolnick, assistant professor of anthropology at The University of Texas at Austin. “This study therefore provides no support for the hypothesis that Paleoamericans migrated from Southeast Asia, Australia or Europe. Instead, it shows that Paleoamericans could have come from Beringia, like contemporary Native Americans, even though they exhibit some distinctive skull and facial features. The physical differences between Paleoamericans and Native Americans today are more likely due to changes that occurred in Beringia and the Americas over the last 9,000 years.”

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Hong Kong Stage 1 - Stage 3 # Estimating Percentages Lesson A lot of the time it's hard for us to accurately calculate percentages of amounts in real life, so we'll have to estimate! Because percentages are expressed as something out of a hundred, we can also express them in diagrams of $5,10,100$5,10,100 things or more! #### Example Someone has been eating the brand new $10\times10$10×10 square block of chocolate! Can you figure out how much of the original chocolate block is left in percentages? Think about the chocolate block as a fraction first Do :We can see that there used to $10\times10=100$10×10=100 blocks of chocolate here, and now there are $67$67 blocks. So the fraction that represents how much is left of the original is $\frac{67}{100}$67100 . This is easily translated into a percentage as the denominator is already $100$100 , so the answer is $67%$67% . #### Worked Examples ##### QUESTION 1 Which point on the line is closest to $56%$56%? 1. $A$A A $C$C B $D$D C $B$B D ##### QUESTION 2 Ellie bought a $454$454 mL drink that claimed to be orange juice. In the ingredients list it said that orange juice made up $17%$17% of the drink. To estimate the amount of orange juice in the drink, which of the following would give the closest answer? 1. $10%\times454$10%×454 A $20%\times454$20%×454 B $10%\times400$10%×400 C ##### QUESTION 3 In a census, people are asked their gender and age. The graph shows the results: the percentage of females and males in each age group. 1. To the nearest $1%$1%, what percentage of females are between $5$5 and $9$9 years of age? $7%$7% A $2%$2% B $11%$11% C 2. To the nearest $1%$1%, what percentage of males are between $30$30 and $34$34 years of age? $7%$7% A $4%$4% B $2%$2% C 3. The percentage of females between the ages of $20$20 and $29$29 is about: $15%$15% A $7%$7% B $25%$25% C 4. The percentage of males below $20$20 years of age is about: $15%$15% A $10%$10% B $30%$30% C $50%$50% D

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Physicists announce antimatter discoveryBy Steve Koppes Mother Nature likes matter better than antimattera preference physicists technically refer to as charge-parity violation. First observed in 1964 by James Cronin and Val Fitch, the indirect CP violation they studied won them the 1980 Nobel Prize in physics. Since then, theorists have worked to devise a model of physics that could account for CP violation, but there was no independent evidence to test the models against. Nothing, that is, until Wednesday, Feb. 24, when Chicago graduate student Peter Shawhan announced at a Fermilab seminar the discovery of direct CP violation, an entirely new type of inequality between matter and antimatter. Its an uncharted territory, said Bruce Winstein, the Samuel Allison Distinguished Service Professor in Physics, who headed up the 21-year effort that led to the discovery. For 34 years weve had one measurement of CP violation, just one manifestation of it. This is the first new one since that time. In 1964 at Brookhaven National Laboratory, Cronin and Fitch observed indirect CP violation, the unbalanced mixing of neutral subatomic kaon particles with their charged antiparticles. The Fermilab team has observed direct CP violation. To study the process, the Fermilab team produces enormous quantities of kaons with the worlds highest-energy proton beam at Fermilabs TeVatron accelerator. Kaons decay into other types of particles within a tiny fraction of a second after they are produced, so the KTeV detectors must identify and measure their position and energy quickly. The experiment, called Kaons at the TeVatron at Fermilab, is a collaboration involving 80 physicists from 12 institutions. About 15 of the KTeV physicists are from the University; eight of these Chicago scientists analyzed the data that led to the Feb. 24 announcement. Winstein began experimenting with CP violation in 1978. Construction on the latest experiment, the third in a successively more accurate series, began in 1992. The experiment began running 24 hours a day in late 1996. Its an extremely high-precision experiment, said Shawhan, the senior Chicago graduate student on the project. First we have to design the experiment well. Then we have to be very certain that we understand our detector and our analysis in greater detail than most other high-energy experiments because were looking for such a subtle effect. A great deal of work has gone into that effort. The experiment attempts to measure a quantity called epsilon prime divided by epsilon. If the quantity had turned out to be zero, it would have verified the Superweak Model of CP violation. A nonzero value would favor the Standard Model, to which most physicists subscribe. The result that Shawhan announced Feb. 24 was 0.00280 with an error of 0.00041. This eliminates the Superweak Model as the sole explanation for CP violation, but a problem remains. The number that we got was larger than most theorists had predicted, said Edward Blucher, Assistant Professor in Physics at Chicago and a member of the Fermilab team for five years. Blucher and his students, Jim Graham and Val Prasad, along with graduate student Colin Bown, postdoctoral scientists Rick Kessler and Sasha Glazov, and former member Aaron Roodman, made up the Chicago team for this analysis. The European laboratory for particle physics, CERN, in Switzerland, found evidence for direct CP violation before the Fermilab team, but the CERN measurements were less precise. It wasnt definitive evidence, Winstein said. The Chicago researchers initially reacted to the latest result with mixed emotions. There was a mixture of jubilation, shock and a feeling of, oh my God, did we screw up, all at once, Winstein said. But there is no question about the latest Fermilab results, Cronin said: Its final. The experiment has doubled scientific knowledge about CP violation independent of any theory or speculation, said Cronin, Professor in Physics and Astronomy & Astrophysics at Chicago. This wonderful discovery is a beautiful surprise, Cronin said. Its just wonderful because I dont think anybody expected it. Thats what makes it especially delicious.

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Women have played a unique role in the history of clothing manufacture in the United States. During the American Revolution, white women—and, in the case of slaveowning families, black female slaves—wove homespun clothing in order to sustain colonial boycotts on manufactured English goods. Female slaves were an integral part of the cotton cultivation and harvesting that produced the raw materials for textile production during the antebellum period. After emancipation, black women continued their integral role in cotton production as sharecroppers, either working the fields alongside their husbands or providing the childcare and cooking that sustained their husbands and children in the fields. Black women also worked as laundresses throughout the South and in other areas, since it was one of the few paid occupations considered "low" enough for black women. In 1840, lower- and middle-class women made up almost half of manufacturing workers in the nation, and two-thirds of those in New England.172 These young women moved to factory towns like Lynn, Massachusetts and lived in same-sex dormitories with strict schedules and curfews; they usually sent most or all of their meager earnings home to support their families. In the late nineteenth century, poor women—primarily immigrants—who came to America from Southern and Eastern Europe toiled in the garment industry, centered in New York City. They worked endless hours from home doing outwork (or piecework), in which they were paid by the number of items they sewed in a given time period. Advocates claimed that such work remunerated employees in accordance with their ability, while opponents argued that piecework encouraged quantity at the expense of quality and forced workers to the limits of endurance in order to make a living wage. Women doing outwork had to pay for their own supplies; a heavy investment, especially when it came to the purchase of an expensive sewing machine. Thus some of the earliest workers' protests centered on the heavy burden of having to buy those machines. Other textile and apparel workers labored outside the home in unsanitary, dangerous sweatshops for low wages. Shoe and clothing manufacturers no longer apprenticed young artisans, teaching them how to make an entire shoe or shirt; instead workers were trained in how to sew or stitch a single piece (like a shirt collar, a shirtwaist, or a part of a shoe), and they were only paid for that piece, not for the sale of the final finished product. They had no marketable skills, and were therefore easily replaced and seldom promoted. One sweatshop typical of the late nineteenth-century period was located at 23-29 Washington Place, at the northern corner of Washington Square East in Manhattan. It was called the Triangle Waist Company, a shirtwaist manufacturer. The building owners subcontracted their work out to men who then paid their workers any wage they chose, since there was, until 1938, no federally mandated minimum wage. Clearly this system enabled the owners of the factory to maintain a comfortable measure of ignorance as to the real workings of the sweatshops that produced their rigid quotas, while workers were exploited in terrible working conditions with long hours (as many as 70 hours a week) and no overtime pay. Most of these workers had no choice; they were immigrants or otherwise unskilled or impoverished, and desperately needed the work. They were also afraid to unionize, or they simply did not have the requisite English language skills to do so. At Triangle, shirtwaist makers toiled ten to twelve hours a day. Supervisors watched the workers constantly; if they talked, whistled, or sang on the job, were a few minutes late to work, or missed a Sunday shift, their pay was docked. As historian Alice Kessler-Harris has explained, "women's industries like clothing and textiles became centers of strike activity," in part because of the deplorable working conditions but also because of the advertising of the fashion industry itself. The garment producers had created their own paradox: they sought ever-increasing production output at the cheapest possible wages by exploiting their labor force as much as possible, yet in order to sell their products, they marketed a glamorous lifestyle filled with extravagance and ease. Female garment workers compared their unclean, unsafe, and exhausting working conditions with the luxurious world showcased all around them in radio advertisements and popular magazines. Kessler-Harris explains that "much of urban America had already begun to absorb the values of consumerism," and female workers "increasingly began to demand their share of material benefits."173 In 1909, 400 workers—mostly Jewish women—reached their limit and spontaneously walked out of the Triangle Shirtwaist factory. Organized by the International Ladies' Garment Workers Union (ILGWU) and with help from the progressive middle-class members of the Women's Trade Union League (WTUL), this spontaneous eruption of discontent grew into a general strike of shirtwaist makers, and the largest women's strike in American history. The strike lasted for thirteen weeks; 20,000 people ultimately walked out on their jobs, shutting down the industry. News on the strike was printed in English, Italian, and Yiddish, reflecting the diversity of the city and its workers. Thousands of activists marched arm-in-arm on City Hall, and dozens of women were beaten by hostile police, arrested, and even carted off to Blackwell's Island as workhouse prisoners. The workers won widespread public support and as time dragged on, many small and medium shops settled with the union's wage and hour demands. The agreements varied, but generally they involved an employer's recognition of worker's union, an arbitration process to determine piece rates, and an end to the policy of charging workers for needles, thread, and electricity. On 15 February 1910, the ILGWU called off the strike and declared victory, having won 320 separate signed contracts with various employers. Yet the union's success was hollow; there was no industry-wide agreement to enforce these individual shop contracts, and the 70 large manufacturers who dominated the garment industry—including Triangle Shirtwaist—had not made any agreements by strike's end.174 Just a year later, on 25 March 1911, a fire broke out in the supposedly "fireproof" Asch building where Triangle Waist Company occupied the eighth, ninth, and tenth floors. The shirtwaists that hung on lines above the workers' heads and the shirtwaist cuttings that littered the floors quickly ignited, allowing the blaze to spread rapidly through the building. As one reporter described, the sewing machines were "placed so closely together that there was hardly aisle room for the girls between them."175 The workers had been locked inside the factory, a standard practice that the owners employed—supposedly to prevent theft. This policy turned out to be deadly when the fire broke out, as it trapped the workers inside the burning building. A few made it down the stairs, but flames soon blocked that exit route. There was one small fire escape in the corner of the building, but not everyone could make it down. Many women, desperate and suffocating from the fire's dense black smoke, stepped out on the ledge and plunged 100 feet to their deaths. Fire ladders extended up towards some of the women, but were not high enough to reach them. Bodies soon littered Washington Place and Greene Street. Others stayed in the factory and burned alive. Of 500 shirtwaist makers who reported to work that awful day, 146 died in the blaze, all within half an hour. As the New York Times reported the next day, most of the victims were "girls from 16 to 23 years of age... Most of them could barely speak English. Many of them came from Brooklyn. Almost all were the main support of their hard-working families."176 New Yorkers and Americans across the country were shocked by the tragedy. Only a handful of the Triangle workers were ILGWU members, and Triangle Shirtwaist was a non-union shop. Unions capitalized on this fact, using the disaster to illustrate their contention that an organized workforce could demand safer working conditions. Several unions, including the ILGWU, the WTUL, and the United Hebrew Trades formed the Joint Relief Committee, which raised relief money—some $30,000—for fire survivors and their families. The ILGWU organized a rally to protest the unsafe working conditions that created the disaster, and the Women's Trade Union League collected testimonies and campaigned for an investigation of the working conditions at Triangle. Within a month, New York's governor appointed the Factory Investigating Commission, which held a series of hearings over five years and helped to pass groundbreaking factory safety legislation. Eight months after the fire, a jury acquitted building owners Max Blanck and Isaac Harris of any wrongdoing. Despite subsequent gains in workplace safety legislation, sweatshops continue to plague the garment and textile manufacturing industries, both at home and abroad. The U.S. Department of Labor has conducted several studies in the twenty-first century, finding that 67% of Los Angeles garment factories and 63% of New York garment factories violate minimum wage and overtime laws. In Los Angeles, 98% of garment factories have workplace health and safety problems serious enough to lead to severe injuries or death. Abroad, the situation is even worse; workers in northern Mexico have seen manufacturers migrate even farther south, where wages are lower and labor protections often go unenforced. One 2002 Los Angeles Times article profiled a mother of five in a Mexican border town two hours southwest of San Antonio, a woman who earned about $55 a week sewing cloth bags at a local factory. Just two years earlier, the same woman had been able to earn twice that amount sewing jeans in a Levi's' factory, but that plant had shut down and moved its jobs to Central America and Asia. The same article profiled Lisa Rahman, a 19-year-old garment factory worker in Dhaka, Bangladesh, who made fifteen cents an hour in 2002. She could only afford to eat chicken along with her usual meal of rice about once every two months, had never gone to school, ridden a bicycle or seen a movie, and lived with her parents and two young relatives in one room amid the slums. She often worked from 8 a.m. until 10 p.m., seven days a week, and had done so since she was ten years old. One of Lisa's most recent jobs had been making a Winnie the Pooh shirt that the Walt Disney Company sold in the United States for $17.99. In the wake of the negative publicity generated by the article, Disney's licensee subsequently suspended its work at that factory; licensees in today's globalized garment industry work much the same way as subcontractors did in Triangle Shirtwaist Company. Disney remains at least partially removed from the manufacturing process—and such scandals—if the responsibility for working conditions and wages is passed onto their licensees.177 Anti-sweatshop activists invoke human rights as the central principle of their cause. Sweatshops, they argue, not only take the place of domestic jobs in the U.S., but they employ desperately poor people in working conditions that are often unsafe, unclean, and exploitative. "In the cold war," explained Michael Posner, head of the Lawyers Committee for Human Rights, "the main issue was how do you hold governments accountable when they violate laws and norms. Today the emerging issue is how do you hold private companies accountable for the treatment of their workers at a time when government control is ebbing all over the world, or governments themselves are going into business and can't be expected to play the watchdog or protection role."178 Activists also argue that Americans have the power to determine "what comes into our country." The Union of Needletrades, Industrial and Textile Employees (or UNITE, which merged with the Hotel Employees and Restaurant Employees International Union—or HERE—in 2004) has represented most American apparel workers in recent lawsuits. Jay Mazur, UNITE's retired president, compares sweatshop-produced goods to cocaine, and argues that if we can legislate against the latter, we can also legislate against the former.179 In April 2003, the 600-member American Apparel and Footwear Association called on the U.S. government to ban imports of apparel, textiles and footwear from the Asian country of Myanmar (a.k.a. Burma), where a military regime had seized power and was committing numerous human rights abuses, including the use of forced labor and child labor. Association President Kevin Burke explained why his group of retailers—who would benefit from the lower labor costs under such oppressive regimes—took the unprecedented step of calling for federal action: Myanmar's military junta had expressed a "total disdain" for basic human rights, and by allowing the country's rulers "to produce products and send them here, we're putting money in their pocket while they're taking money out of other people's pockets and abusing them."180 Thus the amount of net gain from cheap labor does not always prove worthwhile for retailers, if the bad press from countries like Myanmar provokes consumer boycotts on stores that carry the sweatshop-produced goods. Yet the lure of inexpensive goods and maximized profit margins remains very strong. Despite U.S. efforts to isolate the Myanmar government and ban new investment in the country, in 2002, the U.S. imported $350 million in goods from Myanmar, mostly apparel and textiles.181 Despite the manifest problems with sweatshop labor, observers like New York economist Michael M. Weinstein argue that it would be "unconscionable to clamp down on sweatshops" that make foreign worker's lives "better than they would otherwise be."182 Weinstein also points out that "if we bar low-cost goods from abroad, it would be the poorest among us who depend on these products who would be punished most harshly."183 Constant pressure from investors to maximize profits, and from consumers to find good bargains, is likely to ensure that sweatshops will not go away any time soon.

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Mises Daily Articles On Equality and Inequality [Day 12 of Robert Wenzel's 30-day reading list that will lead you to become a knowledgeable libertarian, this article is excerpted from chapter 14 of Money, Method, and the Market Process, edited by Richard M. Ebeling. It was originally published in Modern Age (Spring 1961).] Different and Unequal The doctrine of natural law that inspired the 18th century declarations of the rights of man did not imply the obviously fallacious proposition that all men are biologically equal. It proclaimed that all men are born equal in rights and that this equality cannot be abrogated by any man-made law, that it is inalienable or, more precisely, imprescriptible. Only the deadly foes of individual liberty and self-determination, the champions of totalitarianism, interpreted the principle of equality before the law as derived from an alleged psychical and physiological equality of all men. The French declaration of the rights of the man and the citizen of November 3, 1789, had pronounced that all men are born and remain equal in rights. But, on the eve of the inauguration of the regime of terror, the new declaration that preceded the Constitution of June 24, 1793, proclaimed that all men are equal "par la nature." From then on this thesis, although manifestly contradicting biological experience, remained one of the dogmas of "leftism." Thus we read in the Encyclopaedia of the Social Sciences that "at birth human infants, regardless of their heredity, are as equal as Fords."1 However, the fact that men are born unequal in regard to physical and mental capacities cannot be argued away. Some surpass their fellow men in health and vigor, in brain and aptitudes, in energy and resolution and are therefore better fitted for the pursuit of earthly affairs than the rest of mankind — a fact that has also been admitted by Marx. He spoke of "the inequality of individual endowment and therefore productive capacity (Leistungsfähigkeit)" as "natural privileges" and of "the unequal individuals (and they would not be different individuals if they were not unequal)."2 In terms of popular psychological teaching we can say that some have the ability to adjust themselves better than others to the conditions of the struggle for survival. We may therefore — without indulging in any judgment of value — distinguish from this point of view between superior men and inferior men. History shows that from time immemorial superior men took advantage of their superiority by seizing power and subjugating the masses of inferior men. In the status society there is a hierarchy of castes. On the one hand are the lords who have appropriated to themselves all the land and on the other hand their servants, the liegemen, serfs, and slaves, landless and penniless underlings. The inferiors' duty is to drudge for their masters. The institutions of the society aim at the sole benefit of the ruling minority, the princes, and their retinue, the aristocrats. Such was by and large the state of affairs in all parts of the world before, as both Marxians and conservatives tell us, "the acquisitiveness of the bourgeoisie," in a process that went on for centuries and is still going on in many parts of the world, undermined the political, social, and economic system of the "good old days." The market economy — capitalism — radically transformed the economic and political organization of mankind. Permit me to recapitulate some well-known facts. While under precapitalistic conditions superior men were the masters on whom the masses of the inferior had to attend, under capitalism the more gifted and more able have no means to profit from their superiority other than to serve to the best of their abilities the wishes of the majority of the less gifted. In the market, economic power is vested in the consumers. They ultimately determine, by their buying or abstention from buying, what should be produced, by whom and how, of what quality and in what quantity. The entrepreneurs, capitalists, and landowners who fail to satisfy in the best possible and cheapest way the most urgent of the not-yet-satisfied wishes of the consumers are forced to go out of business and forfeit their preferred position. In business offices and in laboratories, the keenest minds are busy fructifying the most complex achievements of scientific research for the production of ever-better implements and gadgets for people who have no inkling of the theories that make the fabrication of such things possible. The bigger an enterprise is, the more is it forced to adjust its production to the changing whims and fancies of the masses, its masters. The fundamental principle of capitalism is mass production to supply the masses. It is the patronage of the masses that make enterprises grow big. The common man is supreme in the market economy. He is the customer who "is always right." In the political sphere, representative government is the corollary of the supremacy of the consumers in the market. Office-holders depend on the voters as entrepreneurs and investors depend on the consumers. The same historical process that substituted the capitalistic mode of production for precapitalistic methods substituted popular government — democracy — for royal absolutism and other forms of government by the few. And wherever the market economy is superseded by socialism, autocracy makes a comeback. It does not matter whether the socialist or communist despotism is camouflaged by the use of aliases like "dictatorship of the proletariat" or "people's democracy" or "Führer principle." It always amounts to a subjection of the many to the few. It is hardly possible to misconstrue more thoroughly the state of affairs prevailing in capitalistic society than by calling the capitalists and entrepreneurs a "ruling" class intent upon "exploiting" the masses of decent men. We will not raise the question of how the men who under capitalism are in business would have tried to take advantage of their superior talents in any other thinkable organization of production. Under capitalism they are vying with one another in serving the masses of less gifted men. All their thoughts aim at perfecting the methods of supplying the consumers. Every year, every month, every week something unheard of before appears on the market and is soon made accessible to the many. What has multiplied the "productivity of labor" is not some degree of effort on the part of manual workers, but the accumulation of capital by the savers and its reasonable employment by the entrepreneurs. Technological inventions would have remained useless trivia if the capital required for their utilization had not been previously accumulated by thrift. Man could not survive as a human being without manual labor. However, what elevates him above the beasts is not manual labor and the performance of routine jobs, but speculation, foresight that provides for the needs of the — always uncertain — future. The characteristic mark of production is that it is behavior directed by the mind. This fact cannot be conjured away by a semantics for which the word "labor" signifies only manual labor. Are Consumers Stupid? To acquiesce in a philosophy stressing the inborn inequality of men runs counter to many people's feelings. More or less reluctantly, people admit that they do not equal the celebrities of art, literature, and science, at least in their specialties, and that they are no match for athletic champions. But they are not prepared to concede their own inferiority in other human matters and concerns. As they see it, those who outstripped them in the market, the successful entrepreneurs and businessmen, owe their ascendancy exclusively to villainy. They themselves are, thank God, too honest and conscientious to resort to those dishonest methods of conduct that, as they say, alone make a man prosper in a capitalistic environment. Yet, there is a daily growing branch of literature that blatantly depicts the common man as an inferior type: the books on the behavior of consumers and the alleged evils of advertising.3 Of course, neither the authors nor the public that acclaims their writings openly state or believe that that is the real meaning of the facts they report. As these books tell us, the typical American is constitutionally unfit for the performance of the simplest tasks of a householder's daily life. He or she does not buy what is needed for the appropriate conduct of the family's affairs. In their inwrought stupidity they are easily induced by the tricks and wiles of business to buy useless or quite worthless things. For the main concern of business is to profit not by providing the customers with the goods they need, but by unloading on them merchandise they would never take if they could resist the psychological artifices of "Madison Avenue." The innate incurable weakness of the average man's will and intellect makes the shoppers behave like "babes."4 They are easy prey to the knavery of the hucksters. Neither the authors nor the readers of these passionate diatribes are aware that their doctrine implies that the majority of the nation are morons, unfit to take care of their own affairs and badly in need of a paternal guardian. They are preoccupied to such an extent with their envy and hatred of successful businessmen that they fail to see how their description of consumers' behavior contradicts all that the "classical" socialist literature used to say about the eminence of the proletarians. These older socialists ascribed to the "people," to the "working and toiling masses," to the "manual workers" all the perfections of intellect and character. In their eyes, the people were not "babes" but the originators of what is great and good in the world, and the builders of a better future for mankind. It is certainly true that the average common man is in many regards inferior to the average businessman. But this inferiority manifests itself first of all in his limited ability to think, to work, and thereby to contribute more to the joint productive effort of mankind. Most people who satisfactorily operate in routine jobs would be found wanting in any performance requiring a modicum of initiative and reflection. But they are not too dull to manage their family affairs properly. The husbands who are sent by their wives to the supermarket "for a loaf of bread and depart with their arms loaded with their favorite snack items"5 are certainly not typical. Neither is the housewife who buys regardless of content, because she "likes the package."6 It is generally admitted that the average man displays poor taste. Consequently business, entirely dependent on the patronage of the masses of such men, is forced to bring to the market inferior literature and art. (One of the great problems of capitalistic civilization is how to make high quality achievements possible in a social environment in which the "regular fellow" is supreme.) It is furthermore well known that many people indulge in habits that result in undesired effects. As the instigators of the great anticapitalistic campaign see it, the bad taste and the unsafe consumption habits of people and the other evils of our age are simply generated by the public relations or sales activities of the various branches of "capital" — wars are made by the munitions industries, the "merchants of death"; dipsomania by alcohol capital, the fabulous "whiskey trust," and the breweries. This philosophy is not only based on the doctrine depicting the common people as guileless suckers who can easily be taken in by the ruses of a race of crafty hucksters. It implies in addition the nonsensical theorem that the sale of articles which the consumer really needs and would buy if not hypnotized by the wiles of the sellers is unprofitable for business and that on the other hand only the sale of articles which are of little or no use for the buyer or are even downright detrimental to him yields large profits. For if one were not to assume this, there would be no reason to conclude that in the competition of the market the sellers of bad articles outstrip those of better articles. The same sophisticated tricks by means of which slick traders are said to convince the buying public can also be used by those offering good and valuable merchandise on the market. But then good and poor articles compete under equal conditions and there is no reason to make a pessimistic judgment on the chances of the better merchandise. While both articles — the good and the bad — would be equally aided by the alleged trickery of the sellers, only the better one enjoys the advantage of being better. We need not consider all the problems raised by the ample literature on the alleged stupidity of the consumers and their need for protection by a paternal government. What is important here is the fact that, notwithstanding the popular dogma of the equality of all men, the thesis that the common man is unfit to handle the ordinary affairs of his daily life is supported by a great part of popular "leftist" literature. The doctrine of the inborn physiological and mental equality of men logically explains differences between human beings as caused by postnatal influences. It emphasizes especially the role played by education. In the capitalistic society, it is said, higher education is a privilege accessible only to the children of the "bourgeoisie." What is needed is to grant every child access to every school and thus educate everyone. Guided by this principle, the United States embarked upon the noble experiment of making every boy and girl an educated person. All young men and women were to spend the years from 6 to 18 in school, and as many as possible of them were to enter college. Then the intellectual and social division between an educated minority and a majority of people whose education was insufficient was to disappear. Education would no longer be a privilege; it would be the heritage of every citizen. Statistics show that this program has been put into practice. The number of high schools, of teachers and students multiplied. If the present trend goes on for a few years more, the goal of the reform will be fully attained; every American will graduate from high school. But the success of this plan is merely apparent. It was made possible only by a policy that, while retaining the name "high school," has entirely destroyed its scholarly and scientific value. The old high school conferred its diplomas only on students who had at least acquired a definite minimum knowledge in some disciplines considered as basic. It eliminated in the lower grades those who lacked the abilities and the disposition to comply with these requirements. But in the new regime of the high school, the opportunity to choose the subjects he wished to study was badly misused by stupid or lazy pupils. Not only are fundamental subjects such as elementary arithmetic, geometry, physics, history, and foreign languages avoided by the majority of high school students, but every year boys and girls receive high school diplomas who are deficient in reading and spelling English. It is a very characteristic fact that some universities found it necessary to provide special courses to improve the reading skill of their students. The often passionate debates concerning the high school curriculum that have now been going on for several years prove clearly that only a limited number of teenagers are intellectually and morally fit to profit from school attendance. For the rest of the high school population the years spent in classrooms are simply wasted. If one lowers the scholastic standard of high schools and colleges in order to make it possible for the majority of less gifted and less industrious youths to get diplomas, one merely hurts the minority of those who have the capacity to make use of the teaching. The experience of the last decades in American education bears out the fact that there are inborn differences in man's intellectual capacities that cannot be eradicated by any effort of education. The desperate, but hopeless, attempts to salvage, in spite of indisputable proofs to the contrary, the thesis of the inborn equality of all men are motivated by a faulty and untenable doctrine concerning popular government and majority rule. This doctrine tries to justify popular government by referring to the supposed natural equality of all men. Since all men are equal, every individual participates in the genius that enlightened and stimulated the greatest heroes of mankind's intellectual, artistic, and political history. Only adverse postnatal influences prevented the proletarians from equaling the brilliance and the exploits of the greatest men. Therefore, as Trotsky told us,7 once this abominable system of capitalism will have given way to socialism, "the average human being will rise to the heights of an Aristotle, a Goethe, or a Marx." The voice of the people is the voice of God, it is always right. If dissent arises among men, one must, of course, assume that some of them are mistaken. It is difficult to avoid the inference that it is more likely that the minority errs than the majority. The majority is right, because it is the majority and as such is borne by the "wave of the future." The supporters of this doctrine must consider any doubt of the intellectual and moral eminence of the masses as an attempt to substitute despotism for representative government. However, the arguments advanced in favor of representative government by the liberals of the 19th century — the much-maligned Manchestermen and champions of laissez-faire — have nothing in common with the doctrines of the natural inborn equality of men and the superhuman inspiration of majorities. They are based upon the fact, most lucidly exposed by David Hume, that those at the helm are always a small minority as against the vast majority of those subject to their orders. In this sense every system of government is minority rule and as such can last only as long as it is supported by the belief of those ruled that it is better for themselves to be loyal to the men in office than to try to supplant them by others ready to apply different methods of administration. If this opinion vanishes, the many will rise in rebellion and replace by force the unpopular office-holders and their systems by other men and another system. But the complicated industrial apparatus of modern society could not be preserved under a state of affairs in which the majority's only means of enforcing its will is revolution. The objective of representative government is to avoid the reappearance of such a violent disturbance of the peace and its detrimental effects upon morale, culture, and material well-being. Government by the people, i.e., by elected representatives, makes peaceful change possible. It warrants the agreement of public opinion and the principles according to which the affairs of state are conducted. Majority rule is for those who believe in liberty not as a metaphysical principle, derived from an untenable distortion of biological facts, but as a means of securing the uninterrupted peaceful development of mankind's civilizing effort. The Cult of the Common Man The doctrine of the inborn biological equality of all men begot in the 19th century a quasi-religious mysticism of the "people" that finally converted it into the dogma of the "common man's" superiority. All men are born equal. But the members of the upper classes have unfortunately been corrupted by the temptation of power and by indulgence in the luxuries they secured for themselves. The evils plaguing mankind are caused by the misdeeds of this foul minority. Once these mischief makers are dispossessed, the inbred nobility of the common man will control human affairs. It will be a delight to live in a world in which the infinite goodness and the congenital genius of the people will be supreme. Never-dreamt-of happiness for everyone is in store for mankind. For the Russian Social Revolutionaries this mystique was a substitute for the devotional practices of Russian Orthodoxy. The Marxians felt uneasy about the enthusiastic vagaries of their most dangerous rivals. But Marx's own description of the blissful conditions of the "higher phase of Communist Society"8 was even more sanguine. After the extermination of the Social-Revolutionaries the Bolsheviks themselves adopted the cult of the common man as the main ideological disguise of their unlimited despotism of a small clique of party bosses. The characteristic difference between socialism (communism, planning, state capitalism, or whatever other synonym one may prefer) and the market economy (capitalism, private enterprise system, economic freedom) is this: in the market economy the individuals qua consumers are supreme and determine by their buying or not buying what should be produced, while in the socialist economy these matters are fixed by the government. Under capitalism the customer is the man for whose patronage the suppliers are striving and to whom after the sale they say "thank you" and "please come again." Under socialism the "comrade" gets what "big brother" deigns to give him and he is to be thankful for whatever he got. In the capitalistic West the average standard of living is incomparably higher than in the communistic East. But it is a fact that a daily increasing number of people in the capitalistic countries — among them also most of the so-called intellectuals — long for the alleged blessings of government control. It is vain to explain to these men what the condition of the common man both in his capacity as a producer and in that of a consumer is under a socialist system. An intellectual inferiority of the masses would manifest itself most evidently in their aiming at the abolition of the system in which they themselves are supreme and are served by the elite of the most talented men and in their yearning for the return to a system in which the elite would tread them down. Let us not fool ourselves. It is not the progress of socialism among the backward nations, those that never surpassed the stage of primitive barbarism and those whose civilizations were arrested many centuries ago, that shows the triumphant advance of the totalitarian creed. It is in our Western circuit that socialism makes the greatest strides. Every project to narrow down what is called the "private sector" of the economic organization is considered as highly beneficial, as progress, and is, if at all, only timidly and bashfully opposed for a short time. We are marching "forward" to the realization of socialism. The classical liberals of the 18th and 19th centuries based their optimistic appreciation of mankind's future upon the assumption that the minority of eminent and honest men would always be able to guide by persuasion the majority of inferior people along the way leading to peace and prosperity. They were confident that the elite would always be in a position to prevent the masses from following the pied pipers and demagogues and adopting policies that must end in disaster. We may leave it undecided whether the error of these optimists consisted in overrating the elite or the masses or both. At any rate it is a fact that the immense majority of our contemporaries is fanatically committed to policies that ultimately aim at abolishing the social order in which the most ingenious citizens are impelled to serve the masses in the best possible way. The masses — including those called the intellectuals — passionately advocate a system in which they no longer will be the customers who give the orders but wards of an omnipotent authority. It does not matter that this economic system is sold to the common man under the label "to each according to his needs" and its political and constitutional corollary, unlimited autocracy of self-appointed office-holders, under the label "people's democracy." In the past, the fanatical propaganda of the socialists and their abettors, the interventionists of all shades of opinion, was still opposed by a few economists, statesmen, and businessmen. But even this often lame and inept defense of the market economy has almost petered out. The strongholds of American snobbism and "patricianship," fashionable, lavishly endowed universities and rich foundations, are today nurseries of "social" radicalism. Millionaires, not "proletarians," were the most efficient instigators of the New Deal and the "progressive" policies it engendered. It is well known that the Russian dictator was welcomed on his first visit to the United States with more cordiality by bankers and presidents of big corporations than by other Americans. The tenor of the arguments of such "progressive" businessmen runs this way: "I owe the eminent position I occupy in my branch of business to my own efficiency and application. My innate talents, my ardor in acquiring the knowledge needed for the conduct of a big enterprise, my diligence raised me to the top. These personal merits would have secured a leading position for me under any economic system. As the head of an important branch of production I would also have enjoyed an enviable position in a socialist commonwealth. But my daily job under socialism would be much less exhausting and irritating. I would no longer have to live under the fear that a competitor can supersede me by offering something better or cheaper on the market. I would no longer be forced to comply with the whimsical and unreasonable wishes of the consumers. I would give them what I — the expert — think they ought to get. I would exchange the hectic and nerve-wracking job of a business man for the dignified and smooth functioning of a public servant. The style of my life and work would resemble much more the seigniorial deportment of a grandee of the past than that of an ulcer-plagued executive of a modern corporation. Let philosophers bother about the true or alleged defects of socialism. I, from my personal point of view, cannot see any reason why I should oppose it. Administrators of nationalized enterprises in all parts of the world and visiting Russian officials fully agree with my point of view." There is of course, no more sense in the self deception of these capitalists and entrepreneurs than in the daydreams of the socialists and communists of all varieties. The Task of the Rising Generation As ideological trends are today, one has to expect that in a few decades, perhaps even before the ominous year 1984, every country will have adopted the socialist system. The common man will be freed from the tedious job of directing the course of his own life. He will be told by the authorities what to do and what not to do, he will be fed, housed, clothed, educated, and entertained by them. But, first of all, they will release him from the necessity of using his own brains. Everybody will receive "according to his needs." But what the needs of an individual are, will be determined by the authority. As was the case in earlier periods, the superior men will no longer serve the masses, but dominate and rule them. Yet, this outcome is not inevitable. It is the goal to which the prevailing trends in our contemporary world are leading. But trends can change and hitherto they always have changed. The trend toward socialism too may be replaced by a different one. To accomplish such a change is the task of the rising generation. - 1. Horace Kallen, "Behaviorism," in Encyclopaedia of the Social Sciences, vol. 2 (New York: Macmillan, 1930), p. 498. - 2. Karl Marx, Critique of the Social Democratic Program of Gotha [Letter to Bracke, May 5, 1875] (New York: International Publishers, 1938). - 3. [For example, John K. Galbraith, The Affluent Society (Boston: Houghten Mifflin, 1958) — Ed.] - 4. Vance Packard, "Babes in Consumerland," The Hidden Persuaders (New York: Cardinal Editions, 1957) pp. 90-97. - 5. Ibid., p. 95 - 6. Ibid., p. 93. - 7. Leon Trotsky, Literature and Revolution, R. Strunsky, trans. (London: Geroge Allen and Unwin, 1925), p. 256. - 8. Marx, Critique of the Social Democratic Program of Gotha.

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San Diego State professors recently assisted NASA in discovering the first cicumbinary planet – a planet that orbits two suns. The professors worked as part of the Kepler Mission team at the SETI Institute in Mountain View, California. Kepler Mission primarily searches for Earth-size and smaller planets in the habitable zone of other stars in our neighborhood of the galaxy, according to NASA. Astronomy professors Jerome Orosz and William Welsh, along with former College of Sciences Dean Donald Short, analyzed the Kepler-16 data. They were able to determine the properties of the stars including their sizes and to measure the planet's mass. “The discovery of Kepler-16 is perhaps the biggest discovery in exoplanet studies since the discovery of 51 Pegasi,” said Orosz. The discovery of 51 Pegasi in 1995 was the first sun-like star found to have a planet orbiting it. The planet is similar to the fictional planet Tatooine in Star Wars, according to NASA. But unlike Tatooine, Kepler-16b is cold, gaseous and not thought to harbor life. “Kepler-16b shows us that planetary bodies can exist in circumbinary orbits,” said Orosz. “The Kepler Mission represents a huge step forward not only in planetary science, but in the study of stars.”

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GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video It is currently 01 Jun 2020, 08:35 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # (44^4 − 44)/44 = Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 64114 ### Show Tags 28 Aug 2018, 04:28 1 5 00:00 Difficulty: 15% (low) Question Stats: 77% (00:53) correct 23% (00:56) wrong based on 144 sessions ### HideShow timer Statistics $$\frac{44^4 − 44}{44} =$$ A. 16,432 B. 70,321 C. 83,244 D. 85,183 E. 93,155 _________________ Director Joined: 20 Feb 2015 Posts: 722 Concentration: Strategy, General Management Re: (44^4 − 44)/44 =  [#permalink] ### Show Tags 28 Aug 2018, 04:32 Bunuel wrote: $$\frac{44^4 − 44}{44} =$$ A. 16,432 B. 70,321 C. 83,244 D. 85,183 E. 93,155 44(44^3 -1)/44 = last digit should be 4-1 = 3 D Director Status: Learning stage Joined: 01 Oct 2017 Posts: 950 WE: Supply Chain Management (Energy and Utilities) Re: (44^4 − 44)/44 =  [#permalink] ### Show Tags 28 Aug 2018, 04:35 Bunuel wrote: $$\frac{44^4 − 44}{44} =$$ A. 16,432 B. 70,321 C. 83,244 D. 85,183 E. 93,155 $$\frac{44^4 − 44}{44} =\frac{44(44^3-1)}{44}$$=$$44^3-1$$ unit digit of 44^3 is 4. hence $$44^3-1$$ has unit digit, 4-1=3 Ans. (D) _________________ Regards, PKN Rise above the storm, you will find the sunshine NUS School Moderator Joined: 18 Jul 2018 Posts: 1120 Location: India Concentration: Operations, General Management GMAT 1: 590 Q46 V25 GMAT 2: 690 Q49 V34 WE: Engineering (Energy and Utilities) Re: (44^4 − 44)/44 =  [#permalink] ### Show Tags 28 Aug 2018, 04:39 =$$\frac{44^4−44}{44}$$ =$$\frac{44^344-44}{44}$$ =$$\frac{44(44^3-1)}{44}$$ =$$44^3-1$$ =Since 4 has a cyclicity of 2. Then $$44^3$$ will end in 4. Hence the unit digit should be 3. VP Joined: 31 Oct 2013 Posts: 1489 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: (44^4 − 44)/44 =  [#permalink] ### Show Tags 28 Aug 2018, 04:39 Bunuel wrote: $$\frac{44^4 − 44}{44} =$$ A. 16,432 B. 70,321 C. 83,244 D. 85,183 E. 93,155 $$\frac{44^4 − 44}{44} =$$ = $$\frac{44(44^3 -1)}{44}$$ = $$44^3 - 1$$ Unit digits of 44^3 is the same as 4^3 . $$4^3 = 64.$$ Now deduct 1 from 4. 4-1 = 3. The only option is D . Target Test Prep Representative Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2800 Re: (44^4 − 44)/44 =  [#permalink] ### Show Tags 30 Aug 2018, 17:09 Bunuel wrote: $$\frac{44^4 − 44}{44} =$$ A. 16,432 B. 70,321 C. 83,244 D. 85,183 E. 93,155 Re-expressing the single fraction as two separate fractions, we have: 44^4/44 - 44/44 44^3 - 1 Instead of calculating the actual difference, let’s only calculate the units digit of the difference. Recall that the pattern of units digits of 4 raised to positive integer exponents is 4, 6, 4, 6, … , so odd powers of 44 will end in 4, and even powers of 44 will end in 6. Thus, we see that 44^3 ends in a 4, so 44^3 - 1 must have a units digit of 3. The only answer choice that is a number with a units digit of 3 is choice D. _________________ # Jeffrey Miller [email protected] 214 Reviews 5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE NOW WITH GMAT VERBAL (PRE-BETA) See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: (44^4 − 44)/44 =   [#permalink] 30 Aug 2018, 17:09

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# 10 imperial gallons in imperial cups ## Conversion 10 imperial gallons is equivalent to 160 imperial cups.[1] ## Conversion formula How to convert 10 imperial gallons to imperial cups? We know (by definition) that: $1\mathrm{imperialgallon}\approx 16\mathrm{brcup}$ We can set up a proportion to solve for the number of imperial cups. $1 ⁢ imperialgallon 10 ⁢ imperialgallon ≈ 16 ⁢ brcup x ⁢ brcup$ Now, we cross multiply to solve for our unknown $x$: $x\mathrm{brcup}\approx \frac{10\mathrm{imperialgallon}}{1\mathrm{imperialgallon}}*16\mathrm{brcup}\to x\mathrm{brcup}\approx 160\mathrm{brcup}$ Conclusion: $10 ⁢ imperialgallon ≈ 160 ⁢ brcup$ ## Conversion in the opposite direction The inverse of the conversion factor is that 1 imperial cup is equal to 0.00625 times 10 imperial gallons. It can also be expressed as: 10 imperial gallons is equal to $\frac{1}{\mathrm{0.00625}}$ imperial cups. ## Approximation An approximate numerical result would be: ten imperial gallons is about one hundred and sixty imperial cups, or alternatively, a imperial cup is about zero point zero one times ten imperial gallons. ## Footnotes [1] The precision is 15 significant digits (fourteen digits to the right of the decimal point). Results may contain small errors due to the use of floating point arithmetic.

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In endurance sports “peaking” refers to the art of attaining maximum performance capacity on the day of a major competition. Peaking is important because the human body is not capable of sustaining maximum performance capacity for a long period of time. If it were, athletes could compete at 100 percent of their potential whenever they pleased. But the training that is required to squeeze out the last 5 percent of one’s potential can be kept up only for a matter of weeks. After that it’s necessary to rest and regenerate. Then, the athlete can start to build toward another peak. Traditionally, peaking has been thought of as an entirely physiological phenomenon. The training load is increased step by step over a period of weeks and the body adapts, becoming stronger and stronger. However, there is evidence that—at least for experienced athletes who are always very fit—peaking may be largely a psychological phenomenon. College cross-country runners, for example, usually start their season with a solid base of fitness that they built up over the summer. They then try to build toward a performance peak that is timed to coincide with the championship races at the end of the season. In a 2010 study, researchers Corey Baumann and Thomas Wetter measured a number of performance variables (anaerobic power, VO2max, running economy, ventilatory threshold, and lactate threshold) in members of the University of Wisconsin-Stevens Point Men’s Cross Country Team at the start of a cross country season and again at the end. Anaerobic power actually decreased significantly while all of the other variables were unchanged. Yet most of the runners produced faster race times at the end of the season than they did at the beginning and reported feeling fitter as well. How were these runners able to race faster despite not getting physically fitter? Baumann and Wetter speculated that psychological factors might be responsible. Specifically, as the season unfolded, the runners’ pain tolerance might have increased through exposure to pain in hard workouts and minor races. Also, their motivation might have increased as the more important championship races drew nearer. Interestingly, psychologists have learned that willpower, much like physical endurance, is a limited resource. In his book, Willpower, psychologist Roy Baumeister wrote, “You have a finite amount of willpower that becomes depleted as you use it.” When you put a lot of willpower into some challenge you must then take a mental break and replenish it before you can be mentally ready for another challenge. But, again like physical endurance, willpower can also be increased through training. Baumeister wrote that “willpower, like a muscle, becomes fatigued from overuse but can also be strengthened over the long term through exercise.” What this means is that the art of peaking applies to both physical and mental challenges (partly because physical challenges are also mental). You can’t expect to perform at 100 percent of your potential every day. It’s better to choose a finite number of important goals to pursue and work incrementally toward each, then give yourself a well-earned break after you’ve achieved them.

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# Resources tagged with: Angle properties of polygons Filter by: Content type: Age range: Challenge level: ### There are 25 results Broad Topics > Angles, Polygons, and Geometrical Proof > Angle properties of polygons ### Bow Tie ##### Age 11 to 14 Challenge Level: Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling. ##### Age 11 to 16 Challenge Level: Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem? ### Tessellating Hexagons ##### Age 11 to 14 Challenge Level: Which hexagons tessellate? ### Polygon Rings ##### Age 11 to 14 Challenge Level: Join pentagons together edge to edge. Will they form a ring? ### Semi-regular Tessellations ##### Age 11 to 16 Challenge Level: Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations? ### Gibraltar Geometry ##### Age 11 to 14 Challenge Level: Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them? ### Arclets Explained ##### Age 11 to 16 This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website. ### Angles Inside ##### Age 11 to 14 Challenge Level: Draw some angles inside a rectangle. What do you notice? Can you prove it? ### Polygon Pictures ##### Age 11 to 14 Challenge Level: Can you work out how these polygon pictures were drawn, and use that to figure out their angles? ### Getting an Angle ##### Age 11 to 14 Challenge Level: How can you make an angle of 60 degrees by folding a sheet of paper twice? ### Convex Polygons ##### Age 11 to 14 Challenge Level: Show that among the interior angles of a convex polygon there cannot be more than three acute angles. ### Star Polygons ##### Age 11 to 14 Challenge Level: Draw some stars and measure the angles at their points. Can you find and prove a result about their sum? ### Which Solids Can We Make? ##### Age 11 to 14 Challenge Level: Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids? ### Always, Sometimes or Never? Shape ##### Age 7 to 11 Challenge Level: Are these statements always true, sometimes true or never true? ### Name That Triangle! ##### Age 7 to 11 Challenge Level: Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know? ### LOGO Challenge 4 - Squares to Procedures ##### Age 11 to 16 Challenge Level: This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles. ### Logo Challenge 3 - Star Square ##### Age 7 to 16 Challenge Level: Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles ### Triangle Pin-down ##### Age 7 to 11 Challenge Level: Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs. ### Fred the Class Robot ##### Age 7 to 11 Challenge Level: Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw? ### Possible Pairs ##### Age 7 to 11 Challenge Level: In this game, you turn over two cards and try to draw a triangle which has both properties. ### Triangles All Around ##### Age 7 to 11 Challenge Level: Can you find all the different triangles on these peg boards, and find their angles? ### Cartesian Isometric ##### Age 7 to 11 Challenge Level: The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form? ### Transformations on a Pegboard ##### Age 7 to 11 Challenge Level: How would you move the bands on the pegboard to alter these shapes? ### First Forward Into Logo 9: Stars ##### Age 11 to 18 Challenge Level: Turn through bigger angles and draw stars with Logo. ### First Forward Into Logo 7: Angles of Polygons ##### Age 11 to 18 Challenge Level: More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

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Composting is a truly simple and highly beneficial process. Yet often, many individuals choose instead simply to dispose of food scraps and other compostable materials into the garbage. Statistically, organic materials are the largest component of municipal waste, with paper and paperboard making up 31% of waste, and yard trimmings and food scraps comprising an additional 26% of total waste. Sent away to landfills, these substances must decompose anaerobically, releasing harmful methane gas into the environment and taking years to break down. In reality, none of these organic materials needs to end up in a landfill, where nutrients that could otherwise offer great enrichment to soil are instead trapped indefinitely. An easy and positive alternative, composting offers a way for every individual to tread a little more lightly upon the environment, and to contribute to rich, healthy soil instead of growing, unmanageable heaps of garbage. Inspired by the popular card game UNO®, Compost Pile UpTM is designed in pursuit of the idea that perhaps the first step to encouraging individuals to compost is to introduce them to the behavior through a simple and enjoyable game. In particular, teaching habits to children from an early age with a game offers not only a way to encourage environmentally conscious behaviors for many years to come, but also provides a manner by which children might be able to take their learning home to share with parents and older siblings. Motivation for developing the game was sparked first in a multidisciplinary course focused on promoting agricultural sustainability in Gujarat, India, concluding in a service-learning trip over our winter break. Tasked with handling education on sustainable practices in schools in conjunction with an established NGO in the region, we found that a simple game using pictures and colors would allow a way to make connections across cultural, age, and language barriers. We developed the game over the course of an academic quarter and then printed the cards, taking several decks abroad with us to share with children in the schools we visited. Upon returning, we also introduced the game to the coordinators of the Cincinnati Civic Center, and plans are currently underway to incorporate the game into their Compost Kids field trip program.

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# How To Check How Much Battery On Airpods Posted on If you are looking for the answer of how to check how much battery on airpods, you’ve got the right page. We have approximately 10 FAQ regarding how to check how much battery on airpods. Read it below. ## At the market, 8 batteries cost \$10 How much do Ask: At the market, 8 batteries cost \$10 How much do 6 batteries cost 7.5 Step-by-step explanation: 8:10 = 6:n [tex] frac{8}{10} = frac{6}{n} \ 8n = 60 \ frac{8n}{8 } = frac{60}{8 } \ n = 7.5[/tex] ## At the market, 8 batteries cost \$10 .How much do Ask: At the market, 8 batteries cost \$10 .How much do 6 batteries cost 7.50\$ Step-by-step explanation: 10÷8=1.25 1.25×6=7.50 \$7.5 Step-by-step explanation: 10÷8= 1.25 ( 1.25 × 8= 10) 1.25×6 =\$7.5 ## At the market 8 batteries cost \$10. How much do Ask: At the market 8 batteries cost \$10. How much do 6 batteries cost? 8\$ Step-by-step explanation: 8=10 25 percent × 4 = 100 percent 8= 2+2+2+2 6= 2+2+2 = 25 percent × 3 = 75 percent What is the 75 percent of 10? =8 #CarryOnLearning #MarkMeAsBrainliest Brainliest answer po sna ## When the flashlight is on, how much current will be Ask: When the flashlight is on, how much current will be drawn from the battery?​ It depends. For AA cells, the digital cameras draw more than a half amp at times. D cells can handle much more than an amp. If you want the batteries to last longer, then the current drain should be less. We’re talking about alkalines here. ## in ₱44.50,how much does each battery cost?​ Ask: in ₱44.50,how much does each battery cost?​ I think, \$50 to \$120, explanation: I’m not sure but hopeitshelp. 5 peso / 20 peso. ## how much voltage is needed in our battery in a Ask: how much voltage is needed in our battery in a phone?​ A typical smartphone battery has a capacity of ABOUT 1500 mAh. This would have C = 1500 mA = max charge current. The phone will charge the battery either at C if ample energy is available or at the lower available rate until a predefined battery voltage is reached (usually 4.2V) Explanation: Mobile phones use Li-Ion batteries. They are nominally 3.7v which is 50% charge and shipped at the voltage. At 100% charge they are 4.2v. So you need a 5v charger. ## When the flashlight is on,how much current will be shown Ask: When the flashlight is on,how much current will be shown from the battery? It depends. For AA cells, the digital cameras draw more than a half amp at times. D cells can handle much more than an amp. If you want the batteries to last longer, then the current drain should be less. We’re talking about alkalines here. ## At the market, 8 batteries cost \$10. how much does Ask: At the market, 8 batteries cost \$10. how much does six batteries cost? \$60 Step-by-step explanation: \$10 x 6 batteries 10 x 6 = \$60 Step-by-step explanation: 8 batteries —> 10\$ For 1 battery —> 10÷8 = 5/4 For 6 Batteries —> (5/4) * 6 = 7.5\$ ## At the market 8 batteries cost 10 dollars how much Ask: At the market 8 batteries cost 10 dollars how much do 6 batteries cost 0.80 dollar just need to make my answer big ## how much Current (A) of 3 batteries?​ Ask: how much Current (A) of 3 batteries?​

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# Question 64184 Jul 17, 2015 You'd need 62 mL of concentrate for the second solution. #### Explanation: So, you know that 5 L of concentrate are used to make a 166-L solution. Assuming that you're dealing with a volume by volume percent concentration, you know that $\text{%v/v" = V_"solute"/V_"solution} \cdot 100$ The volume by volume percent concentration of a solution is defined as the volume of solute divided by the total volume of the solution and multiplied by 100. In your case, the solution will have a v/v percent concentration of $\text{%v/v" = (5cancel("L"))/(166cancel("L")) * 100 = "3.01%}$ Now, for your second solution, the total volume of the solution will be ${V}_{\text{solution" = V_"solute" + V_"water}}$ This means that, in order to get a 3.01% v/v solution that uses 2 L of water, you need to add $\text{%v/v" = V_"solute"/V_"solution} \cdot 100$ "3.01%" = V_"solute"/(V_"solute" + "2 L") * 100# $3.01 \cdot {V}_{\text{solute" + 6.02 = 100 * V_"solute}}$ ${V}_{\text{solute" = 6.02/96.99 = "0.0621 L" = "62 mL}}$ So, to prepare a 3.01% v/v solution with 2 L of water, you need to use 62 mL of concentrate. ALTERNATIVE METHOD Alternatively, you can use something called the dilution factor, which is defined as $\text{DF} = {V}_{f} / {V}_{i}$, where ${V}_{i}$ - the volume of the aliquot; ${V}_{f}$ - the volume of the solution. The first solution will have a dilution factor of $\text{DF" = (166cancel("L"))/(5cancel("L")) = "33.2}$ For the second solution, you know that the volume of the solution is ${V}_{f} = {V}_{\text{solute" + V_"water" = V_"solute" + "2 L}}$ The dilution factor must be the same, so you have $\text{DF" = (V_"solute" + "2 L")/V_"solute} = 33.2$ ${V}_{\text{solute" = "2 L"/32.2 = "0.0621 L" = "62 mL}}$

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What is light pollution? Simply put, light pollution is the unwanted illumination of the night sky created by human activity. Light pollution is sometimes said to be an undesirable byproduct of our industrialized civilization. Light pollution is a broad term that refers to multiple problems, all of which are caused by inefficient, annoying, or arguably unnecessary use of artificial light. Specific types of light pollution include light trespass, over-illumination, and sky glow. Where is light pollution found? The now-classic Earth at Night composite image (left) suggests that light pollution is a problem in many parts of the world, with the worst concentration of light pollution being found in urbanized areas. In the highly industrialized and populated areas such as many parts of Europe, Asia, and North America, light pollution is a real problem. For example, in the Eastern United States, there are many areas where large expanses of land are illuminated at night. As cities and suburban areas grow, the number of lights at night also increases. Why do we care about light pollution? Light pollution is a strong indicator of wasted energy. Lights, contrast, and glare all impact the number of stars that are visible in a given location. Only the brightest stars are visible when there is a lot of nighttime lighting. Many people in the urban locations have never seen the Milky Way. Astronomers (both professional and amateur) have been concerned about the deteriorating quality of the night sky for some time. The excess of light has resulted in obscuring the night sky making observations difficult. It is not surprising to learn that astronomers need very dark skies to conduct their observations and research. In addition to the concerns of astronomers, we have learned that light pollution causes problems to human and environmental health. Medical research on the effects of excessive indoor light on the human body suggests a variety of adverse health effects including increased headaches, fatigue, and stress. There is also a strong case that light pollution is harmful to the economy as well as our ecology. When you look at the Earth at Night image above, think about all that light escaping into space. All of this light is wasted, so all the energy that was produced and consumed to create the light was also wasted. Ultimately, everyone pays for this wasted energy. With the pervasive level of light pollution, the natural patterns of light and dark have been altered, impacting animal behavior. Lights at night can impact both the biology and ecology of species in the wild. Some examples include the disorientation of sea turtle hatchlings by beachfront lighting; nesting choices and breeding success of birds; behavioral and physiological changes in salamanders; disturbances of nocturnal animals; and altered natural light regimes in terrestrial and aquatic ecosystems. Since the 1980's, there has been a global movement to learn more about light pollution, its impacts, and ways to mitigate or reduce its effects. Light pollution impacts most of the world's citizens in one way or another. It may be that you no longer are able to go outside and enjoy an unobstructed view of the night sky.

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Once the fourth largest lake on Earth, the Aral Sea has shrunk dramatically over the past few decades as the primary rivers that fed the Sea were almost completely diverted for cotton farming and other agriculture. The decline of the sea has produced severe environmental, social, and public health problems. As part of a last-hope restoration effort, the World Bank funded the construction of a dam to separate the smaller, but less polluted and salty northern Aral Sea from the southern part. According to a recent article on the New York Times Website, since the dam’s completion in the summer of 2005, the northern Aral Sea has been filling up more rapidly than planners expected. This pair of images from the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite shows the changes in the northern Aral Sea over the past year. The top image is from April 9, 2006, while the bottom image is from April 8, 2005. The most obvious expansion of the lake’s area is in the northeast, where a narrow channel from the main body of the lake connects to a widening pool of shallow, sediment-clouded water. The former shorelines of the lake appear paler brown than the surrounding landscape. A more subtle change is in the width of the channel that connects the main body of the lake to the lake’s most western part; the tip of the peninsula jutting down into the lake appears farther from the southern shore in 2006 than it did in 2005. Some ice remains at the western side of the lake in both images. A thinner strip of ice hugs the southeastern shoreline in the 2005 scene. At lower right in each image is the Syrdar’ya, the northern Aral Sea’s only tributary. NASA images created by Jesse Allen, Earth Observatory, using data obtained courtesy of the Goddard Earth Sciences DAAC

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Learn to Print Worksheets 1-4 Students will practice tracing upper and lower case letters on the first worksheet and they will trace the names of shapes on worksheets 2-4. Each shape word is accompanied by a goofy dragon holding a shape. Similar to Zaner Bloser style font. Grade recommendation: k-1 • Common Core State Standards Alignment: RF.K.1, L.K.1, K.G.2, L.1.1 Skills: handwriting practice | tracing upper case letters| tracing lower case letters | trace and print the names of shapes | math | vocabulary | reading | Zaner Bloser®* style font Item 3491 | 4 pages | Publisher: T. Smith Publishing ©2011 | by Tracey Smith Printing Tip: If a worksheet page does not appear properly, reload or refresh the .pdf file. Click the worksheet preview for the full printable version of Learn to Print Worksheets 1-4. Here are some of the ways our visitors are using these worksheets.• Be the first to share your comments about these worksheets!

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# 6.2.2 SHM Graphs ### SHM Graphs • The displacement, velocity and acceleration of an object in simple harmonic motion can be represented by graphs against time • All undamped SHM graphs are represented by periodic functions • This means they can all be described by sine and cosine curves The displacement, velocity and acceleration graphs in SHM are all 90° out of phase with each other • Key features of the displacement-time graph: • The amplitude of oscillations A can be found from the maximum value of x • The time period of oscillations T can be found from reading the time taken for one full cycle • The graph might not always start at 0 • If the oscillations starts at the positive or negative amplitude, the displacement will be at its maximum • Key features of the velocity-time graph: • It is 90o out of phase with the displacement-time graph • Velocity is equal to the rate of change of displacement • So, the velocity of an oscillator at any time can be determined from the gradient of the displacement-time graph: • An oscillator moves the fastest at its equilibrium position • Therefore, the velocity is at its maximum when the displacement is zero • Key features of the acceleration-time graph: • The acceleration graph is a reflection of the displacement graph on the x axis • This means when a mass has positive displacement (to the right) the acceleration is in the opposite direction (to the left) and vice versa • It is 90° out of phase with the velocity-time graph • Acceleration is equal to the rate of change of velocity • So, the acceleration of an oscillator at any time can be determined from the gradient of the velocity-time graph: • The maximum value of the acceleration is when the oscillator is at its maximum displacement #### Worked Example A swing is pulled 5 cm and then released. The variation of the horizontal displacement x of the swing with time t is shown on the graph below. The swing exhibits simple harmonic motion. Use data from the graph to determine at what time the velocity of the swing is first at its maximum. Step 1: The velocity is at its maximum when the displacement x = 0 Step 2: Reading value of time when x = 0 From the graph this is equal to 0.2 s #### Exam Tip These graphs might not look identical to what is in your textbook, depending on where the object starts oscillating from at t = 0 (on either side of the equilibrium, or at the equilibrium). However, if there is no damping, they will all always be a general sine or cosine curves. Close # Join Save My Exams ## Download all our Revision Notes as PDFs Try a Free Sample of our revision notes as a printable PDF. Already a member?

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The Historic American Buildings Survey (HABS) at the Library of Congress pretends that North America was uninhabited before Jamestown was founded in 1607. The program, administered by the National Park Service, focuses on architecture from the 17th, 18th and 19th centuries. There are two versions of North America’s architectural history. The one that students learn in textbooks might spend a page or two on the “mound builders” in the East and the Anasazi pueblos in the Southwest. It then quickly moves on to the 17th century colonial towns of the St. Lawrence River Valley and Nova Scotia in Canada and on the Atlantic Coast of the United States. The structures built by mankind during the previous 10,000 years are presumed to have been so primitive that they are of no consequence. Obviously, their hovels have melted into the ground from which they came. One must often search the internet for information on the cryptic history of eastern North America. It is the semi-permanent architecture of astronomical observatories, stone veneered mounds; stone cairns, stone effigies, stone-walled agricultural terraces, stone-walled water storage cisterns and the ruins of stone-walled buildings. North America’s Pre-Columbian legacy also includes massive civil engineering projects such as dams, canals, locks and roads built on raised earthen beds. These are undeniable vestiges from the past that rebuke a Eurocentric version of North American history. They were built by peoples who could plan large scale projects, utilize mathematics to make them functional and build long-lasting structures. Examples of these cryptic forms of Pre-Columbian architecture can be found almost everywhere in North America. There are stone monuments on Hudson Bay and hundreds of stone circle observatories elsewhere in Canada. Some predate Stonehenge. There are hundreds of man-made stone structures in the Maritime Provinces and New England states. In the Midwestern United States, one can see stone-walled houses in the suburbs of Kansas City and several, massive stone-walled complexes in the Ohio River Basin that archaeologists, for lack of any complete understanding, label “stone enclosures.” Stone enclosures can also be found in Kentucky, Tennessee and Georgia. The Appalachians and Southern Piedmont are especially rich in stone architecture and monuments. Complexes of ancient stone cairns can be found from Winchester, Virginia southward to northeastern Alabama and central Georgia. The large agricultural terrace complexes are concentrated in northeast Georgia, but have also been reported in the South Carolina Uplands, Tennessee, Kentucky and Virginia. Florida does not have stone architecture, but it contains the ruins of numerous Native American towns around Lake Okeechobee, whose sophistication predates anything else seen north of Mexico. Hundreds of miles of canals with locks, plus earthen causeways interconnected these towns. They were studied and documented by skilled archaeologists in the late 20th century, but “swept under the rugs” by their peers. The early construction dates and technical sophistication of these towns refute the current archaeological orthodoxy. If a person wants to learn about architecture of the Ortona town site, one of the few places for obtaining comprehensive information is in this Examiner column. (See link below.) In the 21st century, this cryptic history is forbidden knowledge. The archaeology profession has fossilized. After the 1950s, most archaeologists didn’t want to discuss Pre-Columbian stone structures because they did not fit into a simplistic understanding of North America’s past adopted at a conference at Harvard University in 1947. Is it coincidence that this conference was concurrent with the “Roswell Incident?” If not understood, it’s a fantasy The best example of how small minds and Eurocentric prejudices created a hidden history in North America is a book by 17th century French Huguenot ethnologist, Charles de Rochefort, entitled, “Histoire Naturelle et Morale des Iles Antilles de l'Amerique. “ In 1658, De Rochefort wrote this comprehensive book about the indigenous peoples, animals and plants of the Caribbean Basin. It included a chapter on the Appalachian Mountains of northern Georgia, because the region had just been made accessible in 1646 when the Spanish built a pack-mule trail from St. Augustine to a fortified trading post in the Nacoochee Valley. The first edition of the book was written anonymously because the Inquisition had banned all books written by Protestant clergy. De Rochefort was also a highly respected, French Huguenot minister. One will have to be fluent in French, Dutch or German to read most contemporary articles on De Rochefort. European anthropologists and historians consider him to be the leading authority on the Caribbean Basin in the 17th century. Their commentaries sometimes express puzzlement as to why the stone structures that De Rochefort described in northern Georgia are not accessible to the public today. De Rochefort is virtually unknown in North American academic circles. The Apalache Chronicles is the only English language book that presents De Rochefort’s translated text about the Appalachian Mountains and then links locations that he mentioned with known archaeological sites and Native American cultural traits. For example, de Rochefort described the colorful clothing of the Apalache Indian elite. Their clothing was almost identical to the traditional clothing worn by the Florida Seminoles today. At some time in the late 19th or early 20th century, North American anthropology and history professors placed a taboo label on De Rochefort’s book. Although the book was still well known in Europe, appreciation of De Rochefort’s book in the United States ceased. What few copies American libraries had were not re-printed for general circulation. The Brown University Library has an original copy of the book written by Charles de Rochefort. It is in the “Fantasy and Utopia” bin of the library. An anonymous professor somewhere in the past had decided that the fictitious description of stone towns and temples on the sides of mountains in Georgia negated the credibility of the book’s entire contents. Obviously, we now know that such structures really existed. In 1939 the famous archaeologist, Robert Wauchope, studied the locations in the Georgia Mountains where De Rochefort described Apalache temples and towns. He was puzzled by the stone ruins and in particular, a massive U-shaped Itza Maya style ball court in the Nacoochee Valley. Actually, he didn’t even realize that it was a ball court. Wauchope was not aware that explorer and botanist, William Bartram, recorded some of these courts still in use during the 1700s. Wauchope assigned the strange stone architecture ruins official site numbers, but didn’t draw or photograph them. He soon moved to Kentucky. In 1951, Harvard archaeologist, Phillip White, followed in Wauchope’s footsteps. He was likewise puzzled by the stone building ruins, U-shaped ball court, stone walls and stone veneered mounds in northeast Georgia , but after then, they were forgotten. Back to the future The HABS program began in 1933 as a make-work program for architects, civil engineers and landscape architects. Teams of architects, engineers, landscape architects and photographers were dispatched by the new National Park Service to document America’s heritage. The program is still in existence, but now accumulates most graphics in the process of buildings being restored with federal funds. Ironically, the unemployment rate and firm closures for architects in the Southeast has been much higher during the current Great Recession than it was during the Great Depression. However, this time around, design professionals are not considered politically significant. HABS became the spark that kicked off the historic preservation movement in the United States. For several decades thereafter, architecture schools generally ignored historic buildings and taught modernism. However, more and more practicing architects became fascinated with America’s architectural heritage. Their enthusiasm eventually filtered back into educational programs. The curricula restructuring did not extend back to architecture before Jamestown, however. The first archaeologists were architects. English architect, Frederick Catherwood, and American diplomat, John Lloyd Stephens, jointly introduced the Maya civilization to the world. However, in the late 19th century, as archaeology matured as a forensic profession focused on artifacts, increasingly fewer American architects were involved with archaeological studies. A 20th century love affair with modernism temporarily ended the American architecture profession’s interest in anything old. In Europe and Latin America, architects continued to be professionally involved with things old and ancient. Something significant was lost in the divorce between architects and archaeologists in North America. While most architects would not have the patience to extract an artifact from the soil with a tooth brush and mini-trowel, they do view communities in an environmental context and at a regional scale. As American archaeologists increasingly focused on the micro-scale, they increasingly missed important evidence from the architecture, town plans and regional context. A good example of this problem occurred during the “Mayas in Georgia” controversy. The archeologist, who dug test pits in the Kenimer Mound near the Track Rock Terrace Complex was puzzled that the large five sided mound was sculpted from a hill. He didn’t realize that pentagonal mounds sculpted from hills and stone box graves were commonplace in the Itza Maya sites of Mesoamerica. Stone box graves were endemic in the valley around the Kenimer Mound, The Itza tradition of five sided mounds sculptured from hills and stone box graves was unknown to those Southeastern archaeologists, who specialize in indigenous artifacts. Some archaeologists in the region went bonkers when someone outside their profession dared to know something that they didn’t know. They were not accustomed to working in a multidisciplinary environment that is the norm for architects, engineers, geologists and surveyors. Shrill banshees screamed, “self-styled historian,” pseudo-archaeologist” and “amateur blogger” to an audience that didn’t care. A 21st century understanding of America's past had already left the train station. One of the things that architects are particularly good at, is documenting and analyzing three dimensional objects. Many of the stone architecture sites are in archaeological zones covering hundreds of acres. To commission full-blown archaeological studies on a substantial percentage of them is fiscally unfeasible. However, documentation is the first step for preservation. The National Park Service's HABS program is the ideal framework to sponsor such documentation. There is much more to America’s architectural heritage than just those buildings done by the newcomers.

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What is Norovirus? Norovirus is the leading cause of gastroenteritis, or what we commonly think of as stomach flu symptoms. It causes 23 million cases of gastroenteritis per year, or over half of all gastroenteritis cases in the U.S., and is the second most common virus after the common cold. Norovirus is usually transmitted from the feces to the mouth, either by drinking contaminated food or water or by passing from person to person. Because noroviruses are easily transmitted, are resistant to common disinfectants, and are hard to contain using normal sanitary measures, they can cause extended outbreaks. What are symptoms of Norovirus infection? The norovirus incubation period tends to be 24 to 48 hours, after which symptoms begin to appear. An infection normally lasts only 24 to 60 hours. However, in some cases, dehydration, malnutrition, and even death can occur. These complications are more likely among children, older people, and patients in hospitals and nursing homes with weakened immune systems. Common symptoms include nausea, diarrhea, vomiting, abdominal pain, headache, and low-grade fever. You can learn more about norovirus food poisoning at FoodborneIllness.com.

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## How To Find If Vectors Are The Basis Of R2 #### Determining if vectors form a basis YouTube This de–nition tells us that a basis has to contain enough vectors to generate the entire vector space. But it does not contain too many. In other words, if we removed one of the vectors, it would no longer generate the space. A basis is the vector space generalization of a coordinate system in R2 or R3. Example 298 We have already seen that the set S = fe 1;e 2gwhere e 1 = (1;0) and e 2 #### Determine whether the set of vectors is a basis for R3 of coordinates of vectors under a change of basis. We will focus on vectors in R2, although all of this generalizes to Rn. The standard basis in R2 is nh 1 0 i; h 0 1 io. We specify other bases with reference to this rectangular coordinate system. Let B = fu;wgand B0= fu0;w0gbe two bases for R2. For a vector v 2V, given its coordinates [v] B in basis Bwe would like to be able to express v in #### How to extend a set to form a basis? Physics Forums The first issue has to do with the order of the basis vectors. A basis was defined to be a certain type of set of vectors. Technically, the order of elements in a set is irrelevant, so the sets {i, j, k} and {i, k, j} are just different ways of writing the same basis. #### Find An Orthonormal Basis {u1u2} For R2 Such That 18/06/2011 · i want to extend the set S={(1,1,0,0),(1,0,1,0)} to be a basis for R4. I know I am going to need 4 vectors, so i need to find 2 more that aren't linear combinations of the first 2. How to find if vectors are the basis of r2 #### How to extend a set to form a basis? Physics Forums 26/11/2017 · These vectors span the subspace of vectors on the form (0,0,z,w), the projection of your vectors onto the orthogonal complement of that subspace clearly form a basis of it. Done. If you would want to check by computing the determinant, it would be 2. #### SOLUTION Find a basis of R^4 which contains the vectors 26/07/2009 · Determine whether the set of vectors is a basis for R3. Given the set of vectors {[1,0,0] ,[0,1,2]} decide which of the following statements is true: A: Set is linearly independent and spans R3. Set is a basis for R3. B: Set is linearly independent but does not span R3. Set is not... #### Find a matrix P such that [x]of R=P[x]of B (please tell me Consider the basis B of R2 consisting of vectors. 2 -2 and 4 5 Find x in R2 whose coordinate vector relative to the basis B is xB= -6 1 (x above looks like the absolute value, but I dont have absolute … #### Let B be the basis of R2 consisting of the vectors [3 0 This de–nition tells us that a basis has to contain enough vectors to generate the entire vector space. But it does not contain too many. In other words, if we removed one of the vectors, it would no longer generate the space. A basis is the vector space generalization of a coordinate system in R2 or R3. Example 298 We have already seen that the set S = fe 1;e 2gwhere e 1 = (1;0) and e 2 #### Determine whether the set of vectors is a basis for R3 The elements of a basis are called basis vectors. Equivalently B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B . [1] In more general terms, a basis is a linearly independent spanning set . #### SOLUTION Find a basis of R^4 which contains the vectors those vectors. Basis and dimension A basis for a vector space is a sequence of vectors v1, v2,v d with two proper­ ties: • v1, v2,v d are independent • v1, v2,v d span the vector space. The basis of a space tells us everything we need to know about that space. 1 Example: R3 1 0 0 One basis for R3 is 0 , 1 , 0 . These are independent because: 0 0 1 1 0 0 0 c1 0 + c2 1 + c3 0 #### Determining if vectors form a basis YouTube 18/11/1996 · In other words, for a set of vectors to form a basis, you have to be able to express any ordered triple (x,y,z) in R^3 as a linear combination of those vectors, and you can't be able to express a vector in the set as a combination of other vectors in the set. For (a) you can't express every possible ordered triple as a combination of those two vectors. A counterexample is (0,0,1). Imagine that #### Let B be the basis of R2 consisting of the vectors [3 0 Yes, your set of vectors is a basis for \$\mathbb R^3\$: they are linearly independent, and they span \$\mathbb R^3\$ – amWhy Jun 16 '13 at 2:21 OK, that's actually a bit of a relief. 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You don’t have to be in high school math to play with conics, orbits, and projectile motion. This week (or month) learners can play with projectile motion, orbits, and conics sections with the activities below: 1.) Slicing cones - Learners can mold cones with clay and slice to see the possible shapes. This will give circles, ellipses, parabolas, and hyperbolas. - Create a cone sculpture with an intersecting plane using paper, string, pipe cleaners, or other mediums. - Try John Sharp’s sliceform template. - Check out this Conics Geogebra tool by Irina Boyadzhiev. 2.) Observe parabolas through projectiles - Create a straw rocket (don’t aim it at someone) and take slow motion videos of their flight and observe the curve that is created. For a template and activity, go to NASA’s website here. Look at various launch angles and analyze the differences and similarities in curves. - Create a water balloon launcher with PVC pipes (or other parent/teacher approved apparatuses). Record their launches and analyze. (Water rockets are also fun.) - Play with a garden hose and the curves created by shooting water up into the air. - Play with the PhET simulator. 3.) Play with ellipses and circles through gravity - Use tacks and string to create ellipses (2 tacks) and circles (1 tack or compass). Create an abstract work of art with these tools. - Play with this gravity simulator by the NSTMF (really fun!) - Universe Sandbox is a program that costs money, but is excellent for playing with orbits and answering a lot of learners’ “what-if’s.” I love, love, love this tool! - JPL learning activities are here. - Use a large piece of elastic cloth and place weights in it. See if you can create orbits with marbles. We have found that a hula hoop works with swimsuit material. Here is a video as well. - Take time to get outside and observe the planets, comets, and astronomy that is with us every day. There are so many other ways to play with these curves, so experiment, draw/paint, and enjoy.

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Reflection: Rigor Skill Based Mixed Review - Section 4: Independent Practice Often times, students are asked solve word problems. I have increased the rigor by asking students to write their own examples.  When writing word problems, students need to make sense of the operation and choose reasonable situations to represent the equation.  To help provide some structure, I ask students to write problems about equations they have already solved.  This allows me to push their thinking to write a problem without expecting them to generate the problem as well. Students are likely to have the most difficulty when writing a problem to represent a fraction multiplied by (x) another fraction situation.  Here, they are finding a part of a whole.  This can seem similar to subtraction of fractions (where they are taking part of a whole away from part of a whole).  I made the decision to let the students try writing these problems with no advance assistance.  I think they will learn more from their mistakes than copying a model problem I create. These ideas are complex and need constant revisiting to help students really make sense of them.  I think moving forward I will do some modeling with students in the class.  Physically moving them into groups to show the difference between subtraction and multiplication with fractions. For example: 5/10 of the class is standing.  If 3/10 of the class sits down, how many will be standing? 5/10 of the class is standing.  If 3/10 of that group sit down, how many will be standing? These complex concepts are challenging for the students, but it is important to push their thinking. By asking them to write their own problems, I am teaching them to consider these important details. Then, when solving problems they can use the same details to determine the operation to use. Skill Based Mixed Review Unit 4: Multiplying and Dividing Fractions Lesson 12 of 13 Big Idea: Students have an opportunity to show what they know about fractions in this skill based mixed review activity. Print Lesson 4 teachers like this lesson Standards: Subject(s): Math, subtracting functions, Fractions, Number Sense and Operations, adding fractions, multiplying fractions, dividing with fractions, Critical Area 35 minutes Julie Kelley Similar Lessons Pretest 6th Grade Math » Fraction Operations Big Idea: What do students already know about fractions? What gaps do students have in their understanding? Students take the fractions pretest in order to inform instruction. Favorites(36) Resources(9) Somerville, MA Environment: Urban 6th Grade Math » Number Sense Big Idea: Using common denominators with fractions will help the students learn to divide fractions. Favorites(17) Resources(24) Plainfield, IL Environment: Suburban

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DNA study reveals evolution of beer yeasts (9/12/2008) Lager lovers convinced that their beer of choice stands alone should prepare to drink their words this Oktoberfest. New research by geneticists at the Stanford University School of Medicine indicates that the brew, which accounts for the majority of commercial beer production worldwide, owes its existence to an unlikely pairing between two species of yeast-one of which has been used for thousands of years to make ale. |Lager, which accounts for the majority of commercial beer production worldwide, owes its existence to an unlikely pairing between two species of yeast-one of which has been used for thousands of years to make ale.| The research offers a fascinating glimpse into the early history of beer brewing, as well as an unheralded sneak peek at the early days of the evolution of a new yeast species. Then, as now, brewers reused yeast in several successive fermentation batches, unconsciously selecting for the traits that made the most desirable beer. "These long-ago brewers were practicing genetics without even knowing it," said geneticist Gavin Sherlock, PhD. "They've given us a very interesting opportunity to look at a relatively young, rapidly changing species, as well as some very good beer." The research was published online Sept. 11 in Genome Research. It all started with some unhappy Bavarians. Dissatisfied with the quality of beer brewed in the summer months, they forbade brewing the beverage when the weather was warm. However, colder winter temperatures inhibited fermentation by the ale yeast that had been used for hundreds of years and fostered an unlikely pairing with a second, heartier species-producing an unusual crisp, clear brew that became today's lager. Sherlock, an assistant professor of genetics, and Barbara Dunn, PhD, a senior research associate at the medical school, studied the genetic sequences of 17 unique lager yeast strains from breweries in Europe and the United States. They used customized DNA microarrays capable of analyzing the relative contribution of each parent, combined with limited DNA sequencing, to determine that the hybridization event actually occurred not once, as previously speculated, but twice. This genetic encore suggests that each partner brought specific, unique advantages to the match. "It's possible that the ale strain provides a certain flavor profile, while the second strain conferred the ability to ferment at cooler temperatures," said Dunn. "Mixing them together is a nice way for the yeast to double its genetic options." Traditionally, ales are fruity-flavored and likely to be cloudy. Although they may have a more complex flavor profile than lagers, they are best consumed at warmer temperatures and are less stable. In fact, the word "lager" is a derivative of a German word that means "storage." Most yeast reproduce primarily by asexual budding-pinching off one identical daughter cell after first duplicating the parent's genetic material. Occasionally they go through sexual reproduction and form spores that can mate with another spore of the same species and then continue to bud asexually. The parental strains of the lager yeast chose yet another path. They looked outside their own kind, hybridizing (or fusing) to form a blend of both species better suited to the new, colder conditions. The participants in this microscopic alliance were members of a larger genus known as Saccharomyces. One species in the group, Saccharomyces cerevisiae, commonly known as "bakers' yeast," has been used for thousands of years to make both bread and ale. S. cerevisiae grows best at temperatures between about 85 and 90 degrees Fahrenheit. The other, S. bayanus, grows best at about 70 to 75 degrees and can tolerate even colder temperatures. Together they formed a lineage known as S. pastorianus. Sherlock and Dunn compared the S. cerevisiae parent of pastorianus to a variety of strains, including those involved in fermenting wine and sake, before pegging it as an ale-specific strain. "We were excited to find this connection, because it makes so much sense," said Sherlock. "The same breweries were used for both ale and lager, so it was really gratifying." As often happens, the offspring of such an unconventional union exhibited abnormal amounts of genetic material. Sherlock and Dunn believe that one lineage began with approximately equal amounts of each yeast's genome, whereas the other has between two to three more times S. cerevisiae than S. bayanus DNA. Studying the spread of the two groups provides a genetic snapshot of lager brewing in Europe during the past 600 years: one lineage is associated primarily with Carlsberg breweries in Denmark and others in what is now Czechoslovakia, while the other group localizes to breweries in the Netherlands, including Heineken. Furthermore, it's normal after such a hybridization event for the progeny to slowly lose excess DNA. Parsing out what has been lost and when in the relatively young hybrids is one way researchers can shed light on the process of evolution and the specific genes responsible for pleasing the palates of beer drinkers worldwide. "When we look at the genes that have either been lost or amplified in copy number, we can make the case that some of them could be related to brewing," said Sherlock. Specifically, the researchers identified differences in genes involved in sugar metabolism and the clumping of the yeast after fermentation. Why was beer so important in the Middle Ages? "Beer, or ale, was the standard drink at the table," said Dunn. "Alcohol was considered healthy, in part because water at that time was often contaminated. And if you're drinking beer every day, you might want something that tasted pretty good." The research was funded by the National Institutes of Health and the National Science Foundation. Note: This story has been adapted from a news release issued by the Stanford University School of Medicine

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Successfully reported this slideshow. Upcoming SlideShare × # Chapter1.7 See all ### Related Audiobooks #### Free with a 30 day trial from Scribd See all • Full Name Comment goes here. Are you sure you want to Yes No • Be the first to comment • Be the first to like this ### Chapter1.7 1. 1. Commutative andCommutative and Associative PropertiesAssociative Properties 2. 2. Commutative and Associative Properties • Properties refer to rules that indicate a standard procedure or method to be followed. • A proof is a demonstration of the truth of a statement in mathematics. • Properties or rules in mathematics are the result from testing the truth or validity of something by experiment or trial to establish a proof. • Therefore, every mathematical problem from the easiest to the more complex can be solved by following step by step procedures that are identified as mathematical properties. 3. 3. Commutative and Associative Properties • Commutative Property means changing the order in which you add or subtract numbers does not change the sum or product. • Associative Property means changing the grouping of numbers when adding or multiplying does not change their sum or product. • Grouping symbols are typically parentheses (),but can include brackets [] or Braces {}. 4. 4. Commutative Property of addition - (Order) Commutative Property of addition - (Order) Commutative Property of multiplication - (order) Commutative Property of multiplication - (order) For any numbers a and b , a + b = b + a.For any numbers a and b , a + b = b + a. For any numbers a and b , a • b = b • a.For any numbers a and b , a • b = b • a. 45 + 5 = 5 + 4545 + 5 = 5 + 45 6 • 8 = 8 • 66 • 8 = 8 • 6 50 = 5050 = 50 48 = 4848 = 48 Commutative PropertiesCommutative Properties 5. 5. Associative Property of addition - (grouping symbols) Associative Property of addition - (grouping symbols) Associative Property of multiplication - (grouping symbols) Associative Property of multiplication - (grouping symbols) For any numbers a, b, and c, (a + b) + c = a + (b + c). For any numbers a, b, and c, (a + b) + c = a + (b + c). For any numbers a, b, and c, (ab) c = a (bc). For any numbers a, b, and c, (ab) c = a (bc). (2 + 4) + 5 = 2 + (4 + 5)(2 + 4) + 5 = 2 + (4 + 5) (2 • 3) • 5 = 2 • (3 • 5)(2 • 3) • 5 = 2 • (3 • 5) (6) + 5 = 2 + (9)(6) + 5 = 2 + (9) 11 = 1111 = 11 (6) • 5 = 2 • (15)(6) • 5 = 2 • (15) 30 = 3030 = 30 Associative PropertiesAssociative Properties 6. 6. Evaluate: 18 + 13 + 16 + 27 + 22 + 24Evaluate: 18 + 13 + 16 + 27 + 22 + 24 Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) Rewrite the problem by grouping numbers that can be formed easily. (Associative property) This process may change the order in which the original problem was introduced. (Commutative property) (18 + 22) + (16 + 24) + (13 + 27)(18 + 22) + (16 + 24) + (13 + 27) (40) + (40) + (40) = 120(40) + (40) + (40) = 120 Commutative and Associative PropertiesCommutative and Associative Properties • Commutative and Associative properties are very helpful to solve problems using mental math strategies. 7. 7. Evaluate: 4 • 7 • 25Evaluate: 4 • 7 • 25 Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property) Rewrite the problem by changing the order in which the original problem was introduced. (Commutative property) Group numbers that can be formed easily. (Associative property) 4 • 25 • 74 • 25 • 7 (4 • 25) • 7(4 • 25) • 7 (100) • 7 = 700(100) • 7 = 700 Commutative and Associative PropertiesCommutative and Associative Properties • Commutative and Associative properties are very helpful to solve problems using mental math strategies. Total views 357 On Slideshare 0 From embeds 0 Number of embeds 40 10 Shares 0

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Spiral galaxies provide us with some of the best views in our night sky, and many of the most well known galaxies are actually spirals. They’re named as such because of their swirling appearance, which means that they end up looking like a throwing ninja star. Unlike irregular galaxies, a spiral galaxy can usually be easily identified – this is made even easier with high powered equipment like the Hubble Space telescope. Spiral Galaxy Facts - There are many different examples of galaxies that are spirals, including the Triangulum Galaxy, the Whirlpool Galaxy and the Pinwheel Galaxy. - Until 2005, we defined the Milky Way as a spiral galaxy. However, upon closer inspection we confirmed that it us actually a barred spiral galaxy. - The center of a spiral galaxy is something we call the Bulge, which is a very large group of stars, giving a super bright appearance. - Along with the other types of galaxy, the Spiral galaxy was first defined by Edwin Hubble in 1936. - Spiral galaxies are further classified by how tight their arms are e.g. A-type have tight arms, whereas C type have loose arms. - The former oldest spiral galaxy in our universe is called BX422. It is thought to be around 11 billion years old, two billion years older than any others. This was replaced in 2020 by the Wolfe Disk galaxy, which is more than 12 billion years old. - The larger a galaxy is, the faster that it spins – larger galaxies can spin twice as fast as smaller ones. - Large spiral galaxies can spin their arms at a speed of more than 1.25 million miles (2 million km) per hour. - The closest spiral galaxy to our Milky Way is the Andromeda galaxy. - The first galaxies were actually discovered in the 17th Century, although they were not called galaxies until much later by Edwin Hubble. What is the structure of a spiral galaxy? When we’re considering a spiral galaxy, we generally look for different parts that make up its structure. We have the bulge. which is a high concentration of stars right in the middle of the galaxy. Another important part of a galaxy is its arms, which are regions of stars that give it its spiral appearance. As well as this, we also potentially have a bar of stars in its center – however, this is only the case for barred spiral galaxies. Many time a spiral galaxy won’t actually have this in its center, in which cases, it’s a regular or ordinary spiral. When a galaxy like this has very well defined spiral arms, then we refer to it as a grand design spiral galaxy. It’s usually very easy to identify these types of spiral arms, in comparison to a multi-arm spiral galaxy, which may be much more difficult to identify. Most Asked Questions about Spiral Galaxies Do elliptical galaxies evolve into spiral galaxies? It was first thought by Edwin Hubble that the elliptical galaxy actually evolved into a spiral galaxy. However, this was later disproven by astronomers (this happens with quite a lot of stuff from past theories, as we get more and more data and ability to study theories from astronomers of the past). What are the two types of spiral galaxy? If you see someone talking about the two different types of spiral galaxy, they’re generally referring to the difference between a spiral galaxy and a barred spiral galaxy. However, there are more classifications of spiral galaxy within each type. How is a spiral galaxy formed? The first thing we need to understand about the arms of the spiral is that they are not connected – they are just stars grouped together to give this appearance. It’s thought that these arms of a spiral galaxy are actually density waves, which are like sound waves, that move around the galaxy much slower than it’s stars. What are the characteristics of a spiral galaxy? Spiral galaxies tend to be very easy to identify from other types of galaxy. They have a big bright spot in the middle, which we called the bulge – this is a big group of stars that are within close proximity of each other. Outside of this is the spiral, or the arms of the galaxy, which are typically spirally around the bulge in the center. What is an example of a spiral galaxy? There are many different spiral galaxies that are visible in our night sky. In fact, more than 75% of all the visible galaxies are spirals! Probably the best example of a true spiral galaxy is the Pinwheel galaxy, which is a face-on spiral galaxy. All in all, spiral galaxies are the most abundant in our night skies, with many people thinking they’re the most attractive galaxies too. With many of our most well known galaxies being spirals, it makes sense that they are the most well known within astronomy.

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Equilateral triangle in hyperbolic plane Show that there is an equilateral triangle with angles $\pi/m$ for any integer $m\ge4$. What is the corresponding result for regular n gon? My attempt: I know that area of triangle in hyperbolic plane is $\pi-(sum \ of \ angles\ of\ triangles)$ . Let y axis be my first line choose second line to be a semicircle with centre right of origin such that it makes an angle $\pi/m$ with y axis .Choose third line to be semicircle with centre on left of origin with angle $\pi/m$ with y axis and the area of triangle by the three lines is $3\pi/m$. 1.Why should the third line intersect second line? 2.How do i write this proof rigourously? I have very little knowledge in this subject so i would prefer an elementary answer. • Which model of hyperbolic geometry do you use? Using the origin works in the Poincaré disk model but semi circles belong to the Poincare halfplane model don't mix them up – Willemien Jul 13 '17 at 18:19 • I am using upper half plane model – user345777 Jul 13 '17 at 18:51 • by right of origin i mean the semi circle has centre on +ve x axis – user345777 Jul 13 '17 at 18:53 • Not sure if your method will work at all maybe better just calculate the side lengths see en.wikipedia.org/wiki/Hyperbolic_triangle general trigonometry start with the point (0,1) then you can calculate the second point on the y axis and so on – Willemien Jul 13 '17 at 19:17 What is the corresponding result for regular $n$ gon? A regular $n$-gon is highly symmetric. If you draw all the axes of reflective symmetry, the portion between two such axes is a right-angled triangle. One of its corners is at the center, with an interior angle of $\pi/n$ (because $2n$ of these form the full circle), another is at a vertex of the $n$-gon, with the interior angle being half that of the $n$-gon. The third corner is a right angle at the center of an edge of the $n$-gon. So if you want interior angles of $\pi/m$ at the corners of a regular $n$-gon, you want to know whether there exists a hyperbolic triangle with angles $\frac\pi{n}, \frac\pi{2m}, \frac\pi2$. The sum of these angles being less than $\pi$ is both necessary and sufficient for the existence of such a triangle. You can then continue by computing the edge lengths of such a triangle, and then constructing the $n$-gon from that. for an equilateral triangle with angle $\alpha$ and side $s$ the following relations hold ( see https://en.wikipedia.org/wiki/Hyperbolic_triangle#Trigonometry_of_right_triangles aand a bit of puzzeling) $$\cos \alpha = \frac {\tanh \frac12 s } {\tanh s }$$ and $$\cosh\frac12 s = \frac {\cos \frac12 \alpha } {\sin \alpha }$$ then with this knowledge you have enough to construct equilateral triangle for the poincare halfplane for example point $A = (0,1)$ and $B = \ln(s)$ and then construct the lines under angle $\alpha$ through $A$ and $B$ good luck

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The analyzer is designed to handle many simultaneous noise and background signals at once, and can concentrate on whichever one you specify, including its harmonics. To do that, you need to specify where on the spectrogram you are interested in. You can look on the spectrogram (drag the magnifying glass over a region to zoom in) and find the approximate region of the spectrogram where your waveform of interest is located (specifically, the approximate time and approximate frequency of its fundamental). |Old Method||Visual inspection ("eyeballing")||⇒||Imprecise result| |New Method||Visual inspection ("eyeballing")| Enclosing an event on the spectrogram with a box -- this causes the program to analyze only what is inside the box, and precisely locate the statistical center of activity. The program provides a statistical description of the sound event, so you can describe the sound using just a few concise numbers. To create a box enclosure, enter command "4" in the command window. You specify one box to enclose the fundamental frequency only. For the center position of the box, enter your guess of the fundamental frequency, and your guess of the time (or equivalently, the exact time you would like to analyze). Thus, the position of the box is established. The next step is to set the width and height of the box (measured in time and frequency). Make sure the box surrounds spectral peak, with approximately a 20% margin around it. Remember again that this initial box should only surround the fundamental of the event. If you specify several harmonics, then the program propagates your original box and creates additional boxes, in order enclose each harmonic separately. If the higher-harmonic boxes miss their respective harmonics, you will need to redo the box trial with a better estimate of the fundamental frequency, since that is what sets the locations of the other boxes. Finally, the program performs some matrix calculations, and determines a very precise readout of the frequency and time of the event enclosed inside the boxes. Remember that enclosing only part of the event's peak produces incorrect results, since the program only considers what is going on inside the boxes. Here is an example of how an event on the spectrogram can be enclosed. We decide we want to measure a tone that occurred around 4.95 seconds. We first zoomed in around the event (with the magnifying glass tool, clicking and dragging over the event to zoom in). To enclose this event with a box, we should decide on a box shape that will capture as much useful information as possible, but reject irrelevant information. To enclose a relatively stable range of frequencies, our box will be centered at 4.95 seconds, with a duration of 0.1 seconds. The fundamental appears to be centered near 200 Hz (though the program will give a much more precise result). We try to enclose the 9 harmonics that are visible. 4 = Enclose a region with a box, and analyze (add trial) 7 = New SPIRAL (same spectrogram) | 17=Zoom Close-up 8 = New SPECTROGRAM (same waveform) | 18=Zoom Harmonics 9 = Open another WAVEFORM | 19=Zoom Entire Spec. 0 = Quit >4 Specify a region of the spectrogram to analyze. Box: Freq at centre: 200 Box: Freq width: 100 Box: Time at centre: 4.95 Box: Time width: .1 1= enclose a frequency-limited event (leaks through sides of box) 2= enclose a time-limited event (leaks through top/bottom of box) 3= enclose an event localized in frequency and time (is contained inside box) >1 Harmonics: Number to examine: 9 Since there are a large number of harmonics, you may wish to Zoom Close-Up, using command 17. [press ENTER to continue.] The boxes show up as follows. Problem: our estimate of 200 Hz is not quite right, and the top boxes are off their mark. To get the box centers to line up better, we notice that the 8th harmonic is somewhere near 1500 Hz, so an easy trick is to enter "1500 / 8" as below. We also slightly increase the frequency width to 120 to make sure the boxes completely surround each of the peaks. 4 = Enclose a region with a box, and analyze (add trial) 7 = New SPIRAL (same spectrogram) | 17=Zoom Close-up 8 = New SPECTROGRAM (same waveform) | 18=Zoom Harmonics 9 = Open another WAVEFORM | 19=Zoom Entire Spec. 0 = Quit >4 Specify a region of the spectrogram to analyze. Box: Freq at centre: 1500 / 8 Box: Freq width: 120 Box: Time at centre: 4.95 Box: Time width: .1 1= enclose a frequency-limited event (leaks through sides of box) 2= enclose a time-limited event (leaks through top/bottom of box) 3= enclose an event localized in frequency and time (is contained inside box) >1 Harmonics: Number to examine: 9 Since there are a large number of harmonics, you may wish to Zoom Close-Up, using command 17. [press ENTER to continue.] This result is much better. We created a much better enclosure, and increased the quality of the frequency measurements from 0dB to 8dB. Each harmonic is neatly surrounded on the top and bottom by the boxes, with a small amount of margin space. The displayed measurements can be put directly into your research results. |The fundamental frequency is 260 Hz +/- 10 Hz (with a measurement quality of 12dB, as per the SAJ-1 specification(1))| Include a footnote: (1) SAJ-1 results are explained at:and/or include a reference to: You can place the graphs in your paper: Ryan Janzen and Laura Bolt (2009). "Improved measurement algorithm for vocal communication research, with application to Lemur Catta", Proc. IBAC 2009, Bioacoustics Journal (to appear) If the frequencies appearing on the spectrogram are too blurry (not enough frequency resolution), then you can press 8 to create a new spectrogram with better frequency resolution. If you are analyzing a quick signal and are interested in exactly what time it occurred, but the spectogram is too blurry in time (not enough time resolution), then you can press 8 to create a new spectrogram with better time resolution. Spiral: Number of loops around = how intricately you would like the algorithm to explore around your region. "2" is a good value to try. Harmonics: Number to examine = how many boxes should be created to enclose harmonics. Do not specify so many boxes that they would spill over the top of the spectrogram. Viewing pause time between each trial = number of seconds to slow down the analysis Finally, the analysis will take a short time to execute. When complete, the markers will sit dormant at the last trial, waiting for you to cause them to snap back to the best trial. Once multiple trials have been run through, the program waits for you to request data from a specific one of the trials. For example, from the main menu you can enter "1" if you are trying to determine the fundamental frequency. Enter "2" if you were trying to determine the time of a percussive event (spread vertically across many frequencies). Enter "3" if you want to know the frequency and time of a short tone that was completely enclosed by your box enclosures. If you wish to jump to the results of any one of the trials (as listed along the x-axis of the multiple-trials graphs), the command is "-[trialNumber]". That is, in the command window, type "-" followed by the trial number. SAJ is an easy way to express your results -- be scientifically precise, without needing to write a whole paragraph on signal-processing -- just write "as per the SAJ-1 specification." Your results from the program are automatically expressed in SAJ-1. This ensures uniformity between different researchers in different fields. To see the exact details of what is contained inside your SAJ-1 data, see here. Online up-to-date downloads and help

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Stories We Like: A Guide to the Comma convection con·vec·tion (kən-věk'shən) Heat transfer in a gas or liquid by the circulation of currents from one region to another. Fluid motion caused by an external force such as gravity. Current in a fluid caused by uneven distribution of heat. For example, air on a part of the Earth's surface warmed by strong sunlight will be heated by contact with the ground and will expand and flow upward, creating a region of low pressure below it; cooler surrounding air will then flow in to this low pressure region. The air thus circulates by convection, creating winds. See Note at conduction. The motion of warm material that rises, cools off, and sinks again, producing a continuous circulation of material and transfer of heat. Some examples of processes involving convection are boiling water, in which heat is transferred from the stove to the air; the circulation of the atmosphere of the Earth, transferring heat from the equator to the North Pole and South Pole; and plate tectonics, in which heat is transferred from the interior of the Earth to its surface.

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$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ # 7.2: Diagonalization $$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ Learning Objectives 1. Determine when it is possible to diagonalize a matrix 2. When possible, diagonalize a matrix ## Similarity and Diagonalization We begin this section by recalling the definition of similar matrices. Recall that if $$A,B$$ are two $$n\times n$$ matrices, then they are similar if and only if there exists an invertible matrix $$P$$ such that $A=P^{-1}BP$ In this case we write $$A \sim B$$. The concept of similarity is an example of an equivalence relation. Theorem $$\PageIndex{1}$$: Similarity is an Equivalence Relation Similarity is an equivalence relation, i.e. for $$n \times n$$ matrices $$A,B,$$ and $$C$$, 1. $$A \sim A$$ (reflexive) 2. If $$A \sim B$$, then $$B \sim A$$ (symmetric) 3. If $$A \sim B$$ and $$B \sim C$$, then $$A \sim C$$ (transitive) Proof It is clear that $$A\sim A$$, taking $$P=I$$. Now, if $$A\sim B,$$ then for some $$P$$ invertible, $A=P^{-1}BP$ and so $PAP^{-1}=B$ But then $\left( P^{-1}\right) ^{-1}AP^{-1}=B$ which shows that $$B\sim A$$. Now suppose $$A\sim B$$ and $$B\sim C$$. Then there exist invertible matrices $$P,Q$$ such that $A=P^{-1}BP,\ B=Q^{-1}CQ$ Then, $A=P^{-1} \left( Q^{-1}CQ \right)P=\left( QP\right) ^{-1}C\left( QP\right)$ showing that $$A$$ is similar to $$C$$. Another important concept necessary to this section is the trace of a matrix. Consider the definition. Definition $$\PageIndex{1}$$: Trace of a Matrix If $$A=[a_{ij}]$$ is an $$n\times n$$ matrix, then the trace of $$A$$ is $\mathrm{trace}(A) = \sum_{i=1}^n a_{ii}.$ In words, the trace of a matrix is the sum of the entries on the main diagonal. Lemma $$\PageIndex{1}$$: Properties of Trace For $$n\times n$$ matrices $$A$$ and $$B$$, and any $$k\in\mathbb{R}$$, 1. $$\mathrm{trace}(A+B)=\mathrm{trace}(A) + \mathrm{trace}(B)$$ 2. $$\mathrm{trace}(kA)=k\cdot\mathrm{trace}(A)$$ 3. $$\mathrm{trace}(AB)=\mathrm{trace}(BA)$$ The following theorem includes a reference to the characteristic polynomial of a matrix. Recall that for any $$n \times n$$ matrix $$A$$, the characteristic polynomial of $$A$$ is $$c_A(x)=\det(xI-A)$$. Theorem $$\PageIndex{2}$$: Properties of Similar Matrices If $$A$$ and $$B$$ are $$n\times n$$ matrices and $$A\sim B$$, then 1. $$\det(A) = \det(B)$$ 2. $$\mathrm{rank}(A) = \mathrm{rank}(B)$$ 3. $$\mathrm{trace}(A)= \mathrm{trace}(B)$$ 4. $$c_A(x)=c_B(x)$$ 5. $$A$$ and $$B$$ have the same eigenvalues We now proceed to the main concept of this section. When a matrix is similar to a diagonal matrix, the matrix is said to be diagonalizable. We define a diagonal matrix $$D$$ as a matrix containing a zero in every entry except those on the main diagonal. More precisely, if $$d_{ij}$$ is the $$ij^{th}$$ entry of a diagonal matrix $$D$$, then $$d_{ij}=0$$ unless $$i=j$$. Such matrices look like the following. $D = \left ( \begin{array}{ccc} \ast & & 0 \\ & \ddots & \\ 0 & & \ast \end{array} \right )$ where $$\ast$$ is a number which might not be zero. The following is the formal definition of a diagonalizable matrix. Definition $$\PageIndex{2}$$: Diagonalizable Let $$A$$ be an $$n\times n$$ matrix. Then $$A$$ is said to be diagonalizable if there exists an invertible matrix $$P$$ such that $P^{-1}AP=D$ where $$D$$ is a diagonal matrix. Notice that the above equation can be rearranged as $$A=PDP^{-1}$$. Suppose we wanted to compute $$A^{100}$$. By diagonalizing $$A$$ first it suffices to then compute $$\left(PDP^{-1}\right)^{100}$$, which reduces to $$PD^{100}P^{-1}$$. This last computation is much simpler than $$A^{100}$$. While this process is described in detail later, it provides motivation for diagonalization. ## Diagonalizing a Matrix The most important theorem about diagonalizability is the following major result. Theorem $$\PageIndex{3}$$: Eigenvectors and Diagonalizable Matrices An $$n\times n$$ matrix $$A$$ is diagonalizable if and only if there is an invertible matrix $$P$$ given by $P=\left (\begin{array}{cccc} X_{1} & X_{2} & \cdots & X_{n} \end{array} \right )$ where the $$X_{k}$$ are eigenvectors of $$A$$. Moreover if $$A$$ is diagonalizable, the corresponding eigenvalues of $$A$$ are the diagonal entries of the diagonal matrix $$D$$. Proof Suppose $$P$$ is given as above as an invertible matrix whose columns are eigenvectors of $$A$$. Then $$P^{-1}$$ is of the form $P^{-1}=\left (\begin{array}{c} W_{1}^{T} \\ W_{2}^{T} \\ \vdots \\ W_{n}^{T} \end{array} \right )$ where $$W_{k}^{T}X_{j}=\delta _{kj},$$ which is the Kronecker’s symbol defined by $\delta _{ij}=\left\{ \begin{array}{c} 1 \text{ if }i=j \\ 0\text{ if }i\neq j \end{array} \right.$ Then \begin{aligned} P^{-1}AP & = & \left (\begin{array}{c} W_{1}^{T} \\ W_{2}^{T} \\ \vdots \\ W_{n}^{T} \end{array} \right ) \left (\begin{array}{cccc} AX_{1} & AX_{2} & \cdots & AX_{n} \end{array} \right ) \\ & = & \left (\begin{array}{c} W_{1}^{T} \\ W_{2}^{T} \\ \vdots \\ W_{n}^{T} \end{array} \right ) \left (\begin{array}{cccc} \lambda _{1}X_{1} & \lambda _{2}X_{2} & \cdots & \lambda _{n}X_{n} \end{array} \right ) \\ &=& \left (\begin{array}{ccc} \lambda _{1} & & 0 \\ & \ddots & \\ 0 & & \lambda _{n} \end{array} \right ) \\\end{aligned} Conversely, suppose $$A$$ is diagonalizable so that $$P^{-1}AP=D.$$ Let $P=\left (\begin{array}{cccc} X_{1} & X_{2} & \cdots & X_{n} \end{array} \right )$ where the columns are the $$X_{k}$$ and $D=\left (\begin{array}{ccc} \lambda _{1} & & 0 \\ & \ddots & \\ 0 & & \lambda _{n} \end{array} \right )$ Then $AP=PD=\left (\begin{array}{cccc} X_{1} & X_{2} & \cdots & X_{n} \end{array} \right ) \left (\begin{array}{ccc} \lambda _{1} & & 0 \\ & \ddots & \\ 0 & & \lambda _{n} \end{array} \right )$ and so $\left (\begin{array}{cccc} AX_{1} & AX_{2} & \cdots & AX_{n} \end{array} \right ) =\left (\begin{array}{cccc} \lambda _{1}X_{1} & \lambda _{2}X_{2} & \cdots & \lambda _{n}X_{n} \end{array} \right )$ showing the $$X_{k}$$ are eigenvectors of $$A$$ and the $$\lambda _{k}$$ are eigenvectors. Notice that because the matrix $$P$$ defined above is invertible it follows that the set of eigenvectors of $$A$$, $$\left\{ X_1, X_2, \cdots, X_n \right\}$$, form a basis of $$\mathbb{R}^n$$. We demonstrate the concept given in the above theorem in the next example. Note that not only are the columns of the matrix $$P$$ formed by eigenvectors, but $$P$$ must be invertible so must consist of a wide variety of eigenvectors. We achieve this by using basic eigenvectors for the columns of $$P$$. Example $$\PageIndex{1}$$: Diagonalize a Matrix Let $A=\left (\begin{array}{rrr} 2 & 0 & 0 \\ 1 & 4 & -1 \\ -2 & -4 & 4 \end{array} \right )$ Find an invertible matrix $$P$$ and a diagonal matrix $$D$$ such that $$P^{-1}AP=D$$. Solution By Theorem [thm:eigenvectorsanddiagonalizable] we use the eigenvectors of $$A$$ as the columns of $$P$$, and the corresponding eigenvalues of $$A$$ as the diagonal entries of $$D$$. First, we will find the eigenvalues of $$A$$. To do so, we solve $$\det \left( \lambda I -A \right) =0$$ as follows. $\det \left( \lambda \left (\begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right ) - \left (\begin{array}{rrr} 2 & 0 & 0 \\ 1 & 4 & -1 \\ -2 & -4 & 4 \end{array} \right ) \right) = 0$ This computation is left as an exercise, and you should verify that the eigenvalues are $$\lambda_1 =2, \lambda_2 = 2$$, and $$\lambda_3 = 6$$. Next, we need to find the eigenvectors. We first find the eigenvectors for $$\lambda_1, \lambda_2 = 2$$. Solving $$\left(2I - A \right)X = 0$$ to find the eigenvectors, we find that the eigenvectors are $t\left (\begin{array}{r} -2 \\ 1 \\ 0 \end{array} \right ) +s\left (\begin{array}{r} 1 \\ 0 \\ 1 \end{array} \right )$ where $$t,s$$ are scalars. Hence there are two basic eigenvectors which are given by $X_1 = \left (\begin{array}{r} -2 \\ 1 \\ 0 \end{array} \right ), X_2 = \left (\begin{array}{r} 1 \\ 0 \\ 1 \end{array} \right )$ You can verify that the basic eigenvector for $$\lambda_3 =6$$ is $$X_3 = \left (\begin{array}{r} 0 \\ 1 \\ -2 \end{array} \right )$$ Then, we construct the matrix $$P$$ as follows. $P= \left (\begin{array}{rrr} X_1 & X_2 & X_3 \end{array} \right ) = \left (\begin{array}{rrr} -2 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & -2 \end{array} \right )$ That is, the columns of $$P$$ are the basic eigenvectors of $$A$$. Then, you can verify that $P^{-1}=\left (\begin{array}{rrr} - \frac{1}{4} & \frac{1}{2} & \frac{1}{4} \\ \frac{1}{2} & 1 & \frac{1}{2} \\ \frac{1}{4} & \frac{1}{2} & - \frac{1}{4} \end{array} \right )$ Thus, \begin{aligned} P^{-1}AP &=&\left (\begin{array}{rrr} - \frac{1}{4} & \frac{1}{2} & \frac{1}{4} \\ \frac{1}{2} & 1 & \frac{1}{2} \\ \frac{1}{4} & \frac{1}{2} & - \frac{1}{4} \end{array} \right ) \left (\begin{array}{rrr} 2 & 0 & 0 \\ 1 & 4 & -1 \\ -2 & -4 & 4 \end{array} \right ) \left (\begin{array}{rrr} -2 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & -2 \end{array} \right ) \\ &=&\left (\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 6 \end{array} \right ) \end{aligned} You can see that the result here is a diagonal matrix where the entries on the main diagonal are the eigenvalues of $$A$$. We expected this based on Theorem [thm:eigenvectorsanddiagonalizable]. Notice that eigenvalues on the main diagonal must be in the same order as the corresponding eigenvectors in $$P$$. Consider the next important theorem. Theorem $$\PageIndex{3}$$: Linearly Independent Eigenvectors Let $$A$$ be an $$n\times n$$ matrix, and suppose that $$A$$ has distinct eigenvalues $$\lambda_1, \lambda_2, \ldots, \lambda_m$$. For each $$i$$, let $$X_i$$ be a $$\lambda_i$$-eigenvector of $$A$$. Then $$\{ X_1, X_2, \ldots, X_m\}$$ is linearly independent. The corollary that follows from this theorem gives a useful tool in determining if $$A$$ is diagonalizable. Corollary $$\PageIndex{1}$$: Distinct Eigenvalues Let $$A$$ be an $$n \times n$$ matrix and suppose it has $$n$$ distinct eigenvalues. Then it follows that $$A$$ is diagonalizable. It is possible that a matrix $$A$$ cannot be diagonalized. In other words, we cannot find an invertible matrix $$P$$ so that $$P^{-1}AP=D$$. Consider the following example. Example $$\PageIndex{2}$$: A Matrix which cannot be Diagonalized Let $A = \left (\begin{array}{rr} 1 & 1 \\ 0 & 1 \end{array} \right )$ If possible, find an invertible matrix $$P$$ and diagonal matrix $$D$$ so that $$P^{-1}AP=D$$. Solution Through the usual procedure, we find that the eigenvalues of $$A$$ are $$\lambda_1 =1, \lambda_2=1.$$ To find the eigenvectors, we solve the equation $$\left(\lambda I - A \right) X = 0$$. The matrix $$\left(\lambda I -A \right)$$ is given by $\left (\begin{array}{cc} \lambda - 1 & -1 \\ 0 & \lambda - 1 \end{array} \right )$ Substituting in $$\lambda = 1$$, we have the matrix $\left (\begin{array}{cc} 1 - 1 & -1 \\ 0 & 1 - 1 \end{array} \right ) = \left (\begin{array}{rr} 0 & -1 \\ 0 & 0 \end{array} \right )$ Then, solving the equation $$\left(\lambda I - A\right) X = 0$$ involves carrying the following augmented matrix to its . $\left (\begin{array}{rr|r} 0 & -1 & 0 \\ 0 & 0 & 0 \end{array} \right ) \rightarrow \cdots \rightarrow \left (\begin{array}{rr|r} 0 & -1 & 0 \\ 0 & 0 & 0 \end{array} \right )$ Then the eigenvectors are of the form $t\left (\begin{array}{r} 1 \\ 0 \end{array} \right )$ and the basic eigenvector is $X_1 = \left (\begin{array}{r} 1 \\ 0 \end{array} \right )$ In this case, the matrix $$A$$ has one eigenvalue of multiplicity two, but only one basic eigenvector. In order to diagonalize $$A$$, we need to construct an invertible $$2\times 2$$ matrix $$P$$. However, because $$A$$ only has one basic eigenvector, we cannot construct this $$P$$. Notice that if we were to use $$X_1$$ as both columns of $$P$$, $$P$$ would not be invertible. For this reason, we cannot repeat eigenvectors in $$P$$. Hence this matrix cannot be diagonalized. The idea that a matrix may not be diagonalizable suggests that conditions exist to determine when it is possible to diagonalize a matrix. We saw earlier in Corollary [cor:distincteigenvalues] that an $$n \times n$$ matrix with $$n$$ distinct eigenvalues is diagonalizable. It turns out that there are other useful diagonalizability tests. First we need the following definition. Definition $$\PageIndex{4}$$: Eigenspace Let $$A$$ be an $$n\times n$$ matrix and $$\lambda\in\mathbb{R}$$. The eigenspace of $$A$$ corresponding to $$\lambda$$, written $$E_{\lambda}(A)$$ is the set of all eigenvectors corresponding to $$\lambda$$. In other words, the eigenspace $$E_{\lambda}(A)$$ is all $$X$$ such that $$AX = \lambda X$$. Notice that this set can be written $$E_{\lambda}(A) = \mathrm{null}(\lambda I - A)$$, showing that $$E_{\lambda}(A)$$ is a subspace of $$\mathbb{R}^n$$. Recall that the multiplicity of an eigenvalue $$\lambda$$ is the number of times that it occurs as a root of the characteristic polynomial. Consider now the following lemma. Lemma $$\PageIndex{2}$$: Dimension of the Eigenspace The probabilities assigned to events by a distribution function on a sample space are given by. Proof Add proof here and it will automatically be hidden If $$A$$ is an $$n\times n$$ matrix, then $\dim(E_{\lambda}(A))\leq m$ where $$\lambda$$ is an eigenvalue of $$A$$ of multiplicity $$m$$. This result tells us that if $$\lambda$$ is an eigenvalue of $$A$$, then the number of linearly independent $$\lambda$$-eigenvectors is never more than the multiplicity of $$\lambda$$. We now use this fact to provide a useful diagonalizability condition. Theorem $$\PageIndex{4}$$: Diagonalizability Condition Let $$A$$ be an $$n \times n$$ matrix $$A$$. Then $$A$$ is diagonalizable if and only if for each eigenvalue $$\lambda$$ of $$A$$, $$\dim(E_{\lambda}(A))$$ is equal to the multiplicity of $$\lambda$$. ## Complex Eigenvalues In some applications, a matrix may have eigenvalues which are complex numbers. For example, this often occurs in differential equations. These questions are approached in the same way as above. Consider the following example. Example $$\PageIndex{2}$$: A Real Matrix with Complex Eigenvalues Let $A=\left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & 1 & 2 \end{array} \right ]$ Find the eigenvalues and eigenvectors of $$A$$. Solution We will first find the eigenvalues as usual by solving the following equation. $\det \left( \lambda \left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right ] - \left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & 1 & 2 \end{array} \right ] \right) =0$ This reduces to $$\left( \lambda -1\right) \left( \lambda^{2}-4 \lambda +5\right) =0.$$ The solutions are $$\lambda_1 =1,\lambda_2 = 2+i$$ and $$\lambda_3 =2-i.$$ There is nothing new about finding the eigenvectors for $$\lambda_1 =1$$ so this is left as an exercise. Consider now the eigenvalue $$\lambda_2 =2+i.$$ As usual, we solve the equation $$\left(\lambda I -A \right) X = 0$$ as given by $\left( \left( 2+i\right) \left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array} \right ] - \left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & 1 & 2 \end{array} \right ] \right) X =\left [ \begin{array}{r} 0 \\ 0 \\ 0 \end{array} \right ]$ In other words, we need to solve the system represented by the augmented matrix $\left [ \begin{array}{crr|r} 1+i & 0 & 0 & 0 \\ 0 & i & 1 & 0 \\ 0 & -1 & i & 0 \end{array} \right ]$ We now use our row operations to solve the system. Divide the first row by $$\left( 1+i\right)$$ and then take $$-i$$ times the second row and add to the third row. This yields $\left [ \begin{array}{rrr|r} 1 & 0 & 0 & 0 \\ 0 & i & 1 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right ]$ Now multiply the second row by $$-i$$ to obtain the , given by $\left [ \begin{array}{rrr|r} 1 & 0 & 0 & 0 \\ 0 & 1 & -i & 0 \\ 0 & 0 & 0 & 0 \end{array} \right ]$ Therefore, the eigenvectors are of the form $t\left [ \begin{array}{r} 0 \\ i \\ 1 \end{array} \right ]$ and the basic eigenvector is given by $X_2 = \left [ \begin{array}{r} 0 \\ i \\ 1 \end{array} \right ]$ As an exercise, verify that the eigenvectors for $$\lambda_3 =2-i$$ are of the form $t\left [ \begin{array}{r} 0 \\ -i \\ 1 \end{array} \right ]$ Hence, the basic eigenvector is given by $X_3 = \left [ \begin{array}{r} 0 \\ -i \\ 1 \end{array} \right ]$ As usual, be sure to check your answers! To verify, we check that $$AX_3 = \left(2 - i \right) X_3$$ as follows. $\left [ \begin{array}{rrr} 1 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & 1 & 2 \end{array} \right ] \left [ \begin{array}{r} 0 \\ -i \\ 1 \end{array} \right ] = \left [ \begin{array}{c} 0 \\ -1-2i \\ 2-i \end{array} \right ] =\left( 2-i\right) \left [ \begin{array}{r} 0 \\ -i \\ 1 \end{array} \right ]$ Therefore, we know that this eigenvector and eigenvalue are correct. Notice that in Example [exa:realmatrixcomplexeigenvalues], two of the eigenvalues were given by $$\lambda_2 = 2 + i$$ and $$\lambda_3 = 2-i$$. You may recall that these two complex numbers are conjugates. It turns out that whenever a matrix containing real entries has a complex eigenvalue $$\lambda$$, it also has an eigenvalue equal to $$\overline{\lambda}$$, the conjugate of $$\lambda$$.

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# Motion in a Straight Road #### nasi112 ##### Full Member A car of mass $$\displaystyle 600 \ kg$$ is driven along a straight road. The resistance to motion of the car is $$\displaystyle kv^2$$ Newtons, where $$\displaystyle v \ m/s$$ is the velocity of the car at time $$\displaystyle t$$ seconds and $$\displaystyle k$$ is a constant. The engine of the car is producing $$\displaystyle 8 \ kW$$ of output power. A. i. Draw a free body diagram of the system. ii. Derive the differential equation of motion of the vehicle, and describe it in the form: $$\displaystyle \frac{dv}{dt} + Av^2 - \frac{B}{v} = 0$$ Where $$\displaystyle A$$ and $$\displaystyle B$$ are constants to be found. B. When the velocity of the car is $$\displaystyle 20 \ m/s$$, the engine is turned off. i. Draw a free body diagram of the system. ii. Derive the differential equation of motion of the car, and describe it in the form: $$\displaystyle \frac{dv}{dt} + Av^2 = 0$$ Where $$\displaystyle A$$ is a constant to be found. iii. Find, in term of $$\displaystyle k$$, an expression for the velocity of the car. Make sure your expression is in the form $$\displaystyle v = f(t)$$ This is what I did for $$\displaystyle A$$ I am not sure if this is the correct free body diagram. Can anyone help me, please? Now, I will try to derive the differential equation. $$\displaystyle F_e - F_R = ma = m\frac{dv}{dt}$$ $$\displaystyle m\frac{dv}{dt} + kv^2 - F_e = 0$$ Now I will use the output power $$\displaystyle F_e = \frac{P}{v}$$ $$\displaystyle m\frac{dv}{dt} + kv^2 - \frac{P}{v} = 0$$ $$\displaystyle \frac{dv}{dt} + \frac{kv^2}{m} - \frac{P}{mv} = 0$$ Is this a correct derivation? Please, let me know if I did something wrong in the derivation or in the free body diagram. I also noticed that if I want to solve this differential equation with separable method, it gives a very complicated solution while wolfram can solve it easily $$\displaystyle v(t) = -Atv^2 + \frac{Bt}{y} + c_1$$, if I let $$\displaystyle A = \frac{k}{m}$$ and $$\displaystyle B = \frac{P}{m}$$ Why is that? #### Attachments • 9.6 KB Views: 0

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The ability to do 3D, large-scale simulations of supernovae, such as above, led to the discovery of an entirely new and unexpected explosion mechanism, termed the gravitationally confined detonation (GCD) model. Click here to view a slideshow of images. | Image: Courtesy Flash Center for Computational Science, University of Chicago It’s said that a picture is worth a thousand words. That’s exponentially more true – in pixelations and calculations – for the crafted and complex images and simulations produced by Energy Department supercomputers through our INCITE program. INCITE, which stands for the “Innovative and Novel Computational Impact on Theory and Experiment,” is jointly managed by the Argonne Leadership Computing Facility and the Oak Ridge National Laboratory. The INCITE program awards billions of processor hours on some of our nation’s best supercomputers to some of our nation’s brightest researchers -- individuals committed to accelerating scientific breakthroughs and bringing real-world benefits to our citizens. Recently, INCITE put out a special report highlighting 22 of its greatest hits and ways in which it is catalyzing discoveries and innovations. For instance, complex simulations of combustion are yielding insights to improve the fuel efficiency of engines, and detailed modeling of chemical processes is helping to pave the way to cleaner energy through a better understanding of electrical energy storage. INCITE simulations range from exploding stars to the San Andreas Fault; from the structure of large proteins to the molecular basis of Parkinson’s disease; and from stressed-out materials to abrupt climate change. Click here to view a slideshow of some of these simulations. For instance, INCITE researchers have thrown new light onto the enormous star explosions known as supernovae, simulating how they detonate and what they illuminate. Their starry-eyed simulations have also shown more about the mysterious dark matter and dark energy that seem to make up most of the mass and energy the universe. Researchers using INCITE supercomputers have also made many advances in the stuff that makes our bodies up, the important molecular machines known as proteins. INCITE simulations have determined the structure of many proteins, have suggested how misshapen proteins can lead to diseases like Alzheimer’s, and even hinted at medicines that might be developed against them. Scientists have also used the INCITE program to model the molecular basis of Parkinson’s disease, a neurological disorder that afflicts more than 2 million people in the United States. INCITE awardees have also used their supercomputer time to study stressed materials – how simple corrosion can lead to significant cracking and ultimate material failure in nickel-based alloys and silica glass, essential materials for advanced nuclear reactors and nuclear-waste management. The program’s studies have aided the design of next-generation nuclear reactors; offered new insights into how to contain the exceptionally hot stuff known as plasma (for potential fusion reactors of the future); and even given scientists and engineers a better understanding of how concrete, the most widely used building material in the world, flows and takes form. In all of these projects – and its many others – the INCITE program is providing outstanding researchers with time on the Department’s supercomputers to achieve both scientific breakthroughs and social benefits. This year, INCITE will provide 57 awardees with 1.7 billion processor hours. And more are likely to be awarded in the next year. Each study and simulation will lead to new insights... and hopefully lasting benefits.

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# KSEEB Solutions for Class 7 Maths Chapter 2 Fractions haand Decimals Ex 2.7 Students can Download Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.7 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams. ## Karnataka State Syllabus Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.7 Question 1. Find: i) 0.4 ÷ 2 Solution: ii) 0.35 ÷ 5 Solution: iii) 2.48 ÷ 4 Solution: iv) 65.4 ÷ 6 Solution: v) 651.2 ÷ 4 Solution: vi) 14.49 ÷ 7 Solution: vii) 3.96 ÷ 4 Solution: viii) 0.80 ÷ 5 Solution: Question 2. 1. 4.8 ÷ 10 2. 52.5 ÷ 10 3. 0.7 ÷ 10 4. 33.1 ÷ 10 5. 272.23 ÷ 10 6. 0.56 ÷ 10 7. 03.97 ÷ 10 Solution: 1. 4.8 ÷ 10 = 0.48 2. 52.5 ÷ 10 = 5.25 3. 0.7 ÷ 10 = 0.07 4. 33.1 ÷ 10 = 3.31 5. 273.23 ÷ 10 = 27.223 6. 0.56 ÷ 10 = 0.056 7. 3.97 ÷ 10 = 0.397. Question 3. i) 2.7 ÷ 100 Solution: ii) 0.3 ÷ 100 Solution: iii) 0.78 ÷ 100 Solution: iv) 432.6 ÷ 100 Solution: v) 23.6 ÷ 100 Solution: vi) 98.53 ÷ 100 Solution: Question 4. Find : i) 7.9 ÷ 1000 Solution: ii) 26.3 ÷ 1000 Solution: iii) 38.53 ÷ 1000 Solution: iv) 128.9 ÷ 1000 Solution: v) 0.5 ÷ 1000 Solution: Question 5. Find: i) 7 ÷ 3.5 Solution: ii) 36 ÷ 2 Solution: iii) 3.25 ÷ 0.5 Solution: iv) 30.94 ÷ 0.7 Solution: v) 0.5 ÷ 0.25 Solution: vi) 7.75 ÷ 0.25 Solution: vii) 76.5 ÷ 0.15 Solution: viii) 37.8 ÷ 1.4 Solution: ix) 2.73 ÷ 1.3 Solution: Question 6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol ? Solution: Distance covered in 2.4 liters petrol = 43.2km Distance covered in 1 liters (∴ vehicle covers 18 km in 1 litre of petrol)

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The University of Arizona's Terry J. Physical Impacts and Predictions: What Science Can Tell Us Experts are discussing the impacts of climate change in the Southwest during a conference that is being held in Tucson today and Friday. Climate change in arid lands has very likely increased the size and number of forest fires, insect outbreaks, and tree mortality in the western and southwestern U.S., and is projected to cause changes in other natural processes, according to a panel of University of Arizona scientists. Extensive forest areas of the Southwest have undergone great changes over the past century as a consequence of livestock grazing, logging, road building, and fire suppression, said Thomas Swetnam, director of the UA's Laboratory for Tree-Ring Research. These changes include increased forest densities and fuels, leading to wildfires of extraordinary severity, Swetnam said. He was among the experts to speak during a conference, "Adaptation to Climate Change in the Desert Southwest: Impacts and Opportunities," being held at the Westward Look Resort today and Friday. Sponsored by several several UA units and departments, the conference brought together scientists and other experts from across the nation to discuss the issue of climate change in the Southwest. Some forest and woodland ecosystems are capable of recovering from high severity fire, while others are not; observations and studies in ponderosa pine forests indicate that many areas that have been burned in severe fires have converted to grasslands or shrub fields, Swetnam said. Adapting to climate change will require the careful restoration and management of forests and woodlands to increase the resiliency of these ecosystems to wildfire events and other disturbances, he added. The response to a loss of tree cover and loss of roots within a burned area is "a more flashy" watershed; rain does not soak into the ground as well as it normally does, resulting in more runoff and increased prospects of floods, said Holly Hartmann, a UA associate research scientist and director of the Arid Lands Information Center. "With those kinds of impacts, you have to think about how to respond to extreme events" other than warmer temperatures or drought, Hartmann said. In addition, climate change in arid lands will create physical conditions conducive to wildfire, and the proliferation of exotic grasses will provide fuel, thus causing fire frequencies to increase in a self-reinforcing fashion, said David Breshears, professor in the UA School of Natural Resources. In arid regions where ecosystems have no co-evolved with a fire cycle, the probability of loss of iconic megaflora, such as saguaro cacti and Joshua trees, is likely, Breshears said. Higher temperature, increased drought, and more intense thunderstorms will very likely promote the invasion of exotic grass species in arid lands and increase erosion, he said. Furthermore, these climate changes are expected to decrease the vegetation cover that protects the ground surface from wind and water erosion.

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Physics Classroom: Newton's Second Law - Revisited Relations Other Related Resources Visit The Physics Classroom's Flickr Galleries and enjoy a visual overview of the topic of circular motion Explore the direction of the normal force for the motion of an object along a curved path with this downloadable Java applet from Open Source Physics (OSP). Improve your problem-solving skills with problems, answers and solutions from The Calculator Pad. Try something new with this problem based learning activity on the design of a highway exit. Looking for a lab that coordinates with this page? Try the Loop the Loop Lab from The Laboratory. Practice makes perfect with this force analysis activity from The Curriculum Corner. This simulation from Open Source Physics (OSP) models the motion of an object along a curved path. The original speed and the path can be modified. Gravity, normal force, and the radius of curvature are displayed. Create a new relation

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Truthfully, an individual car's emissions are relatively low, compared to other sources of pollution. But when hundreds of thousands of people are each sitting in a car, packing a highway to capacity, the cumulative effects are enormous. As you're sitting in a traffic jam, gazing at the smoke coming out of the tailpipe in front of you and rising to join the smog in the sky, think for a moment about what that smoke is. It might not look like much, but that smoke has come a long way since it was pushed through the car's engine just moments before. Concern about our automobiles' effect on the environment is nothing new. The 1970 version of the Clean Air Act gave the EPA its sweeping authority to regulate automotive emissions. As technology advanced, the EPA pushed for more strict standards. And while new cars are much cleaner than those of 40 years ago, people tend to drive greater distances and a lot more often today, contributing to a lot more pollution. The Clean Air Act was revamped and increased in scope in 1977, and then again in 1990. Automotive manufacturers and parts suppliers have had to keep pace with these changes, and as you can imagine, a car's exhaust system has had to evolve considerably, too. Components of an Exhaust -- Smokin' Pipes The exhaust system is comprised mainly of pipes in several different shapes, each designed to connect to one another, and each shaped to conform to a specific part of the underside of the car. (The pipes are often bent to wrap around or otherwise accommodate other nearby components of the car, such as the axles.) Each pipe is responsible for moving the exhaust gases toward the back, but many of the segments are specialized. In other words, from the exterior, the system simply looks like a bunch of connected pipe segments that run from the engine bay to the back bumper, though some serve an additional purpose as the exhaust flows through that particular pipe. For example, the Y pipe (which is simply, well, a Y-shaped pipe) might be installed so the end with two openings bolts up to two corresponding openings in the exhaust manifold, combining the engine's waste to progress through the system. Or, when installed at the back end of the car, a Y pipe can help create a dual exhaust system with a tailpipe on each side of the car (for an often sought-after sporty look). Intermediate pipes might be attached to the muffler or resonator, which are other important system components (we'll get to these on the next page). Balance pipes, found in dual exhaust systems, help equalize the exhaust pulses traveling under the driver and passenger sides of the car. Air gap pipes are specialized nested pipes that act as a heat shield and insulator by providing an extra layer for airflow. And the tail pipe, which is typically peeking out from underneath the rear bumper, usually has a larger opening and might be made of more substantial-looking metal, to give the appearance of a performance exhaust that's a common feature of high-end cars. Though it might seem inefficient to have a ton of pipes instead of just one, really, all those segments serve a purpose. For one, bending pipes is hard work, and it's easier to connect small angled segments to straight pipes than it is to shape one long, expensive, heavy pipe to fit every contour of a car. Also, exhaust system components wear out at regular intervals (depending, of course, on the manufacturer, its materials, driving conditions and environmental factors). It's easier and less expensive to replace one rusted-out segment of pipe, banged-up muffler, or worn-out catalytic converter than it would be to install a whole new system. You might wonder how all those pipes fit together. Well, some ends overlap, while others are mated end-to-end; but not without a little bit of assistance. Other Exhaust Components -- Headers, Hangers and More We discussed the various pipes first, because they're the most visible and prevalent components of the exhaust system, and because they're all over the place. But the exhaust system really starts at the exhaust header (also known as the exhaust manifold). The header looks like a series of adjacent tubes stuck together (though it's often made of heavy-duty cast metal). It collects the exhaust directly from the engine, so it's designed so each opening mates up with one of the engine's exhaust ports, with flanges that form a tight seal to prevent exhaust from escaping. From here, the exhaust begins its flow through the various pipes and other components. The gaskets that are fitted between each pipe play a very important role. It's difficult, if not impossible, to form a flawless metal-to-metal seal, so gaskets are sandwiched between each connection to prevent the poisonous gases from escaping prematurely. They're made of fiber or other heavy-duty, heat resistant materials, which have just enough flexibility to compress slightly when the pipes are clamped tightly together. This helps form a tight seal. The muffler is another key part of the exhaust system. It looks like a large round or oval chamber (usually, but not always, found near the back of the car). That chamber has a very complex design, though -- it's responsible for silencing most of the engine's noise, even though it has to allow the exhaust to continue flowing smoothly. A series of chambers and tubes, filled with rock, wool, or synthetic fibers, absorbs and controls the noise. And that's not all -- the muffler must be reasonably resistant to damage, corrosion and heat retention. The resonator is a secondary or substitute sound elimination component, used to augment the muffler, or in cases where space is at a premium it might even be used instead of a muffler. Catalytic converters, which became commonplace in the 1970s, are the primary and most efficient means of reducing the level of toxins in a car's exhaust. The innards of a catalytic converter (or "cat") are coated with metals. Different types of catalytic converters use different combinations of platinum, palladium and rhodium. Before the exhaust reaches the cat, it contains a potent, super-toxic combination of carbon monoxide, nitrogen oxide and hydrocarbons. (When you take your car for its emissions test, these are the chemical levels that are being tested.) When these poisons come into contact with the metals coating the inside of the cat, a chemical reaction takes place that makes the exhaust gases less harmful. As the exhaust passes through the cat, the level of chemicals should be reduced enough to comply with government regulations. We already talked about gaskets, but the exhaust system requires other basic pieces of hardware. Flanges generally serve the same purpose as gaskets, but these are made of metal (and are sometimes formed right onto the end of a pipe). Assorted clamps and brackets mount the exhaust pieces together and hold them to the vehicle, and exhaust hangers literally hang the pipes from the underbody of the car, with enough strength to keep them in place but also enough flexibility to withstand movement caused by driving. And last, but not least are the heat shields: Metal (sometimes insulated) plates that are used as an extra barrier whenever hot exhaust parts are particularly close to another part of the car or directly below the passenger compartment. The Exit Route If an engine ran perfectly, it would combust all its available fuel as it ran through its cycles, converting all the dirty bits to a source of power. However, leftovers exist as pollutants because an engine simply cannot be engineered to run perfectly -- there are far too many variables. Some amount of fuel will always remain unburned or partially burned, and these remnants must be quickly processed out of the vehicle, in the form of exhaust, to make room for the next cycle of engine combustion. As we mentioned earlier, the exhaust first exits the engine and enters the system through the exhaust manifold. From there, it travels down the system through interconnected pipes until it exits through the tailpipe, near the back bumper. The pipes themselves actually help cool the exhaust, but they're mostly a way for the exhaust to travel to (and through) the catalytic converter and muffler. The cat has to be as close to the engine as possible, because it isn't fully functional until it rises to operating temperature. In many cases, the manufacturer places the cat shortly after the manifold, so heat from the engine helps warm the cat and quickly bring it up to temp. After the gases pass through the cat, which will burn off and remove up to 90 percent of the exhaust's toxins, the next priority is to filter the engine sound [source: Allen]. The muffler and resonator are usually situated right beyond the cat. There are many variations on this combination -- some will soothe the exhaust as much as possible, while others are specifically tuned for aggressive tones. From there, the exhaust moves through the remainder of the pipes until it exits the car. With all those chemicals swirling around, it's quite a feat that the exhaust system actually works as well as it does. A well-maintained exhaust system should last two to three years, but the pipes incur damage both inside and out. On the outside, they're susceptible to road conditions, such as impact from debris and environmental factors, such as snow, ice and road salt. However, a more substantial cause of exhaust system degradation is internal, and it can't be seen until the pipes have corroded through with rust. We know that as the engine combusts fuel to make power, byproducts of this process are left over -- that's why the exhaust system is needed. One of these byproducts is acidic moisture, and it's really damaging to metal. Unfortunately, there's really no way to keep the insides of the pipes clean. When an exhaust pipe rots through or a connection comes loose, an exhaust leak occurs. A leak is almost always immediately apparent with a loud, obnoxious sound and, possibly, drivability issues like an intermittent fluctuation in power. But, believe it or not, these aren't the real problems. It gets a little more serious if the leak occurs before the catalytic converter, which means the exhaust isn't being properly processed and all those hot chemicals are spilling everywhere into the atmosphere. It's always a good idea to get leaks fixed as soon as possible to avoid subjecting yourself, your passengers and your surroundings to unfiltered exhaust fumes. Keeping the Pipes Clean Diesel engines, often blamed for disproportionately high levels of toxic emissions, may find their reputation salvaged somewhat by new and improved exhaust filters that claim to reduce emissions by about 25 percent, with the added benefit of increasing fuel economy. Several automotive manufacturers with a history of offering diesel models have introduced similar systems that combine high-powered catalytic converters with diesel particulate filters. Volkswagen's BlueMotion turbodiesel lineup (sold mostly in Europe and South America) and Mercedes' BlueTec diesels are two such examples. In many cases, these OEM components and car models use weight reduction and other streamlining techniques to improve overall efficiency. Improved exhaust efficiency is critical to getting the most out of your car, and there are even ways to improve an older car (assuming it's in generally good condition -- a performance exhaust system won't work miracles on a total jalopy). A mechanic can usually order identical original replacement parts, but there are also alternatives from aftermarket performance parts suppliers that often give the car a facelift (at least, as much as the car's underbody can be spruced up, anyway). There are several frequently-mentioned benefits of performance exhaust systems. Aftermarket manufacturers are well aware that the auditory experience is critical to a pleasurable drive, and it also lets nearby drivers know that a little extra coin was spent on the car, too. Most manufacturers offer a variety of systems that range in sound from a subtle throatiness to an all-out roar. A good aftermarket performance exhaust can improve throttle response (how fast, and smoothly, the car reacts to the pressure applied to the gas pedal) and give a boost in horsepower. Some systems can even improve fuel economy. Performance exhausts are able to provide this power boost because they're less restrictive than stock exhausts. If the engine can push out more air (which also means it can take in more air) that helps the engine make more power. But contrary to what you might think, a totally free-flowing system will be counterproductive. Aftermarket exhausts are engineered to provide just the right amount of back pressure so that the engine doesn't end up running at sub-peak output. That's why it's important to choose one designed and optimized for your specific vehicle. And before you go ripping out your exhaust pipes, make sure the system you want is street-legal and won't cause your car to fail its emissions test. Understand, too, that a real performance exhaust system cannot provide mind-blowing benefits for a trivial investment. Beware of cheap products like clip-on or screw-on "performance" exhaust system components or exhaust tips that claim to give the look of a full performance system. They won't help the car's drivability and they may even hinder it by adding extra weight and wind resistance. And besides, those gaudy tips really aren't fooling anyone. - Abuelsamid, Sam. "Useless Car Performance Add-Ons." Popular Mechanics. (Jan. 29, 2012) http://www.popularmechanics.com/cars/how-to/products/performance-sapping-aftermarket-add-ons - Allen, Mike. "How to Install a Cat-back Exhaust System." Popular Mechanics. Dec. 18, 2009. (Jan. 29, 2012) http://www.popularmechanics.com/cars/how-to/maintenance/4270747 - Dow Automotive Systems. "Automotive -- Reducing Exhaust Emissions." (Jan. 29, 2012) http://www.dowautomotive.com/capabilities/industry/automotive/reducing.htm - Flowmaster. "Performance Exhaust Systems." 2011. (Jan. 29, 2012) http://www.flowmastermufflers.com/index.php?cat=2 - U.S. Environmental Protection Agency Office of Mobile Sources. "Automobile Emissions -- An Overview." August 1994. (Jan. 29, 2012) http://www.epa.gov/otaq/consumer/05-autos.pdf - Walker Exhaust. "Walker Exhaust 101." (Jan. 29, 2012) http://www.walkerexhaust.com/support/exhaust101/componentsAndDesign.asp

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or Find what you need to study Light Find what you need to study # 1.8 Graphical Representations of Summary Statistics L Lusine Ghazaryan Jed Quiaoit L Lusine Ghazaryan Jed Quiaoit As you comb through Unit 1, you're getting more exposure to statistics in the lens of variables and the various ways to represent them in both tabular and graphical forms. After all, graphical representations and statistics allow us to identify and represent key features of data! This time, we'll take what we know about measure of center and spread to construct graphs that summarize the summary statistics we've encountered so far. ## Five Number Summaries A five number summary provides a concise summary of a dataset. It consists of the minimum value, the (Q1), the , the third quartile (Q3), and the maximum value of a dataset. ๐Ÿ“ Remember that quartiles divide the data into four equal sections. One quarter of the data lies below the lower quartile, Q1, while another quarter of the data lies above the upper quartile, Q3. The quartiles border the middle half of the data. For example, consider the following dataset of 10 numbers: 5, 7, 8, 9, 10, 12, 15, 20, 25, 30 The is 5, the (also known as the lower quartile or Q1) is 8, the is 12, the third quartile (also known as the upper quartile or Q3) is 20, and the maximum value is 30. So, the five number summary for this dataset is: : 5 : 8 : 12 Third quartile: 20 Maximum value: 30 That's it -- we're done. Yay! ๐ŸŽ‰ Five number summaries provide a useful overviews of the range, spread, and central tendency of the data. It is often used in conjunction with box plots, which are graphical representations of the five number summary. ## Box Plots A , also known as a box and whisker plot, graphically represents the five number summary. It is a way to visualize the distribution of a dataset and to identify any outliers or unusual values! ๐Ÿ•ต๏ธ To create a , you start by drawing a horizontal line called the "axis" and marking the minimum, , , third quartile, and maximum values of the dataset on it. These marks are then used to create a box shape: the bottom of the box corresponds to the , the top of the box corresponds to the third quartile, and the line inside the box corresponds to the . The "whiskers" of the extend from the ends of the box to the minimum and maximum values of the dataset. Any points outside of the whiskers are considered outliers and are plotted separately. ๐Ÿญ Source: Simply Psychology Using the interquartile range, or IQR, we can erect fences to detect the outlier in our data: ๐Ÿคบ Upper fence = Q3 + 1.5 IQR and Lower fence = Q1 - 1.5 IQR The fences are not included in the , but it helps us to draw the whiskers of the . Any number beyond the whiskers will be displayed in asterisk, indicating that those values are outliers, something that we could hardly know from other quantitative displays. Source: EzBioCloud ### Box Plots and Skew Box plots can help us find important features about the distribution. The central box stretches from Q1 to Q3 and shows the middle (50%) of data. If the (Q2) is situated in the right middle of the quartiles, then the box will look symmetric. However, we should also look at whiskers. If the whiskers have different lengths, the distribution will be skewed on to the longer whiskerโ€™s side. ๐Ÿ“ Still unsure? Here's another way to word the explanation above with a visual as the cherry on top: To determine whether a is skewed or symmetric, you can look at the position of the relative to the first and third quartiles. • If the is roughly in the middle of the box, with about the same amount of data above and below it, the distribution is symmetric. • If the is closer to one end of the box, with more data on the other end, the distribution is skewed. Source: Statology ### Key Vocabulary • Minimum • Quartile 1 (or ) • Quartile 3 (or Third Quartile) • Maximum • Boxplots • Fences ## Practice Questions (1) Which of the following is NOT a part of a five number summary? A) B) C) D) Range E) Third quartile (2) Consider the following dataset of exam scores for a class of 30 students: 75, 80, 85, 85, 90, 90, 90, 95, 95, 95, 95, 95, 95, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 A. Create a five number summary for the dataset. B. Create a for the dataset. C. What can you conclude about the distribution of the exam scores based on the five number summary and the ? (3) A researcher is studying the heights of a sample of 100 adults. The five number summary for the sample is: : 150 cm : 160 cm : 170 cm Third quartile: 180 cm Maximum value: 200 cm Is a data point with a height of 220 cm considered an outlier according to the 1.5 x IQR rule? (1) D) Range. A five number summary consists of the , the , the , the third quartile, and the maximum value of a dataset. The range, which is the difference between the minimum and maximum values, is not a part of the five number summary. (2) A. To create a five number summary for the dataset, you need to calculate the , the , the , the third quartile, and the maximum value. The is 75, the maximum value is 100, and the is 95. To find the (Q1), you need to find the of the lower half of the dataset. The lower half of the dataset consists of the first 15 scores, which are: 75, 80, 85, 85, 90, 90, 90, 95, 95, 95, 95, 95, 95, 100, 100 The of the lower half of the dataset is 90. To find the third quartile (Q3), you need to find the of the upper half of the dataset. The upper half of the dataset consists of the last 15 scores, which are: 95, 95, 95, 95, 95, 95, 100, 100, 100, 100, 100, 100, 100, 100, 100 The of the upper half of the dataset is 100. Therefore, the five number summary for the dataset is: : 75 : 90 : 95 Third quartile: 100 Maximum value: 100 B. I'll leave it up to you to draw the and get some practice. ๐Ÿ˜‰ C. Based on the five number summary and the , you can conclude that the distribution of the exam scores is skewed to the right, with a long tail of high scores. The (95) is closer to the left side of the box, with more data on the right side. This indicates that there are more high scores in the dataset than low scores. The (75) and the (90) are also relatively low, indicating that there are a few low scores in the dataset. Overall, the distribution of the exam scores is skewed to the right, with a long tail of high scores and a few low scores. (3) To answer this question, you need to calculate the interquartile range (IQR) of the sample. The IQR is the difference between the third quartile and the , and is a measure of the spread of the data. In this case, the IQR is 180 cm - 160 cm = 20 cm. According to the 1.5 x IQR rule, a data point is considered an outlier if it is more than 1.5 times the IQR below the or more than 1.5 times the IQR above the third quartile. In this case, the data point with a height of 220 cm is more than 1.5 times the IQR above the third quartile (180 cm), so it is considered an outlier. The correct answer is: Yes, a height of 220 cm is considered an outlier in our data set! (Notice how we didn't need the raw dataset or the to determine whether a data point is an outlier or not? The five number summary definitely suffices in providing enough information and context.) # 1.8 Graphical Representations of Summary Statistics L Lusine Ghazaryan Jed Quiaoit L Lusine Ghazaryan Jed Quiaoit As you comb through Unit 1, you're getting more exposure to statistics in the lens of variables and the various ways to represent them in both tabular and graphical forms. After all, graphical representations and statistics allow us to identify and represent key features of data! This time, we'll take what we know about measure of center and spread to construct graphs that summarize the summary statistics we've encountered so far. ## Five Number Summaries A five number summary provides a concise summary of a dataset. It consists of the minimum value, the (Q1), the , the third quartile (Q3), and the maximum value of a dataset. ๐Ÿ“ Remember that quartiles divide the data into four equal sections. One quarter of the data lies below the lower quartile, Q1, while another quarter of the data lies above the upper quartile, Q3. The quartiles border the middle half of the data. For example, consider the following dataset of 10 numbers: 5, 7, 8, 9, 10, 12, 15, 20, 25, 30 The is 5, the (also known as the lower quartile or Q1) is 8, the is 12, the third quartile (also known as the upper quartile or Q3) is 20, and the maximum value is 30. So, the five number summary for this dataset is: : 5 : 8 : 12 Third quartile: 20 Maximum value: 30 That's it -- we're done. Yay! ๐ŸŽ‰ Five number summaries provide a useful overviews of the range, spread, and central tendency of the data. It is often used in conjunction with box plots, which are graphical representations of the five number summary. ## Box Plots A , also known as a box and whisker plot, graphically represents the five number summary. It is a way to visualize the distribution of a dataset and to identify any outliers or unusual values! ๐Ÿ•ต๏ธ To create a , you start by drawing a horizontal line called the "axis" and marking the minimum, , , third quartile, and maximum values of the dataset on it. These marks are then used to create a box shape: the bottom of the box corresponds to the , the top of the box corresponds to the third quartile, and the line inside the box corresponds to the . The "whiskers" of the extend from the ends of the box to the minimum and maximum values of the dataset. Any points outside of the whiskers are considered outliers and are plotted separately. ๐Ÿญ Source: Simply Psychology Using the interquartile range, or IQR, we can erect fences to detect the outlier in our data: ๐Ÿคบ Upper fence = Q3 + 1.5 IQR and Lower fence = Q1 - 1.5 IQR The fences are not included in the , but it helps us to draw the whiskers of the . Any number beyond the whiskers will be displayed in asterisk, indicating that those values are outliers, something that we could hardly know from other quantitative displays. Source: EzBioCloud ### Box Plots and Skew Box plots can help us find important features about the distribution. The central box stretches from Q1 to Q3 and shows the middle (50%) of data. If the (Q2) is situated in the right middle of the quartiles, then the box will look symmetric. However, we should also look at whiskers. If the whiskers have different lengths, the distribution will be skewed on to the longer whiskerโ€™s side. ๐Ÿ“ Still unsure? Here's another way to word the explanation above with a visual as the cherry on top: To determine whether a is skewed or symmetric, you can look at the position of the relative to the first and third quartiles. • If the is roughly in the middle of the box, with about the same amount of data above and below it, the distribution is symmetric. • If the is closer to one end of the box, with more data on the other end, the distribution is skewed. Source: Statology ### Key Vocabulary • Minimum • Quartile 1 (or ) • Quartile 3 (or Third Quartile) • Maximum • Boxplots • Fences ## Practice Questions (1) Which of the following is NOT a part of a five number summary? A) B) C) D) Range E) Third quartile (2) Consider the following dataset of exam scores for a class of 30 students: 75, 80, 85, 85, 90, 90, 90, 95, 95, 95, 95, 95, 95, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100 A. Create a five number summary for the dataset. B. Create a for the dataset. C. What can you conclude about the distribution of the exam scores based on the five number summary and the ? (3) A researcher is studying the heights of a sample of 100 adults. The five number summary for the sample is: : 150 cm : 160 cm : 170 cm Third quartile: 180 cm Maximum value: 200 cm Is a data point with a height of 220 cm considered an outlier according to the 1.5 x IQR rule? (1) D) Range. A five number summary consists of the , the , the , the third quartile, and the maximum value of a dataset. The range, which is the difference between the minimum and maximum values, is not a part of the five number summary. (2) A. To create a five number summary for the dataset, you need to calculate the , the , the , the third quartile, and the maximum value. The is 75, the maximum value is 100, and the is 95. To find the (Q1), you need to find the of the lower half of the dataset. The lower half of the dataset consists of the first 15 scores, which are: 75, 80, 85, 85, 90, 90, 90, 95, 95, 95, 95, 95, 95, 100, 100 The of the lower half of the dataset is 90. To find the third quartile (Q3), you need to find the of the upper half of the dataset. The upper half of the dataset consists of the last 15 scores, which are: 95, 95, 95, 95, 95, 95, 100, 100, 100, 100, 100, 100, 100, 100, 100 The of the upper half of the dataset is 100. Therefore, the five number summary for the dataset is: : 75 : 90 : 95 Third quartile: 100 Maximum value: 100 B. I'll leave it up to you to draw the and get some practice. ๐Ÿ˜‰ C. Based on the five number summary and the , you can conclude that the distribution of the exam scores is skewed to the right, with a long tail of high scores. The (95) is closer to the left side of the box, with more data on the right side. This indicates that there are more high scores in the dataset than low scores. The (75) and the (90) are also relatively low, indicating that there are a few low scores in the dataset. Overall, the distribution of the exam scores is skewed to the right, with a long tail of high scores and a few low scores. (3) To answer this question, you need to calculate the interquartile range (IQR) of the sample. The IQR is the difference between the third quartile and the , and is a measure of the spread of the data. In this case, the IQR is 180 cm - 160 cm = 20 cm. According to the 1.5 x IQR rule, a data point is considered an outlier if it is more than 1.5 times the IQR below the or more than 1.5 times the IQR above the third quartile. In this case, the data point with a height of 220 cm is more than 1.5 times the IQR above the third quartile (180 cm), so it is considered an outlier. The correct answer is: Yes, a height of 220 cm is considered an outlier in our data set! (Notice how we didn't need the raw dataset or the to determine whether a data point is an outlier or not? The five number summary definitely suffices in providing enough information and context.)

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# What are Momentum and Impulse Notes pdf ppt ## What is Momentum? Momentum is a word that we hear used colloquially in everyday life. We are often told that sports teams and political candidates have “a lot of momentum”. In this context, the speaker usually means to imply that the team or candidate has had a lot of recent success and that it would be difficult for an opponent to change their trajectory. This is also the essence of the meaning in physics, though in physics we need to be much more precise. Momentum is a measurement of mass in motion: how much mass is in how much motion. It is usually given the symbol Where m is the mass and is the velocity. The standard units for momentum are , and momentum is always a vector quantity. This simple relationship means that doubling either the mass or velocity of an object will simply double the momentum. The useful thing about momentum is its relationship to force. You might recall from the kinematic equations that change in velocity  can also be written as We can then see that any change in momentum following an acceleration can be written as ## What is Impulse? Impulse is a term that quantifies the overall effect of a force acting over time. It is conventionally given the symbol  and expressed in Newton-seconds. For a constant force, As we saw earlier, this is exactly equivalent to a change in momentum . This equivalence is known as the impulse-momentum theorem. Because of the impulse-momentum theorem, we can make a direct connection between how a force acts on an object over time and the motion of the object. One of the reasons why impulse is important and useful is that in the real world, forces are often not constant. Forces due to things like people and engines tend to build up from zero over time and may vary depending on many factors. Working out the overall effect of all these forces directly would be quite difficult. When we calculate impulse, we are multiplying force by time. This is equivalent to finding the area under a force-time curve. This is useful because the area can just as easily be found for a complicated shape—variable force—as for a simple rectangle—constant force. It is only the overall net impulse that matters for understanding the motion of an object following an impulse. The concept of impulse that is both external and internal to a system is also fundamental to understanding conservation of momentum. ## Momentum in Space: Most people are familiar with seeing astronauts working in orbit. They appear to effortlessly push around freely floating objects. Because astronauts and the objects they are working with are both in free-fall, they do not have to contend with the force of gravity. However, heavy moving objects still posses the same momentum that they do on earth, and it can be just as difficult to change this momentum. Suppose that an emergency occurs on a space station and an astronaut needs to manually move a free-floating 4,000 kg space capsule away from a docking area. On earth, the astronaut knows she can hold a 50 kg weight above herself for 3 seconds. How quickly could she get the capsule moving? We first calculate the total impulse that the astronaut can apply. Note that the astronaut is pushing vertically in both cases so we don’t need to keep track of the direction of the force. And, by the impulse-momentum theorem, we can find the velocity of the spacecraft: ## What is Specific Impulse? Specific impulse start subscript, S, P, end subscript—is a specification commonly given to engines which produce a thrust force. Jet engines and rocket engines are two common examples. In this context, specific impulse is a measure of the efficiency of using fuel to produce thrust and is one of the most important specifications of such an engine. When the prefix specific is used in physics, it means “relative to” a particular quantity. Specific gravity and specific heat are two examples of where you may have seen this prefix used. Specific impulse is impulse measured relative to the weight of fuel—on earth—used to produce the impulse. Because we are dividing an impulse by a force—the force on the fuel due to earth’s gravity—the force units cancel out, and the units for specific impulse are simply seconds. ### Feedback is important to us. error: Content is protected !!

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“This the king. Fisher continues, “In New “This history of the present King of Great Britain is a history of repeated injuries and usurpation, all having, in direct object, the establishment of an absolute tyranny over these States. ” King George comes up in the Declaration of Independence because he (along with Parliament) was adamant about controlling the colonies and making sure they stayed under England’s thumb. King George is the one who actually first called the colonists “rebels,” and so, he became the target of the American Revolution.In February of 1775, King George III spoke before Parliament and said that America was in a “state of rebellion. ” This led to several states declaring their own independent resolutions and dissolving their association with Great Britain. One of these declarations was the Mecklenburg resolutions, created by the citizens of Mecklenburg County in North Carolina. Historian Sydney George Fisher writes, “That declaration of rebellion, said the Mecklenburg resolutions, necessarily annulled all British laws in America and suspended for the present all civil government derived from Great Britain” (Fisher 324).While the Mecklenburg declaration had little impact on the rest of the war, it shows the sentiment of the people and their reaction to what they saw as tyranny by King George III and Parliament. Because Americans had been used to governing themselves since they first came to America, when King George and Parliament tried to levy taxes and place more control on the colony, the people did not like it. King George did not enact all the laws affecting the colonies, the Parliament did, but he became a symbol of English tyranny to the Americans.When the Declaration of Independence was first read to the people, many people reacted by showing their hatred of the king. Fisher continues, “In New York as soon as the patriots heard of the Declaration they dragged down the gilt statue of the king on the Bowling Green and cut off its head” (Fisher 461). Americans hated the King because he allowed the injustices to continue, he condoned them, and he had called the colonists rebels.He may not have been responsible for all the problems in the colonies, but he was the figurehead that represented the country that was causing their problems, and so, they came to see him as a symbol of tyranny and repression. King George III began his reign in 1760, and had only a few years to help impose many new laws and tariffs on the Americans, so he was new in their minds and a handy scapegoat. It is not surprising that he was mentioned in the Declaration of Independence, because the founding fathers wrote that document to declare our independence but also to incite Americans to rise up against Great Britain.Americans needed a “villain” to blame their troubles on, and King George was handy, well known, and helpful in starting a Revolution. However, it really was not King George that levied tariffs and taxed the Americans. It was Parliament who really handed out the laws, and Parliament that the Americans really had a quarrel with. As historian John C. Wahlke notes, “Up to 1774 Americans had done little thinking in this vein thinking of the tyranny of King George III.The authority of Parliament had been the bone of contention, and the participation of the King in the exercise of that authority had been studiously or carelessly ignored” (Wahlke 65). Americans began to say that Parliament did not rule them. They might have allegiance to King George, but they chose their allegiance by free will, and they did not “owe” Parliament anything. When King George called them rebels, he became part of the problem, and part of the founding father’s arguments against the tyranny of foreign rule.Wahlke continues, “Having already proved, largely through their own reading of history, that they were totally outside the jurisdiction of Parliament and were subjects of the King by free choice, they had only to prove to a candid world that the latter, not the former, had played the tyrant” (Wahlke 65). Thus, proving King George was a tyrant helped Americans feel better about giving up English rule, and helped justify the American Revolution throughout the country. Mentioning the King in the Declaration of Independence just added fuel to the fire and gave incentive to even more Americans to revolt.King George may have been many things, from illiterate to perhaps even mad, but he did not cause the American Revolution alone. Parliament had a very big hand in creating dissent, and King George and British policies just helped things along. The Declaration of Independence for its’ time was an inflammatory document, and the authors needed a real “villain” to make Americans feel more justified in the upcoming war. King George had called Americans rebels just a few months before the document was written, and so, he was a good and timely target.The Declaration of Independence was not a perfect document, and the Revolutionary War was not a perfect revolt. There were many Americans who still admired their King and did not want to break with Great Britain. Those that did had to convince others however they could. It is just like today when you have to be careful about what media you trust and what you do not trust. The Revolutionaries were advancing their own cause at the expense of rulers like King George. He may not have been a perfect ruler, but the American Revolutionaries were not without fault, either. King George just happened to make good fodder for American aims. He did support the aims of Parliament, and did believe that Americans should pay a fair share of British taxes. However, he was not the only cause of tyranny against America, and he was not the only cause of the Revolutionary War. Bibliography : Fisher, Sydney George. The Struggle for American Independence. Vol. 1. Freeport, NY: Books for Libraries Press, 1971. Wahlke, John C. , ed. The Causes of the American Revolution. Revised ed. Boston: D. C. Heath and Company, 1967.

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The Revolution Glossary is our new series where we dive deeper into words which are part of the conversations about justice happening around all of us. The goal of this series is to provide a resource for people who want to expand their vocabulary around social justice topics, or people who want extra context and perspective on their word choices. Our hope is that this series can spark some important discussions, and help people jump into those discussions with enthusiasm. We’re diving right into our Revolution Glossary with the word “ally,” a word which often lands differently than intended. Broadly, allyship is when a person with a dominant identity acts to counteract the oppression which gives power to their group and takes it away from a marginalized group. The first social justice related instances of the term ally probably referred to straight people in movements for LGBTQIA+ rights in the 70s. But in recent years ally has become a widely used and debated term. Within the idea of “allyship” lies a bigger question. What role should people with dominant identities play in movements for the liberation of oppressed people? Oppressed people often disagree. In the present day activists have called for white people looking to take action on racial justice to redistribute their resources, use their bodies to protect the lives of Black people, and intentionally redirect focus towards the voices of Black people and other people of color. If a white person does all of these things, can they then claim the title of ally? The obvious danger here is that regardless of the changes any individual person makes, racial inequity and colonialism aren’t math problems that can be solved by a simple transaction. A person with a dominant identity can go to great lengths to untangle themselves from one part of their privilege while still benefiting from it in other ways. And can a donation — or attending a protest — undo every microaggression, biased decision, or moment of privilege that person has experienced? Obviously not, but it’s easy to see how a privileged person might want to think so. There’s no way to make up for being racist or benefiting from racism, but when activists for racial justice put out calls like the ones above, they often report being inundated by white people who are looking for absolution. For that reason, many activists and advocates have decided that the term ally and the concept of allyship do more harm than good, and that they can accept help from people with dominant identities without giving them a specific title. Other terms have arisen as potential replacements. “Co-struggling” emphasizes that everyone who organizes against oppression has to commit to a constant personal struggle, and that charity and pity are unhelpful lenses. “Accomplices” emphasizes that people with dominant identities should try to support an effort rather than lead it, but people in criminalized communities have sometimes pushed back against appropriating justice system language. And other people are fine to stick with the term ally, not necessarily as a title any person can claim, but as a goal to strive toward. Whether or not you, dear reader, should call yourself an ally probably depends on context, and whether the people you’re talking to feel okay with you using that language. Either way, knowing a bit about the term’s history and controversy will help you use it better in conversation, and understand the debate around it.

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