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Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.
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Mathematics, 21.06.2019 19:50
Prove (a) cosh2(x) − sinh2(x) = 1 and (b) 1 − tanh 2(x) = sech 2(x). solution (a) cosh2(x) − sinh2(x) = ex + e−x 2 2 − 2 = e2x + 2 + e−2x 4 − = 4 = . (b) we start with the identity proved in part (a): cosh2(x) − sinh2(x) = 1. if we divide both sides by cosh2(x), we get 1 − sinh2(x) cosh2(x) = 1 or 1 − tanh 2(x) = .
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Mathematics, 21.06.2019 20:30
Solve this riddle: i am an odd number. i an less than 100. the some of my digit is 12. i am a multiple of 15. what number am i?
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Mathematics, 21.06.2019 21:00
Abakery recorded the number of muffins and bagels it sold for a seven day period. for the data presented, what does the value of 51 summarize? a) mean of bagels b) mean of muffins c) range of bagels d) range of muffins sample # 1 2 3 4 5 6 7 muffins 61 20 32 58 62 61 56 bagels 34 45 43 42 46 72 75
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