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NSQ2.6

NSQ2.6 - 76 Part 1 Introduction a How does the value of t...

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76 Part 1 Introduction a. How does the value of t at which the height of the ball is at a maximum depend on the parameter g1 b. Use your answer to part (a) to describe how maximum height changes as the parameter g changes. c. Use the envelope theorem to answer part (b) directly. d. On the Earth g = 32, but this value varies somewhat around the globe. If two locations had gravitational constants that differed by 0.1, what would be the difference in the maximum height of a ball tossed in the two places1 2.6 A simple way to model the construction of an oil tanker is to start with a large rectangular sheet of steel that is x feet wide and 3x feet long. Now cut a smaller square that is t feet on a side out of each corner of the larger sheet and fold up and weld the sides of the steel sheet to make a traylike structure with no top. a. Show that the volume of oil that can be held by this tray is given by V = t(x - 2t)(3x - 2t) = 3tx 2 - 8t 2 X + 4t 3 .
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