How long will it take for the temperature of the

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Unformatted text preview: ? A solid metal sphere at room temperature of 20◦ C is dropped into a container of boiling water (100◦ C ). If the temperature of the sphere increases 2◦ in 2 seconds, what will the temperature be at time t = 6 seconds? How long will it take for the temperature of the sphere to reach 90◦ C ? An object falling from rest in air is subject not only to the gravitational force but also to air resistance. Assume that the air resistance is proportional to the velocity and acts in a direction opposite to the motion. Then the velocity of the object at time t satisfies v = 32 − kv(t ), k > 0 constant , v(0) = 0. (a) Find i if i(0) = i0 . (b) Does lim i(t ) exist? Compare with Exercise 39. t →∞ (c) Sketch the graph of i. 41. A 200-liter tank initially full of water develops a leak at the bottom. Given that 20% of the water leaks out in the first 5 minutes, find the amount of water left in the tank t minutes after the leak develops: (a) if the water drains off at a rate that is prop...
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