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A sphere is expanding with time. Assume that the volume of the sphere is V= = "(t) = t2 + 2. What is the formula for the rate of change of the volume of the balloon, with respect to time?4TT 3 A sphere is expanding with time. Assume that the volume of the sphere is V=- 3 r(t) = to + 2. What is the formula for the rate of change of the volume of the balloon, with respect to time?A triangle with constant base b and height h is changing with time where h(t) = 3t + 1. What is the rate of change of the area of the triangle when t = 1?A square with side x cm, is changing with time where x(t) = 3t + 1. What is the rate of change of the area of the square when t = 2 seconds?What function should be used to maximize the volume of an open box whose surface area is equal to 20 where the box has a square bottom? h X XWhat function should be used to maximize the volume of a closed box whose surface area is equal to 16 where the box has a square bottom? h X X\fWhat point on the function, y = 3x- is the closest to (0, 1)?Jim is running along a parabolic track where his position can be described as y = 332. He knows that his friend is waiting for him at position {0. 1L which is not on the track. Where will Jim he the closest to his friend? An object is traveling along a path described by = \\* +3 . Where along that path will the object be the closest to the point (2, 0)