Sand falls from a conveyor belt at a rate of 13 m / min onto the top of a conical pile. The height of the pile is always three-eighths of the base diameter. How fast are the height and the radius changing when the pile is 8 m high?A spherical balloon is inflating with helium at a rate of 300x it" / min. How fast is the balloon's radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing? . . . The balloon's radius is increasing at a rate of 3 ft / min at the instant the radius is 5 ft. (Simplify your answer.) The surface area is increasing at a rate of its / min at the instant the radius is 5 ft. (Type an exact answer, using It as needed.)A balloon is rising vertically above a level, straight road at a constant rate of s(t) is increasing by 5 ft/sec. 4 ft / sec. Just when the balloon is 52 ft above the ground, a bicycle moving at a constant rate of 16 ft / sec passes under it. How fast is the distance s(t) between (Simplify your answer.) the bicycle and balloon increasing 3 seconds later? 7(t) s( t) ( t)dx dy The coordinates of a particle in the metric xy-plane are differentiable functions of time t with = - 1 m / sec and dt dt = -8 m / sec. How fast is the particle's distance from the origin changing as it passes through the point (12,9)? The particle's distance is changing at a rate of - 5 m / sec from the origin as it passes through the point (12,9). (Type an integer or a simplified fraction.)A spherical iron ball 10 in. in diameter is coated with a layer of ice of uniform thickness. If the ice melts at a rate of 15 in." / min, how fast is the thickness of the ice decreasing when it is 2 in. thick? How fast is the outer surface area of ice decreasing