10. A search and rescue airplane is flying in a circle with radius expanding at a rate of 3 mph. At what rate is the search area expanding when the radius is 12 miles? (Answers should be exact.) 11. A stone dropped in a pond sends out a circular ripple whose radius increases at a constant rate of 4 ft/sec. After 12 seconds, how rapidly is the area enclosed by the ripple increasing? 12. A 17-foot ladder is leaning against a wall when it begins to slide away from the wall. At what rate is the ladder moving when the top of the ladder is at a height of 15 feet and the base of the ladder is slipping away from the wall at a rate of 5ft/sec? (Answers should be exact.) 13. The position of a body moving on a coordinate line is given by s(t) = t27t + 4, with s in meters and t in seconds. What is the body's speed at t = 2 sec? What is the body's acceleration at t = 2 sec? 14. A ball is thrown up from a cliff 500 ft high. If the height of the ball is given by s(t) = 500 + 64t - 16t, when the ball reach its maximum height? 15. A solid spherical ball is heated and begins to expand. At what rate is the radius increasing when the radius is 4 m and the volume is increasing at a rate of 2 m/sec? (Answers should be exact.) (Volume of a sphere is V = r.) 16. A child, standing 15 feet away from the balloon seller's cart, watches as the balloon seller releases a balloon vertically into the sky. The balloon's height is increasing at the rate of 2 ft/sec when the balloon is 17 feet from the child. How fast is the balloon moving away from the child? (Answers should be exact.)