Find the derivative of y with respect to t. - y = sec 7\fA 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 5 ft from the house, the base is moving away at the rate of 24 ftlsec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? Sand falls from a conveyor belt at a rate of 14 m3/min onto The height is Changing at a rate of D cm/min the top of a conical pile. The height of the pile is when the height is 7 m. always threeeighths of the base diameter. How fast are (Type an exact answer, using :1: as needed.) the height and the radius changing when the pile is 7 m high? Answer in centimeters per minute. A dinghy is pulled toward a dock by a rope from the bow through a ring Ring at edge on the dock 9 ft above the bow. The rope is hauled in at the rate of 2 of dock ft/sec. Complete parts (a) and (b). 19' . . . a. How fast is the boat approaching the dock when 15 ft of rope are out? ft/sec (Type an integer or a simplified fraction.)