An angler hooks a trout and reels in his line at 5 in. / s. Assume the tip of the fishing rod is 13 ft above the water and directly above the angler, and the fish is Decreasing pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is 19 ft from the angler. at 5 in. /s 13 ft Let x be the horizontal distance from the angler to the fish and z be the length of the fishing line, where both x and z are measured in inches. Write an equation relating x and z.A piston is seated at the top of a cylindrical chamber with radius 2 cm when it starts moving into the chamber at a constant speed of 7 cm/s (see gure). What is the Piston rate of change of the volume of the cylinder when the piston is 1 cm from the base of the chamber? Let V, r, and h be the volume, radius, and height of a cylinder, respectively. Write an equation relating V, r, and h. (Type an exact answer, using 1: as needed.) A 25-foot ladder is leaning against a vertical wall (see gure) when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.5 ft / 5. How fast is the top of the ladder sliding down the wall when the foot of the ladder is 7 ft from the wall? Let x be the distance from the foot of the ladder to the wall and let y be the distance from the top of the ladder to the ground. Write an equation relating x and y. A 6-foot-tall woman walks at 9 ft/s toward a street light that is 36 ft above the ground. What is the rate of change of the length of her shadow when she is 14 ft from the street light? At what rate is the tip of her shadow moving? Let L be the length of the woman's shadow and let X be the woman's distance from the street light. Write an equation that relates L and x. Asurface ship is moving in a straight line (horizontally) at 9 km/hr. At the same time, an enemy submarine maintains a position directly below the ship while diving at an angle that is 20 below the horizontal. How fast is the submarine's altitude decreasing? Let x be the distance traveled by the surface ship and y be the altitude of the submarine. Write an equation relating x and y. Choose the correct answer below. >