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 waterand directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find thehorizontal speed of the fish when it is 18 ft from the angler.Decreasingat 5 in./s13 ftLet 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. Writeequation relating x and z.Differentiate both sides of the equation with respect to t.dxdzdtdtWhen the fish is 18 ft from the angler, its horizontal speed is about Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. Suppose the height of the pile increases at a rate of2 cm /s when the pile is 18 cm high. At what rate is the sand leaving the bin at that instant?Let V and h be the volume and height of the cone, respectively. Write an equation that relates V and h and does not include the radius of the cone.(Type an exact answer, using n as needed.)Differentiate both sides of the equation with respect to t.dVdh%3Ddtdt(Type an exact answer, using T as needed.)The sand is leaving the bin at a rate of(Type an exact answer, using t as needed.)

Pythagoras theorem: h2=b2+p2 , where h is the hypotenuse , b is the base and p is the perpendicular…

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 Decreasing at 5 in./s and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the horizontal speed of the fish when it is 18 ft from the angler. 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 equation relating x and z. Differentiate both sides of the equation with respect to t. dx dz dt dt When the fish is 18 ft from the angler, its horizontal speed is about