E Homework: Homework: Section 3.11 (Related Rates) Question 8, 3.11.33 HW Score: 1.19%, 0.5 of 42 points (Copy) Part 1 of 3 Save Points: 0 of 3 A piston is seated at the top of a cylindrical chamber with radius 7 cm when it starts moving into the chamber at a constant speed of 4 cm/s (see figure). What is the rate of change of the volume of the cylinder when the piston is 13 cm 7 cm Piston 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 it as needed.)Homework: Homework: Section 3.11 (Related Rates) Question 6, 3.11.29 HW Score: 1.19%, 0.5 of 42 points Save (Copy) Part 1 of 3 O Points: 0 of 3 An angler hooks a trout and reels in his line at 4 in. / s. Assume the tip of the fishing rod is 13 it above the water and directly above the angler, and the fish is pulled horizontally directly toward the angler (see figure). Find the Decreasing horizontal speed of the fish when it is 15 it from the angler. at 4 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.E Homework: Homework: Section 3.11 (Related Rates) Question 7, 3.11.30 HW Score: 1.19%, 0.5 of 42 points Save (Copy) Part 1 of 3 Points: 0 of 3 An arrow is shot into the air and moves along the parabolic path y = x(50 -x) (see figure). The horizontal component of velocity is always 30 ft/s. What is the vertical component of velocity when (i) x = 5 and (ii) x = 45? 30 50 (i) Calculate the derivative of y = x(50 - x) with respect to time. dy dtHomework: Homework: Section 3.11 (Related Rates) Question 13, 3.11.50 HW Score: 1.19%, 0.5 of 42 points Part 1 of 4 O Points: 0 of 3 Save (Copy) A lighthouse stands 475 m off a straight shore and the focused beam of its light revolves five times each minute. As shown in the figure, P is the point on shore closest to the lighthouse and Q is a point on the shore 275 m from P. What is the speed of the beam along the shore when it strikes the point Q? Describe how the speed of the beam along the shore varies with the distance between P and Q. Neglect the height of the lighthouse. 1475 m TO 275 m Let x be the distance along the shore from point P to the beam and let 0 be the angle through which the light revolves. Write an equation that relates x and 0.Homework: Homework: Section 3.11 (Related Rates) Question 9, 3.11.36 HW Score: 1.19%, 0.5 of 42 points Copy) Save Part 1 of 3 O Points: 0 of 3 An inverted conical water tank with a height of 8 it and a radius of 4 it is drained through a hole in the vertex at a rate of 7 ft / s (see Let V be the volume of water in the tank and let h be the depth of the water. Write an equation that relates V and h. figure). What is the rate of change of the water depth when the water depth is 3 ft? (Hint: Use similar triangles.) (Type an exact answer, using it as needed.) 4 ft S f Outflow 7 f /3