All edges of a cube are expanding at a rate of 7 centimeters per second. (a) How fast is the volume changing when each edge is 2 centimeter(s)? cm3/sec (b) How fast is the volume changing when each edge is 12 centimeters? cm/secA swimming pool is 12 meters long, 5 meters wide, 1 meter deep at the shallow end, and 3 meters deep at the deep end (see figure below). Water is being pumped into the pool at 1/3 cubic meter per minute, and there is 1 meter of water at the deep end. (a) What percent of the pool is filled? (b) At what rate is the water level rising? :lm/min A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. 25 ft 2- it (a) What is the velocity of the top of the ladder when the base is given below? 7 feet away from the wall |ft/sec 20 feet away from the wall ft/sec 24 feet away from the wall ft/sec (b) Consider the triangle formed by the side of the house, ladder, and the ground. Find the rate at which the area of the triangle is changing when the base of the ladder is 20 feet from the wall. ft2/ sec (c) Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 20 feet from the wall. rad/secA man 6 feet tall walks at a rate of 7 feet per second away from a light that is 15 feet above the ground (see gure). (a) When he is 10 feet from the base of the light, at what rate is the tip of his shadow moving? Ewe: (b) When he is 10 feet from the base of the light, at what rate is the length of his shadow changing? Em The combined electrical resistance R of two resistors R1 and R2, connected in parallel, is given by the equation below, where R, R1, and R2 are measured in ohms. R1 and R2 are increasing at rates of 0.5 and 1.4 ohms per second, respectively. 1 1 1 _ = _ I _ R R1 R2 At what rate is R changing when R1 = 52 ohms and R2 = 89 ohms? (Round your answer to three decimal places.) :] ohm/sec