. . 2 The area of a Circle Increases at a rate of 4 cm Is. a. How fast is the radius changing when the radius is 6 cm? b. How fast is the radius changing when the circumference is 3 cm? a. Write an equation relating the area of a circle, A, and the radius of the circle, r. E (Type an exact answer, using :1: as needed.) The edges of a cube increase at a rate of 2 cm / 5. How fast is the volume changing when the length of each edge is 60 cm? <:> Write an equation relating the volume of a cube, V, and an edge of the cube, 3. D The volume of a cube decreases at a rate of 0.3 ft / min. What is the rate of change of the side length when the side lengths are 7 ft? . . . Write an equation relating the volume of a cube, V, and an edge of the cube, s.4 3 A spherical balloon is inflating with helium at a rate of 144x min . How fast is the balloon's radius increasing at the instant the radius is 3 ft? . . . Write an equation relating the volume of a sphere, V, and the radius of the sphere, r. (Type an exact answer, using it as needed.)A rope passing through a capstan on a dock is attached to a boat offshore. The rope is pulled in at a constant rate of 4 ft/ 5, and the capstan is 4 ft vertically above the water. How fast is the boat traveling when it is 11 ft from the dock? Let x be the horizontal distance from the boat to the dock and 2 be the length of the rope. Write an equation relating x and z. A hot-air balloon is 180 ft above the ground when a motorcycle (traveling in a straight line on a horizontal road) passes directly beneath it going 60 mi / hr (88 ft/s). If the balloon rises vertically at a rate of 12 ft/ 5, what is the rate of change of the distance between the motorcycle and the balloon 10 seconds later? Let x be the horizontal distance from the balloon to the motorcycle, y be the vertical distance from the balloon to the road, and 2 be the distance between the motorcycle and the balloon. Write an equation relating x, y, and z