The voltage V (volts), current I (amperes), and resistance R (ohms) of an electric circuit like the one shown here are related by the equation V = IR. Suppose that V is increasing at the rate of 4 volt/sec while I is decreasing at the rate of = amp/sec. Let t denote time V in seconds. Answer the following questions. R . . . a. What is the value of dv at dV dt volt/sec (Simplify your answer.)When a circular plate of metal is heated in an oven, its radius increases at a rate of 0.02 cm/min. At what rate is the plate's area increasing when the radius is 47 cm? . . . The rate of change of the area is cm / min . (Type an exact answer in terms of J.)A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 7 ft from the house, the base is moving y away at the rate of 72 ft/sec. 25-ft ladder a. What is the rate of change of the height of the top of the ladder? y(t) b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? A c. At what rate is the angle between the ladder and the ground changing then? x(t) X . . . a. The rate of change of the height of the top of the ladder is ft/sec. (Simplify your answer.)A child flies a kite at a height of 80 ft, the wind carrying the kite horizontally away from the child at a rate of 34 ft/sec. How fast must the child let out the string when the kite is 170 ft away from the child? . . . The child must let out the string at a rate of ft/sec when the kite is 170 ft away from the child. (Simplify your answer.)A dinghy is pulled toward a dock by a rope from the bow through a ring on the dock 10 ft above the bow. The rope is Ring at edge hauled in at the rate of 2 ft/sec. Complete parts (a) and (b). of dock 110' . . . a. How fast is the boat approaching the dock when 26 ft of rope are out? ft/sec (Type an integer or a simplified fraction.)