R R

A 100-W (watt) light bulb has resistance R = 143 2 (ohms) when attached to household current, where voltage varies as V = Vo sin(27ft), where Vo = 110 V, f = 60 Hz. The power supplied to the bulb is P = J/s (joules per second) and the R total energy expended over a time period [0, T] (in seconds) is T U = P(t) dt Compute U if the bulb remains on for 7 hours. (Use decimal notation. Give your answer to one decimal place.) U = J

A cement mixer is pouring concrete in a conical pile. At the time when the height and base radius of the concrete cone are, respectively, 3 and 12 feet, the rate at which the height is increasing is 1 feet per minute, and the rate at which the volume of cement in the pile is increasing is 96π cubic feet per minute. At that moment, how fast is the radius of the cone changing? (Volume of a cone with radius r and height h is given by V=13πr2h.) (Hint: Use the multi-variate chain rule)

A 5m long ladder has its upper end leaning against a vertical wall and lower end on a perfectly leveled ground. The lower end moves away at a constant rate of 3 cm/sec. How fast is the upper end of the ladder moving down, in cm/sec when the lower end is 3m from the wall?