A controller on an electronic arcade game consists of a variable resistor connected across the plates of a 0.227 μF capacitor. The capacitor is charged to 5.03 V, then discharged through the resistor. The time for the potential difference across the plates to decrease to 0.833 V is measured by a clock inside the game. If the range of discharge times that can be handled effectively is from 11.5 μs to 6.33 ms, what should be the (a) lower value and (b) higher value of the resistance range of the resistor?

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)