The lowest key on a piano plays a note called A0 (27.5 Hz). If you push that key down very slowly and hold it, the felt hammer below won't have enough energy to strike the string but the wool damper, which usually rests on top of the string to stop it from vibrating, will stay lifted leaving the string "open." If you then play an A major chord one octave op, consisting of A1 (55 Hz) - C#2 (68.75 Hz) - E2 (82.5 Hz) - A2 (110 Hz), with a quick, hard strike and sudden staccato release, you will hear a soft, long-lived echo of the chord even though the dampers have stopped vibration in the strings of the chord. What is going on here? Explain in a few sentences.

Does work output exceed work input when a machine is used? a) yes, it does, as machines create energy. b) it depends on the type of machine used. c) no, it doesn’t, as machines are inefficient. d) no, it doesn’t, as machines cannot create energy.

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.)

Both independent and dependent clauses