Two waves on one string are described by the wave functions
y1 = 2.5 cos(3.5x - 1.5t)
y2 = 3.5 sin(4.5x - 1.5t)
where x and y are in centimeters and t is in seconds. Find the superposition of the waves y1 + y2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.)
(a) x = 1.00, t = 1.00
cm

(b) x = 1.00, t = 0.500
cm

(c) x = 0.500, t = 0
cm

The pressure, volume, and temperature of a mole of an ideal gas are related by the equation pv = 8.31t, where p is measured in kilopascals, v in liters, and t in kelvins. use differentials to find the approximate change in the pressure if the volume increases from 14 l to 14.6 l and the temperature decreases from 375 k to 370 k. (round the answer to two decimal places.)

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.)

At the negative terminal of the battery the electron has electric potential energy. what happens to this energy as the electron jumps from the negative to the positive terminal?