Abucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 80 ft deep. the bucket is filled with 42 lb of water and is pulled up at a rate of 2 ft/s, but water leaks out of a hole in the bucket at a rate of 0.2 lb/s. find the work done in pulling the bucket to the top of the well. show how to approximate the required work by a riemann sum. (let x be the height in feet above the bottom of the well. enter xi* as xi.)

Four point charges each having charge q are located at the corners of a square having sides of length a. find symbolic expressions for the following. (a) the total electric potential at the center of the square due to the four charges (use any variable or symbol stated above along with the following as necessary: ke.) vtotal= (b) the work required to bring a fifth charge p from infinity to the center of the square (use any variable or symbol stated above along with the following as necessary: w=