Question

help..calculus-balancing point/weighted average

Answer 1

Suppose that a shelf is 6 feet long, with its left end situated at x = 0. If one
book of weight 1 lb is placed at x1 = 0, and another book of weight 1 lb is
placed at x2 = 6, what is the location of x, the point at which the shelf would
(theoretically) balance on a fulcrum?
Now, say that we place four books on the shelf, each weighing 1 lb: at x1 = 0, at x2 = 2, at x3 = 4, and at x4 = 6. Find x, the balancing point of the shelf.