A bucket of water is lifted vertically at a constant rate of 1 .5 ft/sec using a

Question

A bucket of water is lifted vertically at a constant rate of 1 .5 ft/sec using a rope of negligible weight. As it rises, water leaks out at the rate of 0.25 lb/sec. If the bucket weighs 4 lbs when empty and it contained 20 lbs of water when the lifting started, determine the work done in raising the bucket 12 feet Find the center of mass of the thin plate of uniform density delta bounded by the graphs of the equations y = x^2 and y = 4 (see figure) Evaluate the following integral: integral 1/root 4e^4x - 9 dx

Explanation / Answer

2.

Center of Mass

Center of mass or centroid of a thin plate with uniform density ?. The center of mass or centroid of a region is the point in which the region will be perfectly balanced horizontally if suspended from that point.

So, let

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