A bucket that weighs 6 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 1.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.15 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 x₁ * as x₁.) Σ([ Express the work as an integral. lim Evaluate the integral. ft-lb Ax dx

A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bucket is filled with 40 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 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 x.* as x₁.) n 2([ =1 Express the work as an integral. lim n→∞ Evaluate the integral. ft-lb Ax dx

A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 70 ft deep. The bucket is filled with 38 lb of water and is pulled up at a rate of 2.5 ft/s, but water leaks out of a hole in the bucket at a rate of 0.25 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 x₁* as x₁.) lim n→∞;=1 Express the work as an integral. Evaluate the integral. ft-lb Ax Need Help? Talk to a Tutor dx

A tubular metal 3.9 meters long leans against a vertical wall and the other foot of the metal is on the horizontal ground. If the foot of the metal was pushed towards the wall at the rate 1.8m/s, at what rate is the top of the tubular metal move when the foot is 1.5 meters from the wall