A bucket that weighs 4 lb and a rope of negligible weight are used to draw water from a well that is 50 ft deep. The bu is filled with 36 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. Ib/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 w Enter x;" as x₁.) lim 318 Ax Express the work as an integral. ] )dx Evaluate the integral. ft-lb

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

You drop your sun tan lotion on the edge of the swimming pool, and it starts to leak in to the pool, forming a semicircular sun tan oil slick. If the area of the sun tan oil slick is growing at a rate of 10cm2/minute, how fast is the radius growing when the radius is 10cm?

A leaky 10-kg bucket is lifted from the ground to a height of 10 m at a constant speed with a rope that weighs 0.7 kg/m. Initially the bucket contains 30 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 10-m level. How much work is done? (Use 9.8 m/s² for g.) Show how to approximate the required work (in J) by a Riemann sum. (Let x be the height in meters above the ground. Enter x.* as x₁.) Σ( j=1 Express the work (in J) as an integral in terms of x (in m). lim n-∞ Ax dx Evaluate the integral (in J). (Round your answer to the nearest integer.)