The ends of a "parabolic" water tank are the shape of the region inside the graph of y = x2 for 0 ≤ y ≤ 9 ; the cross sections parallel to the top of the tank (and the ground) are rectangles. At its center the tank is 9 feet deep and 6 feet across. The tank is 10 feet long. Rain has filled the tank and water is removed by pumping it up to a spout that is 5 feet above the top of the tank. Set up a definite integral to find the work W that is done to lower the water to a depth of 3 feet and then find the work. [Hint: You will need to integrate with respect to y.] W =_______________ = _____(foot-pounds)
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The ends of a "parabolic" water tank are the shape of the region inside the graph of y = x2 for 0 ≤ y ≤ 9; the cross sections parallel to the top of the tank (and the ground) are rectangles. At its center the tank is 9 feet deep and 6 feet across. The tank is 5 feet long. Rain has filled the tank and water is removed by pumping it up to a spout that is 5 feet above the top of the tank. Set up a definite integral to find the work W that is done to lower the water to a depth of 7 feet and then find the work. [Hint: You will need to integrate with respect to y.]
Brent B.
The ends of a parabolic water tank are the shape of the region inside the graph of Y. The cross sections parallel the top of the tank (and the ground) are rectangles. At its center the tank is feet deep and feet across. The tank feet long. Rain has filled the tank and water removed by pumping it up to a spout that is feet above the top of the tank. Set up a definite integral to find the work W that done over the water to depth of feet and then find the work. [Hint: You will need integrate with respect to Y.]
Adi S.
Water in a vertical cylindrical tank of height 27 ft and radius 2 ft is to be pumped out. The density of water is 62.4 lb/ ft³. (a) The tank is full of water and all of the water is to be pumped over the top of the tank. Find the approximate work for the slice as shown. Use Delta or Δ from the CalcPad. Leave π in your answer. Find the endpoints for the integral that is needed to find the exact amount of work. Lower endpoint = 0 Upper endpoint = 27 (b) The tank is full of water and all but 5 ft of water will be pumped to a height 3 ft above the top of the tank. Find the approximate work for the slice as shown. Use Delta or Δ from the CalcPad. Leave π in your answer. Find the endpoints for the integral that is needed to find the exact amount of work. Lower endpoint = 0 Upper endpoint =
Madhur L.
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