Indow Help a Active Calculus 2.0.pdf (page 393 of 553) 6. Consider the curve f(x) 3 cos() and the...
indow Help a Active Calculus 2.0.pdf (page 393 of 553) 6. Consider the curve f(x) 3 cos() and the portion of its graph that lies in the fi quadrant between the y-axis and the first positive value of x for which f(x) 0. Let R denote the region bounded by this portion of f, the x-axis, and the y-axis. Assume that r and y are each measured in feet. a. Picture the coordinate axes rotated 90 degrees clockwise so that the positive r-axis points straight down, and the positive y-axis points to the right. Suppose that R is rotated about the x axis to form a solid of revolution, and we consider this solid as a storage tank. Suppose that the resulting tank is filled to a depth of 1.5 feet with water weighing 62.4 pounds per cubic foot. Find the amount of work required to lower the water in the tank until it is 0.5 feet deep, by pumping the water to the top of the tank. b. Again picture the coordinate axes rotated 90 degrees clockwise so that the positive r- axis points straight down, and the positive y-axis points to the right. Suppose that R together with its reflection across the x-axis, forms one end of a storage tank that is 10 feet long. Suppose that the resulting tank is filled completely with water weighing 62.4 pounds per cubic foot. Find a formula for a function that tells the amount of work required to lower the water by h feet. c. Suppose that the tank described in (b) is completely filled with water. Find the total force due to hydrostatic pressure exerted by the water on one end of the tank.
indow Help a Active Calculus 2.0.pdf (page 393 of 553) 6. Consider the curve f(x) 3 cos() and the portion of its graph that lies in the fi quadrant between the y-axis and the first positive value of x for which f(x) 0. Let R denote the region bounded by this portion of f, the x-axis, and the y-axis. Assume that r and y are each measured in feet. a. Picture the coordinate axes rotated 90 degrees clockwise so that the positive r-axis points straight down, and the positive y-axis points to the right. Suppose that R is rotated about the x axis to form a solid of revolution, and we consider this solid as a storage tank. Suppose that the resulting tank is filled to a depth of 1.5 feet with water weighing 62.4 pounds per cubic foot. Find the amount of work required to lower the water in the tank until it is 0.5 feet deep, by pumping the water to the top of the tank. b. Again picture the coordinate axes rotated 90 degrees clockwise so that the positive r- axis points straight down, and the positive y-axis points to the right. Suppose that R together with its reflection across the x-axis, forms one end of a storage tank that is 10 feet long. Suppose that the resulting tank is filled completely with water weighing 62.4 pounds per cubic foot. Find a formula for a function that tells the amount of work required to lower the water by h feet. c. Suppose that the tank described in (b) is completely filled with water. Find the total force due to hydrostatic pressure exerted by the water on one end of the tank.