Question of A trough is 9 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x* from x = -1 to x = 1 . The trough is full of water. Find the amount of work in foot-pounds required to empty the trough by pumping the water over the top. Note: In this problem, use 62 pounds per cubic foot as the weight of water. foot-pounds Question Help: Video B Written Example Message instructor Submit Question Question 9 0/1 pt 20 8 Details A circular swimming pool has the shape of a cylinder, with a diameter of 14 m, the sides are 4 m high, and the depth of the water is 3 m. How much work (in Joules, to the nearest integer) is required to pump all of the water over the side? The acceleration due to gravity is 9.8 - 2 and the density of water is 1000 kg m 3 Joules Question Help: Video B Written Example Message instructor Submit Question Question 10 0/1 pt 20 @ Details A tank, shaped like a cone has height 6 meters and base radius 5 meters long. It is placed so that the circular part is upward. It is full of water, and we have to pump it all out by a pipe that is always leveled at the surface of the water. Assume that a cubic meter of water weighs 10000N, i.e. the density of water is 10000- N m3 . (Note: The water in question is not "pure" water with p = 1000 and therefore pg = 9800. It is heavier than that, due to impurities. ) How much work does it require to pump all water out of the tank? Enter the exact value of your answer, as a multiple of 7. W = Joules Question 11 Go/1 pt 9 20 @ Details The city of Pythagorean Pointe is in the shape of a rectangle, whose border is shown in the graph below. A highway running along the &-axis borders one side of the town, and the grid is shown in miles along each axis. 9 -2 -1 2 3 4 5 6 7 8 9 1-2 The population density of Pythagorean Pointe is b(y) = 2500- 2500 people 3 y, where b(y) is measured in mile? and y is measured in miles from the highway. Consider a thin, rectangular slice of the town, cut parallel to the x-axis with thickness Ay. Write an expression that approximates the population living in this region. Population in this region ~ Ay Use an integral to calculate the population in the whole town of Pythagorean Pointe. Round your answer to the nearest whole person. Population in the whole town ~ people