A water tank is created by revolving the graph y=1/x about the y-axis, with the v(h) = √ ^ 72 dy. bottom of tank at y = 1. The volume of the tank is given by where h is the height of the water in the tank. Initially, the tank is empty, but water begins to flow into the tank at a rate of 1.5 cubic feet per minute. Determine how fast the level of the water is rising when the water is 2 feet deep. 0.95 ft/min. 1.91 ft/min. 3.0 ft/min. 6 ft/min. 13.5 ft/min.

Suppose a tank…

At the bottom of a swimming pool, the pressure exerted at a given point is proportional to the depth of the water above it. In particular, the pressure at a given point of depth d is equal to 10, 000d Pascals. We will investigate the total pressure at the bottom of a swimming pool depending on its shape. You may view 3D models of the swimming pools for reference here (note that this is one model plotting the depth as a function of x and y, so represents essentially the pool flipped upside-down): https://www.geogebra.org/m/nnf4yhax (a) Suppose we have a rectangular pool that is 50 meters long and 25 meters wide. The pool has a shallow end that is 1 meter deep at the edge, a deep end 50 meters away that is 3 meters deep at the edge, and is such that the bottom of the pool forms a linear slant in between (so along a line segment parallel to the short side, the pool has constant depth, and along a line segment parallel to the long side, the pool's depth varies linearly). Set up and…