A radioactive bar of radius 5cm and length 2m is submerged along the central axis of a cylindrical pool of cooling water of depth 2m and radius 5m. Assume that the bar is giving off radiation according to the function 8(r) = e(r-0.05)3 Ci m where r measures the distance from the central axis of the radioactive rod. Find the total amount of radiation, in curies (Ci), in the pool. Note, the figure is not to scale. Submit 1

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…