A large metal disk with radius of 2 m has been made. The density of the metal disk is given by p(r, y) = 3+ 8xy kg/m². A section of the disk from 0 = 0 to 0 = /2, as shown in the figure below. %3D

QUESTION 10 The volume of a sphere is given by V=(4/3)rr³. The rate of change of the volume as the radius changes is: dv 2nr2 r2dr O dt dt dv = 12nr O dt dr dt dv 2 dr 4r2 dt dt

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…

the area to the left of z=0.62 is