Problem $1(50$ points$)$

Given: A piece of sheet metal weighing $\backslash (5\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}^\{2\}\backslash )$ is cut into a rectangle, a triangle, and a parabolic shape. After cutting a $2-$in$.$ diameter hole in the rectangular piece, all members are welded to form the assembly shown below. The equation of the parabola is $\backslash (2$ y$=$x$^\{2\}\backslash ),$ with $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ in inches. All dimensions in the diagram below are in inches.

Required: With respect to the $\backslash ($ x y z $\backslash )-$coordinate system shown in the diagram above, the coordinates of the center of gravity of the assembly.