A water tower contains $250$ gallons of water at $t=0.$ During the time interval $0t14$

hours, water is being pumped into the tank at a rate

$P(t)=co{s}^2(\frac{x^2}{31})+5$

During the same time interval, water is being removed from the tank at the rate

$G(t)=-\mathrm{.}27x^2+4x$

A$)$ How many gallons of water are removed from the tank during the time interval $0t14?$

B$)$ Is the level in the tank rising or falling at $t=7?$

C$)$ How many gallons of water are in the tank at time $t=14?$

D$)$ At what time $t$ for $0t14$ is the volume of water in the tank the least?