(Solved): A circle has an initial radius of 50ft when the radius begins decreasing at the rate of 4ft/min. Wh ...

A circle has an initial radius of $50\mathrm{ft}$ when the radius begins decreasing at the rate of $4\mathrm{ft}/\min$. What is the rate in the change of area at the instant that the radius is $23\mathrm{ft}$ ? Write an equation relating the area of a circle, $\mathrm{A}$, and the radius of the circle, $\mathrm{r}$. (Type an exact answer, using $?$ as needed.) Differentiate both sides of the equation with respect to $t$. $\frac{\mathrm{dA}}{\mathrm{dt}}=\frac{\mathrm{dr}}{\mathrm{dt}}$ (Type an exact answer, using $?$ as needed. Type an expression using $\mathrm{r}$ as the variable.) The rate of change of the area is (Type an exact answer in terms of $?$.)