$[8]5.$ A circle is growing with time.

a$)$ At a certain moment, the circle's radius is $20$ inches and is increasing at $3\mathrm{.}5i\frac{n}{sec}.$ At what rate is the circle's area increasing at this same moment?

b$)$ At another moment, the circle's area is increasing at $90i\frac{n^2}{sec}$ and its radius is increasing at $1\mathrm{.}5i\frac{n}{sec}.$ At this moment, what is the radius of the circle?

$[6]6.$ A $10-$foot long ladder is leaning against a wall, but sliding. At a certain moment, the base of the ladder is $5$ feet from the wall, and sliding away from the wall at $2f\frac{t}{sec}.$ At that same moment, how fast is the top of the ladder sliding down the wall?