The radius of a sector of a circle is increasing at a rate of 3 cm/sec while the area is decreasing at a rate of 1 cm2/sec. At what rate is the angle of the sector changing when the area is 20 cm2 and the radius os 5cm?

Answer 1

Huh? How is this even possible? Anyway, just use the product rule to get

a = 1/2 r^2 θ
da/dt = 1/2 * 2rθ dr/dt + 1/2 r^2 dθ/dt

So, now all you ave to do is find θ when a=20 and r=5

Then plug that in to solve for dθ/dt