Question

The radius of a circle is rt=t^3+t^2+1 inches at time t minutes for 0≺t≺10.

The radius of the circle is changing at the rate _______when t=.5 minutes.

The circumference of the circle is changing at the rate ________when t=.5 minutes.

The area of the circle is changing at the rate_______ when t=.5 minutes.

Answer 1

im assuming radius is r.
r = t^3 +t^2 +1
Find dr/dt by taking derivative
dr/dt = 3t^2 +2t

circumference is 2*pi*r
c = 2*pi(t^3 +t^2 +1)
Take derivative
dc/dt = 2*pi(3t^2 +2t)

area is pi*r^2
A = pi [t^3 +t^2 +1] ^2
dA/dt = 2pi(t^3 +t^2 +1)(3t^2+ 2t)