Question

The radius, rcm, of a circle at time is is given by r =t²/³ - 2t, t is bigger or equal to 0.

Find the rate at which the radius is changing when t = 1 and when t = 2.\

Answer 1

The radius, rcm, of a circle at time is is given by r =t²/³ - 2t, the rate at which the radius is changing when t = 1 and t = 2 is -4/3.

Step-by-step explanation:

Given the formula for the radius of a circle at time t, r = t2/3 - 2t, we need to find the rate at which the radius is changing at t = 1 and t = 2.

To find the rate of change, we need to take the derivative of the radius function with respect to time.

The derivative of r = t2/3 - 2t is dr/dt = (2/3)t-1/3 - 2.

Substituting t = 1 into the derivative, we get dr/dt = (2/3)(1)-1/3 - 2 = 2/3 - 2 = -4/3.

Substituting t = 2 into the derivative, we get dr/dt = (2/3)(2)-1/3 - 2 = 2/3 - 2 = -4/3.

So therefore the rate at which the radius is -4/3.