A competitive knitter is knitting a circular place mat. The radius of the mat is given by the formula 363
r(t) = 3 -
with r in centimeters and t in seconds.
(t + 11)
A. Find the rate at which the area of the mat is increasing.
Select an answer
B. Use your expression to find the rate at which the area is expanding at t = 5.
Round your answer to 2 decimal(s).
Select an answer

A.

              B. A'(5) = 1.76 cm/s

Step-by-step explanation: Rate of change measures the slope of a curve at a certain instant, therefore, rate is the derivative.

A. Area of a circle is given by

So to find the rate of the area:

Using

Then

Multipying and simplifying:

The rate at which the area is increasing is given by expression .

B. At t = 5, rate is:

At 5 seconds, the area is expanded at a rate of 1.76 cm/s.

3

step-by-step explanation:

divide 13.5 by 9 to get the scale factor. it equals 1.5

2 * 1.5 = 3

2,160 π

step-by-step explanation: