A rectangle is growing such that the length of a rectangle is 5t+4 and its height is t4, where t is time in seconds and the dimensions are in inches. Find the rate of change of area, A, with respect to time. g

Therefore the rate of change of area square inches/ s

Step-by-step explanation:

Given that,

A rectangle is growing such that the length of rectangle is(5t+4) and its height is t⁴.

Where t is in second and dimensions are in inches.

The area of a rectangle is = length× height

Therefore the area of the rectangle is

A(t) = (5t+4) t⁴

⇒A(t) = t⁴(5t+4)

To find the rate change of area we need to find out the first order derivative of the area.

Rules:

A(t) = t⁴(5t+4)

Differentiate with respect to t

Therefore the rate of change of area square inches/ s

72 is the answer to this problem

answer is 12345678900987654321234567890987654321

step-by-step explanation: