ap calculus question

Question

 

For time 0≤t≤8, people arrive at a venue for an outdoor concert at a rate modeled by the function A defined by A(t)=0.3sin(1.9t)+0.3cos(0.6t)+1.3. For time 0≤t≤1, no one leaves the venue, and for time 1≤t≤8, people leave the venue at a rate modeled by the function L defined by L(t)=0.2cos(1.9t)+0.2sint+0.8. Both A(t) and L(t) are measured in hundreds of people per hour, and t is measured in hours. The number of people at the venue, in hundreds, at time t hours is given by P(t).

A rectangular “standing-only” section at the venue changes size as t increases in order to manage the flow of people. Let x represent the length, in feet, of the section, and let y represent the width, in feet, of the section. The length of the section is increasing at a rate of 6 feet per hour, and the width of the section is decreasing at a rate of 3 feet per hour. What is the rate of change of the area of the section with respect to time when x=16 and y=10 ? Indicate units of measure.

Answer 1

So I only see one question near the end of the second paragraph. What ever described in the first paragraph has nothing to do with this question.

both the x and y are the functions with variable of time - t. So we have

, where and are the changing rate of the x and y, respectively.

The area S is:

.

So the the change rate of the area is:

.

Plug in the numbers of

and then you can get the rate of change of the area of the section in square feet per hour.