Find the greatest possible enclosed area of a rectangular corral given 400 feet of fencing

Maximum area = 10000 square units.

Step-by-step explanation:

We are given the following information:

Rectangular perimeter of coral =  400 units.

Let length of the coral be x. Then,

Perimeter = 400 = 2(Length +Breadth)

Thus, the area of rectangle is given by,

Thus, we have to maximize the function:

We will use double derivative test.

First we differentiate with respect to x.

Equating this to zero to obtain critical points,

Now, again differentiating with respect to x.

Thus, by double derivative test, local maxima occurs for this function at x = 100

So, Length = x = 100 units

Breadth = 200 - x = 100 units

Maximum area = 10000 square units.

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40