Four hundred eighty dollars are available to fence in a rectangular garden. the fencing for the north and south sides of the garden costs $10 per foot and the fencing for the east and west sides costs $20 per foot. find the dimensions of the largest possible garden.

length on the east and west sides

length on the north and south sides

Step-by-step explanation:

Using x for the length of the east side (and is equal to the length  of the west side) and y for the length of the north side (and is equal to the length  of the south side), the equation that gives the total price equalized to 480 is:

Solving for y

The area of the garden is , to find the largest, substitute y in the formula of the area

For the optimization, find the largest area, is needed the critical point. To find this point, derive A and equalize the derivative to zero:

Solve for x:

To see if x=6 is a maximum or a minimum, derive A' and substitute with x=6

In this case, the second derivative of A doesn't depend on x, and it has a negative value, meaning the value found is a maximum. Using x=6 to find y

The area is:

518,400

step-by-step explanation:

the area is multiplying all the given measurements together.

40 * 18 * 30 * 24 = 518,400

3, 12, 48, 384, 1536, 6144, 24576, 98304

step-by-step explanation:

just keep timing it by 4.