Question

The area of a rectangular gated farm is modeled by A = -2(x - 30)^2 + 1800 where x represents the

length of farm, in yards. Find the length that will maximize the area. What is the maximum area?

Answer 1

The length that will maximize the area is 30 yards.

Therefore, the maximum area is 1800 square yards.

Step-by-step explanation:

To find the length that will maximize the area, we need to determine the value of x that corresponds to the maximum value of the function A = -2(x - 30)^2 + 1800. This function represents a downward-facing parabola, and the maximum value occurs at the vertex. The x-coordinate of the vertex can be found using the formula x = -b / (2a), where a = -2 and b = -60.

Substituting these values into the formula, we get x = -(-60) / (2*-2) = 30 yards.

Therefore, the length that will maximize the area is 30 yards.

To find the maximum area, we substitute the value of x = 30 into the area formula: A = -2(30 - 30)^2 + 1800 = 1800 square yards.

Therefore, the maximum area is 1800 square yards.