Question

Farmer John is building a fenced-in region for his sheep. Suppose that the area of the region is given by the formula. A(x)= (120x-2x²) / (3) where 0≤ x≤ 60.

Answer 1

To find the maximum area of the fenced-in region, we can use calculus. First, we find the derivative of the function and set it equal to zero to find the critical points. Then, we evaluate the second derivative to determine if it is a maximum or minimum. Finally, we substitute the critical points into the function to find the maximum area.

Step-by-step explanation:

The question is asking for the subject and grade level of the given problem. This problem involves finding the area of a fenced-in region, which falls under the subject of Mathematics. Given the formula A(x) = (120x - 2x^2)/3 and the condition 0 ≤ x ≤ 60, we can use calculus to find the maximum area of the region.

To find the maximum area, we need to find the derivative of the given function A(x) and set it equal to zero. After finding the critical points, we can evaluate the second derivative to determine if it is a maximum or minimum. Finally, we substitute the critical points into A(x) to find the maximum area.

Answer 2

The length of the fourth side of the fenced-in region can be found by subtracting the sum of the other three sides from 0.

Step-by-step explanation:

The given formula represents the area of the fenced-in region for Farmer John's sheep. The formula is A(x) = (120x - 2x²) / 3, where x represents the length of one side of the region. To find the length of the fourth side of the region, we can subtract the sum of the lengths of the other three sides from 0. Let's call the length of the fourth side D. Therefore, the equation becomes: y + A + B + C + D = 0.