Marilee is creating a garden in her yard. She needs to put up a fence to keep the animals out of it. She has 40 yards of fencing she can erect. This situation is modeled using the equation A = -w²+ 20w, where A is the area of the fence and w is the width of the fence. Using the equation, what is domain when the maximum range is achieved?
• 10 yards
• 5 yards
• 10 square yards
• 100 yards
To find the domain when the maximum range is achieved, we need to find the value of w that maximizes the area A.
The equation for the area of the fence is A = -w² + 20w.
To find the maximum value of A, we can take the derivative of A with respect to w and set it equal to 0.
dA/dw = -2w + 20
Setting -2w + 20 = 0, we get:
-2w = -20
w = 10
So, when w = 10 yards, the maximum range for the area is achieved.
The domain of w is the set of possible values for w. Since the width of the fence cannot be negative, the domain is w ≥ 0.
Therefore, the correct answer is 10 yards.