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
The equation A = -w^2 + 20w represents the area of the fence, where w is the width of the fence.
To find the maximum range, we need to find the vertex of the parabola formed by this equation. The vertex of a parabola in the form y = ax^2 + bx + c is given by (-b/2a, f(-b/2a)), where f(x) is the equation of the parabola.
In this case, a = -1, b = 20, and c = 0. Therefore, the vertex is (-20/(2*(-1)), f(-20/(2*(-1))) = (-10, f(-10)).
The maximum range occurs at the vertex, so the width of the fence at the maximum range is w = -10.
However, the width of the fence cannot be negative, so the domain is limited to positive values. Therefore, the final answer is:
• 10 yards