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?(1 point)
Responses
10 yards
10 yards
5 yards
5 yards
100 yards
100 yards
10 square yards
10 square yards
The domain refers to the possible values of the independent variable, which in this case is the width of the fence (w). To find the domain when the maximum range is achieved, we need to determine the values of w that would maximize the area of the fence (A).
To find the maximum range, we can use the vertex formula. The vertex formula is given by -b/2a, where the quadratic equation is in the form Ax^2 + Bx + C. In this case, the equation A = -w^2 + 20w can be rewritten as -w^2 + 20w = A.
Comparing this equation to the general form Ax^2 + Bx + C, we can see that A = -1, B = 20, and C = 0. Plugging these values into the vertex formula, we have w = -B/2A = -20/2(-1) = 20.
Since the width cannot be negative, the domain of the equation is w ≥ 0. Therefore, the correct answer is:
10 yards