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
100 yards
100 yards
5 yards
5 yards
10 yards
10 yards
10 square yards
10 square yards
The equation provided is A = -w^2 + 20w. To find the domain when the maximum range is achieved, we need to find the maximum point of the quadratic equation. The maximum point of a quadratic equation in the form A = ax^2 + bx + c can be found using the formula x = -b/2a.
In this case, a = -1 and b = 20. Plugging these values into the formula, we get x = -20/(2*-1) = -20/(-2) = 10.
Therefore, the width (w) at which the maximum range is achieved is 10 yards.