Question
Nora is creating a dog run in her backyard for her dog Max she has enough materials to create a run with a perimeter of 120 ft this is represented by the function a equals negative w squared plus 60 w where a is the area of the run and w is the width which of the following identifies the X intercepts
Answers
GPT-4o mini
To find the X-intercepts of the function representing the area \( A(w) = -w^2 + 60w \), we need to determine the values of \( w \) for which the area \( A(w) = 0 \).
We can set the function to zero and solve for \( w \):
\[
-w^2 + 60w = 0
\]
Factoring out \( w \):
\[
w(-w + 60) = 0
\]
This gives us two factors:
1. \( w = 0 \)
2. \( -w + 60 = 0 \) ⇒ \( w = 60 \)
Thus, the X-intercepts of the function are \( w = 0 \) and \( w = 60 \). In the context of the dog run, these values represent the widths at which the area of the run is zero.
So the X-intercepts are:
\[
(w, A(w)) = (0, 0) \text{ and } (60, 0)
\]
We can set the function to zero and solve for \( w \):
\[
-w^2 + 60w = 0
\]
Factoring out \( w \):
\[
w(-w + 60) = 0
\]
This gives us two factors:
1. \( w = 0 \)
2. \( -w + 60 = 0 \) ⇒ \( w = 60 \)
Thus, the X-intercepts of the function are \( w = 0 \) and \( w = 60 \). In the context of the dog run, these values represent the widths at which the area of the run is zero.
So the X-intercepts are:
\[
(w, A(w)) = (0, 0) \text{ and } (60, 0)
\]