anonymous
  • anonymous
Please help :) A farmer wishes to enclose a pasture that is bordered on one side by a river (so one of the four sides won't require fencing). She has decided to create a rectangular shape for the area, and will use barbed wire to create the enclosure. There are 600 feet of wire available for this project, and she will use all the wire. What is the maximum area that can be enclosed by the fence? (Hint: Use this information to create a quadratic function for the area enclosed by the fence, then find the maximum of the function.)
Mathematics
chestercat
  • chestercat
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Mertsj
  • Mertsj
|dw:1437272760059:dw|
anonymous
  • anonymous
how would i solve for the maximum?
mathstudent55
  • mathstudent55
The area function is an inverted parabola. Its maximum value occurs at the axis of symmetry.

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Mertsj
  • Mertsj
Find the vertex of the parabola. The y coordinate of the vertex is the answer you want.
Mertsj
  • Mertsj
Put the equation into this form: A = ax^2 +bx
anonymous
  • anonymous
so would it be a=-2x^2+600x?
Mertsj
  • Mertsj
What is the value of "a"
anonymous
  • anonymous
i don't get it :/
Mertsj
  • Mertsj
|dw:1437273456010:dw|
Mertsj
  • Mertsj
What is the value of a? of b?
anonymous
  • anonymous
ohh -2 and 600
anonymous
  • anonymous
is it 300?
Mertsj
  • Mertsj
Now that is important because the x coordinate of the vertex is "the opposite of b" divided by 2a. Find the x coordinate of the vertex.
Mertsj
  • Mertsj
I posted that wrong. Try again.
anonymous
  • anonymous
150?
Mertsj
  • Mertsj
yes
Mertsj
  • Mertsj
Now go back to the equation A = -2x^2+600x and replace x with 150.
anonymous
  • anonymous
i got 180000
Mertsj
  • Mertsj
\[A=-2(150)^2+600(150)\] \[A=-2(22,500)+90,000\]
Mertsj
  • Mertsj
\[A=-45,000+90,000=45,000\]
anonymous
  • anonymous
oh oops so is the maximum area 45000?
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
okay thank you so much :)
Mertsj
  • Mertsj
And the dimensions are 150 by 300
Mertsj
  • Mertsj
yw

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