anonymous
  • anonymous
find the value of "x" that gives the greatest possible area of a rectangle? with a length of 3x inches and a height of (8-x)inches
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
you can also do 3x(8-x)=0 and find the y-coordinate of the vertex, then solve for x
anonymous
  • anonymous
not =0, rather just find the vertex of 3x(8-x)
anonymous
  • anonymous
Area is length times width; as a function of x,\[A(x)=3x(8-x)=-x^2+24x\]This function is quadratic, opening downward. Its maximum is at the vertex, with x value x=-b/2a=-24/-2=12

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More answers

anonymous
  • anonymous
It seems the maximum area is just about 144 in^2.
anonymous
  • anonymous
One thing I'm noting here is that the height of the rectangle works out to a negative number; I'm a little concerned about that......
anonymous
  • anonymous
you took out the 3 for some reason from your calculation in the vertex
anonymous
  • anonymous
I guess I've had enough math for today; can't even distribute properly any more...LOL
anonymous
  • anonymous
lol
anonymous
  • anonymous
the vertex has x-coordinate of 4, so the dimensions are 3*4 x (8-4) or 12 x 4
anonymous
  • anonymous
Attempt number two: \[A(x)=-3x^2+24x\]Maximum value at x=-b/2a=-24/-6=4 Maximum value about 48 in^2.

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