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May 2nd, 2010, 04:54 AM   #1
 
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optimization - rectangle in a semicircle

A piece of plexiglass is in the shape of a semicircle with radius 2m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass.

- I tried isolating y from x^2 + y^2 = 4 and substituting it in the formula for the area of the rectangle f(A) = 2xy. Then I found the derivative of f(A) and set it to zero, but I just can't seem to factor it correctly. Can anyone help me out? According to the textbook the answer is supposed to be 1.42m by 0.71m.
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May 2nd, 2010, 06:36 AM   #2
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Re: optimization - rectangle in a semicircle

It won't factor, at least with integers. Use the quadratic formula!
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May 2nd, 2010, 07:54 AM   #3
 
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Re: optimization - rectangle in a semicircle


Does the picture look something like that?
If so just solve it by using 3triangles.
y=(square root (r^2-x^2))*2
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