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Math Help - maximum and minimum

  1. #1
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    maximum and minimum

    A wire of length 100cm is cut into two pieces of length xcm and ycm. The piece of length xcm is bent into the shape of a square and the piece of length ycm into the shape of a circle. Find x and y so that the sum of the areas encloseed by the shapes will be (a) a minimum (b) a maximum

    I gathered that one of the equation will be x+y=100 but im not sure what the other equation will be, please help me with this? thanks
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  2. #2
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    solve using whatever method you have been taught
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  3. #3
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    i don't get why the area of a circle is y/4Pi?
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  4. #4
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    oopsie i did it wrong

    circumference = y = 2pi r

    rearrange so you have the area (pi * r * r) on one side.



    the RHS is the area of the circle
    Last edited by SpringFan25; May 1st 2011 at 10:47 AM.
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  5. #5
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    so i subbed in the equations and then differentiate it to get the st. pts. and got

    x=400/(Pii+4)

    and

    y=100Pi/(Pi+4)

    but i test the nature for this and wasn't able to prove it to be a minimum or a maximum point. why is that?
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  6. #6
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    show your calculations, it looks like a minimum to me:
    ]SEE THIS LINK
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