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Math Help - finding the value of x

  1. #1
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    Exclamation finding the value of x

    An open rectangular tank of height h metres with a square base of side x metres is to be constructed so that it has a capacity of 500 cubic metres. Prove that the surface area of the four walls and the base will be


    2000 + x2 (the 2 is squared)

    x


    square metres. Find the value of x for this expression to be a minimum.


    i have no idea where to even start on this one.
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  2. #2
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    Are you saying it's equal to.........

    2000 + x^2
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  3. #3
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    that just how the question was written, and like i say i have no idea
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  4. #4
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    Oh right I see now.


    Volume of the tank = 500

    Volume = x^{2}h

    Thus

    h = \frac{500}{x^2}

    Surface area minus lid = 4hx + x^2

    Substitute h = \frac{500}{x^2} into surface area equation to get.

     4\times\frac{500}{x^2}x + x^2 = S

    Where S is the surface area of the tank base and four walls.

    This simplifies to be

    \frac{2000}{x} + x^2 = S

    Happy new year.

    Regards,
    Ross
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  5. #5
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    would it not be 5x instead of 4x on this bit

    as there are 4 sides and a base so altogether 5 surfaces.?
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  6. #6
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    No, because it's 4 walls are the same surface area but not the base.

    Thus the base is still the x^2 and the four walls are represented by the other component.
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  7. #7
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    oh right. cheers mate.
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