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Math Help - Quadratic Box Question

  1. #1
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    Quadratic Box Question

    What is the maximum volume possible from a piece of cardboard that is made into a cube, that measures 16 inches by 12 inches?

    [___________ ]
    [ __________ ]
    [___________ ] 12 - 2x
    [____________]
    16in - 2x

    • A Box with no top.

    L = 12-2x
    W = 16 - 2x
    n = x

    V = 172 - 32x - 24x + 4x^2(x)

    V = 172x - 32x^2 - 24x^2 + 4x^2

    4x^3 - 24x^2 - 32x^2 + 172x

    4x^3 - 56x^2 +172x

    4x(x^2 - 14x + 43)
    How to solve for X.

    this is where I got stuck.

    Thank you
    Last edited by The D00D; October 1st 2009 at 03:07 PM.
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by The D00D View Post
    Note: One with x#'s, are exponents, since I don't know to do an exponent on here

    Thank you
    Use ^ (it's <shift>6 on most keyboards) so x^2 becomes x^2.
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  3. #3
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    Thank you for that.
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  4. #4
    Super Member Matt Westwood's Avatar
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    Okay so I've been looking at this question and I'm not sure I understand what it's asking, so I'm not sure how you got your initial equations.

    But given your starting equations, I rather think you'll find that in your first step, 12 x 16 is a little bit more than 172.

    Your end equation should be something like
    4x (x^2 - 14x + 48)

    Your quadratic in the brackets factorises easily.
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