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Math Help - Please Help Final Tom!! Word Problem

  1. #1
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    Question Please Help Final Tom!! Word Problem

    An open box is to be made from a square piece of material 12 inches on a side by cutting equal squares of length x from the corners and turning up the sides.
    (a)Write the volume (V) as a function of x.







    (b) What is the domain of this function?

    (Hint: Solve 0 < 12 2 x < 12)
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  2. #2
    GAMMA Mathematics
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    V=x(12 - 2x)^2
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  3. #3
    Senior Member DivideBy0's Avatar
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    If you are looking for the practical domain of V(x) = x(12-2x)^2, since (12-2x)^2 must always be positive, if we have x \leq 0, then x(12-2x)^2 will not be positive, but since Volume is positive, we must have x> 0. So the domain is x \in R^{+}
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  4. #4
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    Quote Originally Posted by DivideBy0 View Post
    ..., since (12-2x)^2 must always be positive, ...
    Hello,

    this statement isn't quite correct. With this problem it is necessary that

    12-2x \geq 0~\wedge~x \geq 0

    Otherwise you cut off more than there exist - and that means you build a box by cutting off parts of the 3-D-space to get a negative space
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