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Problem with solving an equation

  1. Aug 30, 2010 #1
    1. The problem statement, all variables and given/known data
    I have a square 50x50 units. I want to make a pool(box without a lid), and then cut away the corners. The "corner-square" is x^2.
    What I want is a formula X(v) that gives me the x value needed to get a fixed volume.


    2. Relevant equations
    The V(x) function is base x height, x(50-2x)^2. But i have problems isolating x based on this formula.



    3. The attempt at a solution
    If i try solving it in Maple I get:
    25/2 + 1/2sqrt(625-2v) and 25/2 - 1/2sqrt(625-2v)
    but this makes no sense to me.

    I've calculated the max volume at x=25/3 to be 250000/27, and the function is only valid from x=0..25.

    I guess the answers Maple gives me is because it does not know og my 0..25 range, but I dont know how to make that part of the calculation.

    If the problem is unclear, please say so and I will try to explain better.
     
  2. jcsd
  3. Aug 31, 2010 #2

    HallsofIvy

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    Science Advisor

    If each side is 50 and you "cut away" [itex]x^2[/itex] from each corner then you base will have sides of length 50- 2x. The base will have area [itex](50- 2x)^2[/itex] and the box will have height x. The volume is [itex]x(50- 2x)^2[/itex].

    Now, what is it you specifically want to do? Solve [itex]x(50- 2x)^2= v[/itex] for any v? Multiplying out the left side gives [itex]4x^3- 200x^2+ 2500x= v[/itex] or the cubic equation [itex]4x^2- 200x^2+ 2500x- v= 0[/itex]. Your "Maple" solution looks like a quadratic formula- you may have left out an "x".
     
  4. Sep 1, 2010 #3
    Thanks for answering!
    What I want is a function that gives me the x value needed to make a box with a cirtain volume.

    I will check my equations in Maple tonight, when I get back from work.
     
  5. Sep 1, 2010 #4
    I did leave out an x, but still did not get a sensible answer. But when I read the problem text once more a saw that I was not supposed to make a formula, but use the formula V=x(50-2x)^2 and use tables to narrow down to the volume you needed.

    So the problem is solved that way and that I figuerd out :P

    Thanks for the help!
     
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