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Cannot Solve for z

  1. Jan 2, 2009 #1
    Hi,

    I have recently returned to education after 15 years out and I am finding that it is my basic maths that causes me the most problems. I have the following equation

    x = y (1-z)/ [tex]\pi[/tex] [tex]\sqrt{}z[/tex]

    so you know, thats pi multiplied by root z.

    and I cant solve for z, can someone rearrange this equation for me.

    thanks
     
  2. jcsd
  3. Jan 2, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Do you mean
    [tex]x= \ffrac{y(1-z)}{\pi\sqrt{z}}[/itex]?
    That would be the same as [itex]\pi x\sqrt{z}= y- yz[/itex] or [itex]yz+ \pi x\sqrt{z}- y= 0[itex].

    Let [itex]u= \sqrt{z}[/itex] so that [itex]u^2= z[/itex]. Then the equation becomes [itex]yu^2+ \pi xu+ y= 0[/itex], a quadratic equation for u. That can be solved using the quadratic formula and then square u to find z.
     
  4. Jan 2, 2009 #3
    To me that kind of looked like:

    [tex] x = \frac{y(1-z)}{\sqrt[\pi]{z}} [/tex]

    But it could be anything.
     
  5. Jan 2, 2009 #4
    sorry I will try again, the equation should be

    [tex]
    x = \frac{y(1-z)}{\pi\sqrt{z}}
    [/tex]

    then solve for z

    thanks
     
    Last edited: Jan 2, 2009
  6. Jan 2, 2009 #5
    substitute [tex]z'=\sqrt{z}[/tex] and you get a quadratic eq.. Then multiply both sides by [itex]\pi z'[/itex]
     
  7. Jan 2, 2009 #6
    Thanks guys, I got the answer i was looking for after I made it into a quadratic.

    Thanks for your help
     
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