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Math Help - Need help re-arranging an equation!

  1. #1
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    Need help re-arranging an equation!

    Hey all I need some help re-arranging this equation so I can find z here it is:

    also is w^2/wn^2 the same as (w/wn)^2? so I could replace w^2/wn^2 with say r^2?

    x= (w^2/wn^2) / (sqrt( {1-w^2/wn^2}^2 + {2*z*w/wn}^2))

    So I have the value for x and I need to find the value of z. I have had a couple of goes at it and I am honestly not sure if what I am doing is right or not.

    Thanks for any and all assistance in advance!
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  2. #2
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    Re: Need help re-arranging an equation!

    \frac{w^2}{(wn)^2} = \frac{w}{wn} \cdot \frac{w}{wn} = \left(\frac{w}{wn}\right)^2, if that helps you to simplify. You can probably see it can be further simplified.
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  3. #3
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    Re: Need help re-arranging an equation!

    Awesome I thought so! Thanks rowe, where do I go first? Do I get rid of the square root or can I take the entire bottom half of the equation over and times by x ?

    x={r^2}/{sqrt( (1-r^2)^2 + (2*z*r)^2)}
    Last edited by Rhys101; June 18th 2012 at 11:04 PM.
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  4. #4
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    Re: Need help re-arranging an equation!

    will the sqrt just cancel out the squares on the brackets?
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  5. #5
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    Re: Need help re-arranging an equation!

    crap= given wrong equation to start with- real one is here:

    x= (M*R/m)*(r^2) / (sqrt( {1-r^2}^2 + {2*z*r}^2))
    Last edited by Rhys101; June 18th 2012 at 11:24 PM.
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  6. #6
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    Re: Need help re-arranging an equation!

    So your equation is, x = \frac{M\cdot\frac{R}{m}\cdot r^2}{\sqrt{{(1-r^2)}^2+2zr^2}}, and you need to solve for z?
    Last edited by rowe; June 19th 2012 at 12:37 AM.
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  7. #7
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    Re: Need help re-arranging an equation!

    oh, poo, the M*R/m was just set next to the other equation no multiplication sign but a gap between the horizontal divide line if that makes sense? I am sorry
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  8. #8
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    Re: Need help re-arranging an equation!

    No worries; did you mean:

    x = M\cdot\frac{R}{m}\cdot\frac{r^2}{\sqrt{{(1-r^2)}^2+2zr^2}} ?

    You can actually hover over any equation to see the TeX being used. It takes a bit of learning to write what you want but it definitely speeds things up once you know how to write stuff properly.
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  9. #9
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    Re: Need help re-arranging an equation!

    If that is the same as (M*R)/m then thats the one! I'm sorry! Slowly learning this Latex thingimy. Oh, and the 2*z*r was in brackets then squared so : (2*z*r)^2
    I hope that works!


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  10. #10
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    Re: Need help re-arranging an equation!

    Sorry rowe, thanks for your patience with me!
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  11. #11
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    Re: Need help re-arranging an equation!

    Cool, so we have:

    x = \frac{MR}{m}\cdot\frac{r^2}{\sqrt{{(1-r^2)}^2+{(2zr)}^2}} and we need to solve for z. The first step is to remove the square root from the denominator. Do you know how to do this?
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  12. #12
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    Re: Need help re-arranging an equation!

    I am not sure, no sorry, I thought that the squares on the brackets underneath the sqrt would cancel?
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  13. #13
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    Re: Need help re-arranging an equation!

    Anyone else?
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  14. #14
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    Re: Need help re-arranging an equation!

    Quote Originally Posted by Rhys101 View Post
    I am not sure, no sorry, I thought that the squares on the brackets underneath the sqrt would cancel?
    No. There are two terms under the radical, and we cannot split a radical over addition. So

    \sqrt{a^2} = |a|

    but it is not generally true that

    {\color{red}\sqrt{a^2 + b^2} = |a| + |b|}\quad\leftarrow Don't do this.

    To get rid of the square root, you'll need to square both sides of the equation.
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  15. #15
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    Re: Need help re-arranging an equation!

    Ok cool so do I need to flip the equation to square everything? so I get (1/x)^2? and (m/MR)^2? DO I need to square the r^2 on the bottom as well, If I have flipped the equation?
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