# Need help re-arranging an equation!

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• June 18th 2012, 10:44 PM
Rhys101
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!
• June 18th 2012, 10:51 PM
rowe
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.
• June 18th 2012, 10:55 PM
Rhys101
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 ?

$x={r^2}/{sqrt( (1-r^2)^2 + (2*z*r)^2)}$
• June 18th 2012, 11:09 PM
Rhys101
Re: Need help re-arranging an equation!
will the sqrt just cancel out the squares on the brackets?
• June 18th 2012, 11:19 PM
Rhys101
Re: Need help re-arranging an equation!

$x= (M*R/m)*(r^2) / (sqrt( {1-r^2}^2 + {2*z*r}^2))$
• June 19th 2012, 12:20 AM
rowe
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 $z$?
• June 19th 2012, 12:46 AM
Rhys101
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
• June 19th 2012, 12:54 AM
rowe
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.
• June 19th 2012, 01:01 AM
Rhys101
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!

• June 19th 2012, 01:04 AM
Rhys101
Re: Need help re-arranging an equation!
Sorry rowe, thanks for your patience with me! :)
• June 19th 2012, 01:19 AM
rowe
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?
• June 19th 2012, 01:54 AM
Rhys101
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?
• June 19th 2012, 02:23 AM
Rhys101
Re: Need help re-arranging an equation!
Anyone else?
• June 19th 2012, 05:04 AM
Reckoner
Re: Need help re-arranging an equation!
Quote:

Originally Posted by Rhys101
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.
• June 19th 2012, 05:41 AM
Rhys101
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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