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Thread: Urgent help with rearranging formulae

  1. #1
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    Urgent help with rearranging formulae

    Hi people!

    I have to re-arrange a formula for a current piece of coursework but i'm drawing a complete blank on what to do. I have reason to believe i know what the correct rearrangement is but i simply can't get there!

    The formula is

    s= r - √ (r - y)

    and i have to rearrange to make y the subject.

    I have found what is apparently the correct solution and it does appear to give the correct answer but i have no idea how to get there and i need to show each stage of working !

    The formula which gives the right answer is

    y = √(2r - s) * √(s)

    Thank you to everyone who can help and look forward to becoming a part of your community, Matt
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  2. #2
    Senior Member topher0805's Avatar
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    If I understand correctly, you want to solve for y?

    $\displaystyle s = r - \sqrt {r^2 - y^2}$

    Add $\displaystyle \sqrt {r^2 - y^2}$ to both sides:

    $\displaystyle s + \sqrt {r^2 - y^2} = r$

    Subtract s from both sides:

    $\displaystyle \sqrt {r^2 - y^2} = r - s$

    Square both sides:

    $\displaystyle r^2 - y^2 = (r - s)^2$

    Subtract r^2 from both sides:

    $\displaystyle
    -y^2 = (r - s)^2 - r^2$

    Multiply both sides by -1:

    $\displaystyle y^2 = r^2 - (r - s)^2$

    Take the square root of both sides:

    $\displaystyle
    y = \sqrt {r^2 - (r - s)^2}$
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  3. #3
    Moo
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    Hello,

    $\displaystyle s=r-\sqrt{r^2-y^2}$

    Thus,

    $\displaystyle \sqrt{r^2-y^2}=r-s$

    -> $\displaystyle r^2-y^2=(r-s)^2=r^2-2rs+s^2$

    We simplify both sides by r :

    $\displaystyle -y^2=-2rs+s^2=s(-2r+s)$

    $\displaystyle y^2=s(2r-s)$

    If s, r & y are positive, and supposing 2r-s is positive, we can conclude :

    $\displaystyle y=\sqrt{s}*\sqrt{2r-s}$

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  4. #4
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    thank you very much that was very helpful. I like your name btw moo

    I have thanked both of you for your contributions, Matt
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  5. #5
    Moo
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    Why ?

    I've seen a furtive answer from janvdl if i'm not mistaking, if you really want to thank, you can PM him !

    btw, good luck
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