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Math Help - Transposing of formulae

  1. #1
    Junior Member
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    Transposing of formulae

    Hi there, thanks in advance for any help

    Make A the subject of the formula:

    Q = C.A square root (2g.h / (1-A^2/x^2))

    I have got this far but unsure what to do with the fraction of a fraction... the (x^2) bit.

    Q^2 / C^2.A^2 = (2g.h / (1-A^2/x^2))

    Thank you again for any assitance

    Mike
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  2. #2
    MHF Contributor

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    Quote Originally Posted by mikewhant View Post
    Hi there, thanks in advance for any help

    Make A the subject of the formula:

    Q = C.A square root (2g.h / (1-A^2/x^2))

    I have got this far but unsure what to do with the fraction of a fraction... the (x^2) bit.

    Q^2 / C^2.A^2 = (2g.h / (1-A^2/x^2))

    Thank you again for any assitance

    Mike
    I would first isolate that square root:
    \frac{Q}}{CA}= \sqrt{\frac{2gh}{1- \frac{A^2}{x^2}}
    and then square both sides.

    [tex]\frac{Q^2}{C^2A^2}= \frac{2gh}{1- \frac{A^2}{x^2}}

    Multiply both numerator and denominator, on the right, by x^2
    \frac{Q^2}{C^2A^2}= \frac{2ghx^2}{x^2- A^2}

    Get rid of the fractions by multiplying both sides by the denominators, C^2A^2 and x^2- A^2

    Q^2(x^2- A^2)= 2ghx^2C^2A^2
    Q^2x^2- Q^2A^2= 2ghx^2C^2A^2

    Add Q^2A^2 to both sides

    Q^2x^2= 2ghx^2C^2A^2+ Q^2A^2

    Factor [tex]A^2[/quote] out of the right side

    Q^2x^2= (2gx^2C^2+ Q^2)A^2

    Divide both sides by 2gx^2C^2+ Q^2

    \frac{Q^2x^2}{2gx^2C^2+ Q^2}= A^2

    Finally, take the square root of both sides

    A= \sqrt{\frac{Q^2x^2}{2gx^2C^2+ Q^2}}
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  3. #3
    Junior Member
    Joined
    Oct 2009
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    Thanks alot, great help, i just needed a worked example, now I can do them!

    Cheers
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