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Math Help - Changing the subject of an equation.

  1. #1
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    Changing the subject of an equation.

    Could you help me with making x the subject of this equation please?

    v^2 = w^2(a^2-x^2)

    The answer in my text book is x = ((w^2 a^2 - v^2)^(1/2))/w
    Sorry that may not make sense, I wasn't sure how to write it...


    I've tried things like...

    (v^2/w^2) = a^2 - x^2
    (v^2/w^2) - a^2 = x^2

    But never seem to get the right answer.


    Thanks.
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  2. #2
    Moo
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    Hello,

    You're in the right way


    (v^2/w^2) = a^2 - x^2
    (v^2/w^2) - a^2 = x^2


    -> this is false, it's (v^2/w^2) - a^2 = -x^2

    So a^2 - (v^2/w^2) = x^2

    Put it on the same denominator.

    This will make :

    (aw-v)/w=x

    So x=sqrt((aw-v)/w)=sqrt(aw-v)/w

    And sqrt is equivalent to ^(1/2)

    I'm not sure my notations make sense... If necessary, i can make it easier to read
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hello,

    You're in the right way


    (v^2/w^2) = a^2 - x^2
    (v^2/w^2) - a^2 = x^2


    -> this is false, it's (v^2/w^2) - a^2 = -x^2

    So a^2 - (v^2/w^2) = x^2

    Put it on the same denominator.

    This will make :

    (aw-v)/w=x

    So x=sqrt((aw-v)/w)=sqrt(aw-v)/w

    And sqrt is equivalent to ^(1/2)

    I'm not sure my notations make sense... If necessary, i can make it easier to read
    Thanks, that makes sense.

    Why is it that it's x = sqrt(aw-v)/w not x = sqrt(aw-v)/w.
    There's probably a really obvious reason, I just can't see it!
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  4. #4
    Moo
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    Because you keep the square :

    x=(aw-v)/w

    Do you agree with it ?

    so x=sqrt(aw-v)/sqrt(w) (assuming that x is positive)

    And sqrt(w)=w


    You can't simplify aw-v, you can only factor it
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  5. #5
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    Quote Originally Posted by Moo View Post
    Because you keep the square :

    x=(aw-v)/w

    Do you agree with it ?

    so x=sqrt(aw-v)/sqrt(w) (assuming that x is positive)

    And sqrt(w)=w


    You can't simplify aw-v, you can only factor it
    Ok, thankyou.
    One more thing... how does the x^2 get from being -x^2 to +x^2?
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  6. #6
    Moo
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    I changed the order of the terms on the left hand side of the equation when multiplying by (-1)
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  7. #7
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    Quote Originally Posted by Moo View Post
    I changed the order of the terms on the left hand side of the equation when multiplying by (-1)
    Ok.
    I completely get it now
    Thanks so much.
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