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Thread: Transposition

  1. #1
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    Transposition

    hello my name is ben, im currenty revising to start my hnc in mechanical engineering,

    i have come across a equation that im struggling to transpose and cant find any examples to help me, just wondering if anybody could help me out and show me the steps to follow? its been long time since ive done anything like this :S

    D/d=√f+p/f-p for f


    tanks
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  2. #2
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    Re: Transposition

    $\dfrac{D}{d} = \sqrt{f} + \dfrac{p}{f} - p$

    $\left(\dfrac{D}{d}+p\right) f - f^{3/2} -p =0$

    let $u = \sqrt{f},~\left(\dfrac{D}{d}+p\right)=a$

    $a u^2 - u^3 -p=0$

    This has 3 solutions. At least 1 will be real depending upon the parameters.

    You'll just have to solve this with the parameters substituted in to know whether you have 1 or 3 real solutions for $u$

    Given the solution(s) for $u$

    $f = u^2$
    Last edited by romsek; Aug 23rd 2017 at 01:43 AM.
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  3. #3
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    Re: Transposition

    If we graph g(x)=\sqrt{x}+\frac{p}{x} say for p>0 we get

    Transposition-gr23-1.jpg

    so the equation g(x)=\frac{D}{d}+p has either two solutions, one double solution, or no solution

    The solutions can be found using a numerical method
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  4. #4
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    Re: Transposition

    Quote Originally Posted by trungdien View Post
    D/d=√f+p/f-p for f
    just wondering if the original equation is actually

    $\dfrac{D}{d}=\dfrac{\sqrt{f}+p}{f-p}$

    ... ?
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