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Thread: Solve for the Identified Variable

  1. #1
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    Solve for the Identified Variable

    a.) A = P+P*r*t for r

    Does anyone else get r = (A/P-1)/t ?

    b.) d = (sqrt(4*R^2-C^2))/2 for C

    Does anyone else get C = sqrt((-2d)^2)/4)+R^2

    c.) 1/f = 1/q+1/p for q

    Does anyone else just get f^-1-p^-1=q^-1?
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by ZE2001 View Post
    a.) A = P+P*r*t for r

    Does anyone else get r = (A/P-1)/t ?

    b.) d = (sqrt(4*R^2-C^2))/2 for C

    Does anyone else get C = sqrt((-2d)^2)/4)+R^2

    c.) 1/f = 1/q+1/p for q

    Does anyone else just get f^-1-p^-1=q^-1?
    a) Your answer is correct, but I would have done it this way. Less complex:

    $\displaystyle A=P+Prt$

    $\displaystyle A-P=Prt$

    $\displaystyle r=\frac{A-P}{Pt}$

    b) You lost me on this one.

    $\displaystyle d=\frac{\sqrt{4R^2-C^2}}{2}$

    $\displaystyle d^2=\frac{4R^2-C^2}{4}$

    $\displaystyle 4d^2=4R^2-C^2$

    $\displaystyle 4d^2-4R^2=-C^2$

    $\displaystyle 4R^2-4d^2=C^2$

    $\displaystyle C^2=4R^2-4d^2$

    $\displaystyle C=\sqrt{4(R^2-d^2)}$

    $\displaystyle C=2\sqrt{R^2-d^2}$

    c) I don't see where you solved for q in your attempt.

    $\displaystyle \frac{1}{f}=\frac{1}{q}+\frac{1}{p}$

    Multiply through by the LCD of fqp

    $\displaystyle qp=fp+fq$

    $\displaystyle qp-fq=fp$

    $\displaystyle q(p-f)=fp$

    $\displaystyle q=\frac{fp}{p-f}$
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