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Math Help - How to extract values from an equation

  1. #1
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    How to extract values from an equation

    How do I get n from this:


    I get stuck at

    v/R - 1/4 = 1/n^2
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  2. #2
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    Quote Originally Posted by prettiestfriend View Post
    How do I get n from this:


    I get stuck at

    v/R - 1/4 = 1/n^2
    Go ahead and do the subtraction on the left. The "common denominator" is 4R so you have 4v/(4R)- R/(4R)= (4v- R)/(4R)= 1/n^2. Now take the reciprocal of both sides: 4R/(4v- R)= n^2. Finally, just take the square root of both sides.
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  3. #3
    Super Member Deadstar's Avatar
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    v = R \bigg{(}\frac{1}{4} - \frac{1}{n^2} \bigg{)}

    => \frac{v}{R} = \frac{1}{4} - \frac{1}{n^2}

    => \frac{v}{R} - \frac{1}{4} = -\frac{1}{n^2}

    => \frac{1}{4} - \frac{v}{R} = \frac{1}{n^2}

    Now \frac{1}{4} - \frac{v}{R}= \frac{R - 4v}{4R} and then multiply both sides by n^2...

    => n^2 \cdot \frac{R - 4v}{4R} = 1

    Then divide both sides by \frac{R - 4v}{4R}...

    n^2 = \frac{1}{\frac{R - 4v}{4R}} = \frac{4R}{R - 4v}

    Then take the square root of each side to get...

    n = \sqrt{\frac{4R}{R - 4v}}
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  4. #4
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    Hello, prettiestfriend!

    Solve for n\!:\;\;v \;=\;R\left(\frac{1}{4} - \frac{1}{n^2}\right)
    Get rid of the fractions as soon as possible . . .

    We have: . v \;=\;\frac{R}{4} - \frac{R}{n^2}

    Multiply by 4n^2\!:\quad 4n^2(v) \;=\;{\color{red}\rlap{/}}4n^2\left(\frac{R}{{\color{red}\rlap{/}}4}\right) - 4{\color{red}\rlap{//}}n^2\left(\frac{R}{{\color{red}\rlap{//}}n^2}\right)

    . . and we have: . 4vn^2 \;=\;Rn^2 - 4R\quad\Rightarrow\quad Rn^2 - 4vn^2 \:=\:4R


    Factor: . (R - 4v)n^2 \;=\;4R \quad\Rightarrow\quad n^2 \;=\;\frac{4R}{R - 4v}


    Take the square root: . n \;=\;\pm\sqrt{\frac{4R}{R - 4v}}

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