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Thread: show by intergration that the equation of the curve is y=...

  1. #1
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    show by intergration that the equation of the curve is y=...

    Hi

    another q.

    The diagram shows a curve for which $\displaystyle \frac{dy}{dx}\ = - \frac{k}{k^3}$ where k is a constant. the curve passes through the points (1,18) and (4,3).

    Show by intergration that the equation of the curve is $\displaystyle y = \frac{16}{x^2}\ +2 $
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  2. #2
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    Quote Originally Posted by pederjohn View Post
    Hi

    another q.

    The diagram shows a curve for which $\displaystyle \frac{dy}{dx}\ = - \frac{k}{k^3}$ where k is a constant. the curve passes through the points (1,18) and (4,3).

    Show by intergration that the equation of the curve is $\displaystyle y = \frac{16}{x^2}\ +2 $
    I assume you mean
    $\displaystyle \frac{dy}{dx}\ = - \frac{k}{x^3}$
    $\displaystyle \Rightarrow y = -k\int x^{-3}dx$
    $\displaystyle =-k\frac{x^{-2}}{(-2)}+c$

    $\displaystyle =\frac{k}{2x^2}+c$

    Plug in the two pairs of values $\displaystyle (1, 18)$ and $\displaystyle (4,3)$, and solve the resulting simultaneous equations for $\displaystyle k$ and $\displaystyle c$.

    Can you complete it now?

    Grandad
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