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Thread: Direct and inverse proportions

  1. #1
    jpp
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    Direct and inverse proportions

    If x is directly proportional to the square root of y, then y is inversely proportional to...?


    Thank you in advance!
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jpp View Post
    If x is directly proportional to the square root of y, then y is inversely proportional to...?


    Thank you in advance!
    lets begin with definitions. what does it mean for x to be proportional to y?
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  3. #3
    jpp
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    x = ky

    in this problem..

    x = k * sqrt(y)

    is that correct?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jpp View Post
    x = ky

    in this problem..

    x = k * sqrt(y)

    is that correct?
    yes, correct! now what does it mean to be inversely proportional? Lets say i said "a is inversely proportional to b", what equation would go along with that?
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  5. #5
    jpp
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    Quote Originally Posted by Jhevon View Post
    yes, correct! now what does it mean to be inversely proportional? Lets say i said "a is inversely proportional to b", what equation would go along with that?
    a = k / b, right?
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    MHF Contributor harish21's Avatar
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    Quote Originally Posted by jpp View Post
    a = k / b, right?

    Correct.

    so according to your question: $\displaystyle x = {k}{\sqrt{y}}$

    can you complete it now by finding what y is inversely proportional to?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jpp View Post
    a = k / b, right?
    right. so you know $\displaystyle \displaystyle x = k \sqrt y$ and you want to get to $\displaystyle \displaystyle y = \frac C{f(x)}$ (by solving for y and, perhaps, rearranging)

    where $\displaystyle \displaystyle C$ is a constant and $\displaystyle \displaystyle f(x)$ is some function of $\displaystyle \displaystyle x$. That $\displaystyle \displaystyle f(x)$ is the answer to your question. can you find it?
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  8. #8
    jpp
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    I rearranged x = k * sqrt(y) to get y = x^2/k^2

    y = C/f(x) -> x^2/k^2 = C/f(x)

    does C = k?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jpp View Post
    I rearranged x = k * sqrt(y) to get y = x^2/k^2

    y = C/f(x) -> x^2/k^2 = C/f(x)

    does C = k?
    C is just a constant. and you do not yet have the form you need to get to. you need to write it as a constant over a function of x.
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  10. #10
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    Quote Originally Posted by jpp View Post
    I rearranged x = k * sqrt(y) to get y = x^2/k^2

    y = C/f(x) -> x^2/k^2 = C/f(x)

    does C = k?
    the crucial point is not "C", but f(x). What is f(x) here?
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