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Homework Help: RE: variation

  1. Nov 5, 2006 #1
    oic. thanks a lot.

    y is directly proportional to x2
    x is increased by 100%
    find the percentage increase in y.

    so,
    y= k x2

    then y= k x2
    y=k 4 x2

    so 4 x2 is already increased by 100%?
    then to find k which is
    y=k 4 x2
    k= y/ 4 x2

    find the percentage increase in y,
    so what i did was :
    y= y/4 x2 *100 x2 :confused:

    can somebody helpp to correct it??
    thanks lotsa.:smile:
     
  2. jcsd
  3. Nov 5, 2006 #2

    arildno

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    First, set up your general equation:
    [tex]y=kx^{2}[/tex]
    Now, let [itex](x_{1},y_{1}),(x_{2},y_{2})[/tex] be two pairs of x and y values that satisfies your equation, that is:
    [tex]y_{1}=kx_{1}^{2}[/tex]
    and
    [tex]y_{2}=kx_{2}^{2}[/tex]

    Now, let [itex]x_{2}[/tex] represent a 100% increase of [itex]x_{1}[/itex], that is:
    [itex]x_{2}=2x_{1}[/tex]

    Now, calculating [itex]y_{2}[/itex], we find:
    [tex]y_{2}=kx_{2}^{2}=k(2x_{1})^{2}=4kx_{1}^{2}=4y_{1}[/tex]
    Thus, calculating the percentwise increase, we have:
    [tex]\frac{y_{2}-y_{1}}{y_{1}}*\frac{100}{100}=\frac{4y_{1}-y_{1}}{y_{1}}*\frac{100}{100}=3*\frac{100}{100}=\frac{300}{100}[/tex]
    Thus, if x increases with 100% , y increases with 300%.
     
    Last edited: Nov 5, 2006
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