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Variations

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These are the solutions to the CSEC past questions on Variations.
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Formula Sheet: List of Formulae
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(2.) Given that y is inversely proportional to (x − 2) and x = 11 when y = 9, find the value of y when x = 29.


$ y \alpha \dfrac{1}{x - 2} ...\text{Inverse Variation} \\[5ex] y = \dfrac{k}{x - 2} ...\text{where k is the constant of proportionality} \\[5ex] x = 11, \hspace{2em} y = 9, \hspace{2em}, k = ? \\[3ex] 9 = \dfrac{k}{11 - 2} \\[5ex] 9 = \dfrac{k}{9} \\[5ex] k = 9(9) \\[3ex] k = 81 \\[5ex] x = 29, \hspace{2em} k = 81, \hspace{2em}, y = ? \\[3ex] y = \dfrac{k}{x - 2} \\[5ex] y = \dfrac{81}{29 - 2} \\[5ex] y = \dfrac{81}{27} \\[5ex] y = 3 $
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