Inverse variation with a quadratic expression

Inverse variation with a quadratic expression

Secondary 2
6 marks
TGM Original Questions

Optional extension

The quantity \(y\) varies inversely with \(x^2+5\), and \(y=2\) when \(x=1\).

  1. Express \(y\) in terms of \(x\).[2]
  2. Find the values of \(x\) when \(y=0.75\).[2]
  3. Find the percentage decrease in \(y\) when \(x\) increases by \(20\%\) from 1, to 3 significant figures.[2]

Solution:

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Answer:(a) \(y=\dfrac{12}{x^2+5}\) (b) \(x=\pm\sqrt{11}\) (c) \(6.83\%\) decrease.

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