Question

y a x² and y = 128 when x = 16 find

(i) The value of y when x = 10
(ii) The value of x when y = 72.

Answer 1

$$\begin{gathered} y\alpha x^2 \\ \Rightarrow y=k{x}^2(k\mathrm{i}\mathrm{s}\mathrm{a}\mathrm{constant}.) \\ \Rightarrow 128=k{\left(16\right)}^2(y=128\mathrm{when}x=16.) \\ \Rightarrow 128=256k \\ \Rightarrow k=\frac{128}{256} \\ \Rightarrow k=\frac{1}{2} \\ \Rightarrow y=\frac{1}{2}{x}^2(\mathrm{This}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{variation}.) \\ \left(\mathrm{i}\right)y=\frac{1}{2}{\left(10\right)}^2(\because x=10) \\ \therefore y=50 \\ \left(\mathrm{ii}\right)72=\frac{1}{2}{x}^2(\because y=72) \\ \Rightarrow x^2=72\times 2 \\ \Rightarrow x^2=144 \\ \Rightarrow x=12 \end{gathered}$$