Question

y a$\sqrt{x}$ and y = 8 when x = 4 then, find

(i) The value of y when x = 9
(ii) The value of x when y = 144

Answer 1

$$\begin{gathered} y\alpha \sqrt{x} \\ \therefore y=k\sqrt{x} \\ \Rightarrow 8=k\times \sqrt{4}\left(y=8\mathrm{when}x=4.\right) \\ \Rightarrow k=\frac{8}{2}=4 \\ \Rightarrow y=4\sqrt{x}(\mathrm{It}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{variation}.) \\ \left(\mathrm{i}\right)y=4\sqrt{9}\left(\because x=9\right) \\ \Rightarrow y=12 \\ \left(\mathrm{ii}\right)144=4\sqrt{x} \\ \Rightarrow \sqrt{x}=36 \\ \Rightarrow x={\left(36\right)}^2=1296 \end{gathered}$$