Question

If y $\alpha$$\frac{1}{x^3}$ and y = 4 when x =3. Find y when x = 4.

Answer 1

$$\begin{gathered} y\alpha \frac{1}{x^3} \\ \therefore y{x}^3=k\left(k\mathrm{is}a\mathrm{constant}.\right) \\ And, \\ 4{\left(2\right)}^3=k\left(y=4\mathrm{when}x=2.\right) \\ \Rightarrow k=32 \\ Wehave: \\ y{x}^3=32\left(\mathrm{Equation}\mathrm{of}\mathrm{variation}\right) \\ \Rightarrow y{\left(4\right)}^3=32\left(x=4\right) \\ \Rightarrow y=\frac{32}{64} \\ \Rightarrow y=\frac{1}{2} \end{gathered}$$