Question

Y varies directly with the square of x. If y=12 when x=-2, find y when x =3

Answer 1

Answer:

$y=27$

Explanation: The statement y varies with the square of x and be translated into mathematics as follows:

$y\propto x^2$

The statement implies that there is a proportional relationsip:

$y=k\cdot x^2\rightarrow(1)$

Using the condition that y = 12 when x = 2 we can calculate the value of k for the equation (1) as follows:

$\begin{gathered} 12=k\cdot(2)^2 \\ k=\frac{12}{(2)^2}=\frac{12}{4}=3 \\ k=3 \\ \therefore\rightarrow \\ y=3\cdot x^2\rightarrow(2) \end{gathered}$

Finally, the value of y when the x = 3 is as follows:

$\begin{gathered} y=3\cdot(3)^2 \\ y=3\cdot9 \\ y=27 \end{gathered}$

Conclusion: Therefore when x = 3 the y = 27