Question

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

Answer 1

`y=27`

Step-by-step 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=(12)/((2)^2)=(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