Question

If $x$ varies directly as a square of $y$ for $y=6,x=72$. Find $x$ for $y=9$.

Answer 1

Solution:

Since $x$ varies directly as a square of $y$.

$\therefore x=k{y}^2$ , where $k$ is any constant.

Substitute $y=6,x=72$ in above relation.

$$\begin{gathered} \Rightarrow 72=k·6^2 \\ \Rightarrow k=\frac{72}{36} \\ \therefore k=2 \end{gathered}$$

Thus, the above expression becomes $x=2y^2$.

We have to find $x$ for $y=9$.

$$\begin{gathered} \Rightarrow x=2\times 9^2 \\ \Rightarrow x=2\times 81 \\ \therefore x=162 \end{gathered}$$

Hence, the value of $x$ is $162$.