Question

If $x$ and $y$ vary inversely, fill in the following blanks:​

​$\left(iii\right)$
$\begin{array}{ccccc}x& 9& \cdots & 81& 243\\ y& 27& 9& \cdots & 1\end{array}$

Answer 1

Step : Complete the table

Given : $x$ varies inversely as $y$

$\begin{array}{ccccc}x& 9& \cdots & 81& 243\\ y& 27& 9& \cdots & 1\end{array}$

As $x$ and $y$ are in inverse variation. Therefore, the
product of the corresponding values of $x$ and $y$ remain constant.
Consider ${}^{\prime }{k}^{\prime }$ to be the constant of inverse variation

When $x=9$ and $y=27$
$k=xy=9\times 27=243$

When $y=9$
$\because xy=k\Rightarrow x\times 9=243\Rightarrow x=27$

When $x=81$
$\because xy=k\Rightarrow 81\times y=243\Rightarrow y=3$

Hence, the complete table is :
$\begin{array}{ccccc}x& 9& 27& 81& 243\\ y& 27& 9& 3& 1\end{array}$