If $ x $ and $ 3 y $ vary inversely with each other and $ x=\frac{1}{3} $ when $ y=14 $, find $ y $, when $ x $ is $ \frac{1}{2} $.
Given:
\( x \) and \( 3 y \) vary inversely with each other and \( x=\frac{1}{3} \) when \( y=14 \).
To do:
We have to find \( y \), when \( x \) is \( \frac{1}{2} \).
Solution:
$x \propto \frac{1}{3y}$
This implies,
$x \times 3y=k$
$3xy=k$
\( x=\frac{1}{3} \) when \( y=14 \)
This implies,
$3\times \frac{1}{3}\times14=k$
$k=14$
Therefore,
$3\times(\frac{1}{2})\times y=14$
$y=\frac{14\times2}{3}$
$y=\frac{28}{3}$
The value of $y$ when $x$ is $\frac{1}{2}$ is $\frac{28}{3}$.
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