ANSWER
[tex]y = \frac{1}{25} [/tex]
EXPLANATION
If y varies inversely as x, we can write the relation,
[tex]y \propto \frac{1}{x} [/tex]
When we introduce the constant of proportionality, we get the equation.
[tex]y = \frac{k}{x} [/tex]
When
[tex]y = \frac{2}{5} [/tex]
and
[tex]x = \frac{1}{20} [/tex]
We get,
[tex] \frac{2}{5} = \frac{k}{ \frac{1}{20} } [/tex]
We solve for k, by multiplying both sides of the equation by
[tex] \frac{1}{20} [/tex]
This implies that,
[tex] \frac{2}{5} \times \frac{1}{20} = k [/tex]
This simplifies to give
[tex]k = \frac{1}{50} [/tex]
The variation equation now becomes,
[tex]y = \frac{ \frac{1}{50} }{x} [/tex]
or
[tex]y = \frac{1}{50x} [/tex]
When
[tex]x = \frac{1}{2} [/tex]
[tex]y = \frac{1}{50 \times \frac{1}{2} } [/tex]
This gives us,
[tex]y = \frac{1}{25} [/tex]
The correct answer is B.
