Question

If y varies inversely as x and y= 2/5 when x= 1/20, find y when x=1/2 ?

Answer 1

ANSWER


`y = (1)/(25)`

Step-by-step explanation

If y varies inversely as x, we can write the relation,


`y \propto (1)/(x)`

When we introduce the constant of proportionality, we get the equation.



`y = (k)/(x)`


When

`y = (2)/(5)`
and


`x = (1)/(20)`


We get,



`(2)/(5) = (k)/( (1)/(20) )`
We solve for k, by multiplying both sides of the equation by

`(1)/(20)`


This implies that,



`(2)/(5) * (1)/(20) = k`

This simplifies to give



`k = (1)/(50)`



The variation equation now becomes,



`y = ( (1)/(50) )/(x)`


or



`y = (1)/(50x)`


When

`x = (1)/(2)`


`y = (1)/(50 * (1)/(2) )`


This gives us,



`y = (1)/(25)`


The correct answer is B.