x varies directly with y and inversely with z. when y =5 ,z=9 then x `=1/6 ` . Find the relation among three variation x ,y and z if y =6 and z=`1/5` , then calculate the value of x .

Explanation

x varies directly with y and inversely with z.
`therefore x prop y /z rArr x=k ,y/z ..........(1)` (where k `ne`0=variation constant)
As per question , if y =5 and z =9 , then x =`1/6 `.
` therefore` from (1) we get , `1/6 =k. 5/9 or , k =(9)/(5xx6) =(3)/(10)`
`therefore` (1) becomes ,x =`(3)/(10) . y/z ..........(2)`
Hence the required relation between x, y and z is x =`(3y)/(10z)`
Now , if y =6 and z=`1/5 , then "from"(2) we "get" , x `=`(3)/(10) xx(6)/(1/5) or , x =(3xx6xx5)/(10xx1) =9`
Hence the required path of x =9 .