Question

y varies directly as x and inversely as the square of z. y=8 when x=16 and z=4. Find y when x=3 and z=9.

Answer 1

The value of y is
`(8)/(27)`

Step-by-step explanation:

Given that y varies directly as x and inversely as the square of z.

Thus, it can be written as

`y=(kx)/(z^2)`

Also, given that
`y=8` when
`x=16` and
`z=4`

Substituting these values in the above expression, we have,

`8=(k(16))/(4^2)`

`8=(k(16))/(16)`

`8=k`

Thus, the value of the constant is 8

Now, we shall find the value of y.

The value of y can be determined by substituting
`x=3` ,
`z=9` and
`k=8` in the expression
`y=(kx)/(z^2)`

Thus, we have,

`y=(8(3))/(9^2)`

Simplifying, we get,

`y=(24)/(81)`

Dividing, we get,

`y=(8)/(27)`

Thus, the value of y is
`(8)/(27)`