Question

If a varies directly as the square of b, and a=5 when b=7, find a when b=3. when b=3 a=​

Answer 1

When
`b=3`

`a=(45)/(49)`

Explanation:

Given

`a=5`

`b=7`

`a` ∝
`b^2` [As
`a` varies directly with square of
`b`]

∴
`a=kb^2`

where
`k` represents the constant of proportionality.

Plugging in values to find
`k`

`5=k(7)^2`

`5=k(49)`

Dividing both sides by 49.

`(5)/(49)=(k(49))/(49)`

`(5)/(49)=k`

∴
`k=(5)/(49)`

When
`b=3`

`a=(5)/(49)(3)^2`

`a=(5)/(49)(9)`

∴
`a=(45)/(49)`