Question

11. y is directly proportional to x*2 and y = a for a

particular value of x. Find an expression for y in
terms of a, when this value of x is doubled.​

Answer 1

The expression for y in terms of "a" when value of x is doubled is
`y_1=4a`

Solution:

Given that,

y is directly proportional to
`x^2`

Therefore,

`y \propto x^2`

`y = kx^2`

Where "k" is the constant of proportionality

y = a for particular value of x

Therefore,

`a=kx^2` --------- eqn 1

We have to find when x is doubled

x is doubled means 2x

Let it be
`y_1`

Hence we get,

`y_1=k(2x)^2\\\\y_1=k * 4x^2` --------- eqn 2

Substitute value of k from eqn 1, we get

`y_1=(a)/(x^2) * 4x^2\\\\y_1=4a`

Thus expression for y in terms of "a" when value of x is doubled is
`y_1=4a`