Question

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

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,

$y_1=k(2x)^2\\\\y_1=k \times 4x^2$ --------- eqn 2

Substitute value of k from eqn 1, we get

$y_1=\frac{a}{x^2} \times 4x^2\\\\y_1=4a$

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