Question

Given that y is directly proportional to x^2 and that y=2 when x=3 find the value of y when x=6

Answer 1

Answer:y=4/3

y is directly proportional to x^2 is written as

$y \alpha {x}^{2}$ introducing a constant,

y=kx^2

but from the question, when y=2 , x=3 . putting it in the formula to get the value of k

$2 = {3}^{2} \times k$

2=9k . dividing through by 9 to get the value of k

$\frac{2}{9} = \frac{9k}{9}$

$k = \frac{2}{9}$

putting it in the general expression

$y = \frac{2}{9} x$

the value of y when x=6

$y = \frac{2}{9} \times 6$

$y = \frac{4}{3}$

therefore the value of y when x=6 is

4/3