Question

Let y ∝ x^2.

a) What happens to y if x is doubled?

b) What happens to y if x is tripled?

c) What happens to y if x is halved?

d) What happens to y if x is quartered?

Answer 1

Answer:

a) y is four times bigger

b) y is 9 times bigger

c) y is four times smaller

d) y is 16 times smaller

Step-by-step explanation:

Let's assume that our initial comparisson value is y0.

$y_0 = \alpha *x_{0}^2$

a) if x is doubled: $X=2X_0$:

$y = \alpha *(2x_{0})^2=4*\alpha *x_{0}^2=4*y_0$  y is four times bigger

b) if x is tripled: $X=3X_0$:

$y = \alpha *(3x_{0})^2=9*\alpha *x_{0}^2=9*y_0$  y is 9 times bigger

c) if x is halved: $X=X_0/2$:

$y = \alpha *(x_{0}/2)^2=1/4*\alpha *x_{0}^2=1/4*y_0$  y is 4 times smaller

d) if x is quartered: $X=X_0/4$:

$y = \alpha *(x_{0}/4)^2=1/16*\alpha *x_{0}^2=1/16*y_0$  y is 16 times smaller