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?

Question

asked Aug 23, 2020 151k views

1 Answer

Mike Driscoll · Answer 1 · 2020-08-28T20:58:20+0000

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

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