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1 vote
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?

User Adt
by
7.4k points

1 Answer

3 votes

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

User Mike Driscoll
by
8.4k points
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