MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

Answer:a) y is four times biggerb) y is 9 times biggerc) y is four times smallerd) y is 16 times smallerStep-by-step explanation:Let's assume that our initial comparisson value is y0.[tex]y_0 = \alpha *x_{0}^2[/tex]a) if x is doubled: [tex]X=2X_0[/tex]:[tex]y = \alpha *(2x_{0})^2=4*\alpha *x_{0}^2=4*y_0[/tex] y is four times biggerb) if x is tripled: [tex]X=3X_0[/tex]:[tex]y = \alpha *(3x_{0})^2=9*\alpha *x_{0}^2=9*y_0[/tex] y is 9 times biggerc) if x is halved: [tex]X=X_0/2[/tex]:[tex]y = \alpha *(x_{0}/2)^2=1/4*\alpha *x_{0}^2=1/4*y_0[/tex] y is 4 times smallerd) if x is quartered: [tex]X=X_0/4[/tex]:[tex]y = \alpha *(x_{0}/4)^2=1/16*\alpha *x_{0}^2=1/16*y_0[/tex] y is 16 times smaller