If y varies inversely as #x^2# and If y = 2 when x = 6, what is y when x = 3?

1 Answer
May 20, 2016

Answer:

#y=color(green)(8)# when #x=3#

Explanation:

If #y# varies inversely as #x^2#
then
#color(white)("XXX")y*x^2=c# for some constant #c#

Given that #(x,y)=(6,2)# is a solution to this inverse relation:
#color(white)("XXX")rarr 2*6^2=c#

#color(white)("XXX") rarr c=72#

So the complete relation is
#color(white)("XXX")y*x^2=72#
or
#color(white)("XXX")y=72/(x^2)# provided #x!=0#

When #x=3#
#color(white)("XXX")y=72/(3^2)=8#