Assume y varies inversely as x, if y=8 when x=4, how do you find x when y=2?

2 Answers
sjc
Jul 6, 2017

#x=16#

Explanation:

#y" varies inversely as "x=>yprop1/x#

#=>y=k/x" where "k" is the constant of proportionality"#

#y=8, x=4#

we have

#8=k/4=>k=8xx4=32#

#:.y=32/x#

#y=2#

#2=32/x=>x=32/2=16#

#x=16#

Jim G.
Jul 6, 2017

#x=16#

Explanation:

#"the initial statement is " yprop1/x#

#"to convert to an equation multiply by k, the constant "#
#"of variation"#

#rArry=kxx1/x=k/x#

#"to find k, use the condition given for x and y"#

#y=8" when " x=4#

#y=k/xrArrk=xy=4xx8=32#

#"the equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=32/x)color(white)(2/2)|)))#

#"when y = 2"#

#xy=32rArrx=32/y=32/2=16#

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