Suppose z varies directly with x and inversely with the square of y. If z=18 when x=6 and y=2, what is z when x=8 and y=9?

1 Answer
Aug 24, 2017

Answer:

#z=32/27#

Explanation:

#"the initial statement here is "zpropx/(y^2)#

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

#rArrz=(kx)/(y^2)#

#"to find k use the given condition"#

#z=18" when "x=6" and "y=2#

#z=(kx)/(y^2)rArrk=(y^2z)/x=(4xx18)/6=12#

#"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=(12x)/(y^2))color(white)(2/2)|)))#

#"when "x=8" and "y=9#

#z=(12xx8)/81=32/27#