Question

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?

Answer 1

`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`