Question

Y varies directly as x and inversely as the square of z. y=12 when x=64 and z=4. How do you find y when x=96 and z=2?

Answer 1

`y=72`

Explanation:

`"the initial statement is "ypropx/z^2`

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

`rArry=kxx x/z^2=(kx)/z^2`

`"to find k use the given condition"`

`y=12" when "x=64" and "z=4`

`y=(kx)/z^2rArrk=(yz^2)/x=(12xx16)/64=3`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(3x)/z^2)color(white)(2/2)|)))`

`"when "x=96" and "z=2`

`rArry=(3xx96)/4=72`