Question

If y varies directly as x and inversely as the square of z and if `y=20`  when `x=50` and `z=5` how do you find y when `x=3` and `z=6`?  

Answer 1

`y=5/6`

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=20" when "x=50" and "z=5`

`y=(kx)/z^2rArrk=(yz^2)/x=(20xx25)/50=10`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(10x)/z^2)color(white)(2/2)|))`

`"when "x=3" and "z=6" then"`

`y=(10xx3)/36=30/36=5/6`