Question

If y varies directly as x and inversely as the square of z and y=1/6 when x=20 and z =6, how do you find y when x = 14 and z=5?

Answer 1

`y=21/125`

Explanation:

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

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

`rArry=kxxx/z^2=(kx)/z^2`

`"to find k use the given condition"`

`y=1/6" when "x=20" and "z=6`

`y=(kx)/z^2rArrk=(yz^2)/x=(1/6xx36)/20=3/10`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=(3x)/(10z^2))color(white)(2/2)|)))`

`"when "x=14" and "z=5" then"`

`y=(3xx14)/(10xx25)=21/125`