Question

Z varies directly as the square of w, and z = 14 when w = 4. Find z when w = 8?

Answer 1

`z=56`

Explanation:

`"the square of " w" is "w^2`

`rArrzpropw^2`

Convert to an equation by introducing k, `color(blue)"the constant of variation"`

`rArrz=kw^2`

`"Using "z=14" when "w=4` we can find k

`rArrkxx4^2=14`

`rArrk=14/16=7/8`

`"the equation connecting "z" and "w" is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(z=7/8w^2)color(white)(2/2)|)))`

`w=8toz=7/cancel(8)^1xxcancel(64)^8=7xx8=56`