Question

Question #f65fd

Answer 1

`k=2`

Explanation:

Consider each statement separately.

`• ypropx^2larrcolor(blue)" direct variation"`

`• yprop1/zlarrcolor(blue)" inverse variation"`

Combine the right sides as a product.

`• ypropx^2/zlarrcolor(blue)" joint variation"`

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

`rArry=kxxx^2/z`

`rArry=(kx^2)/z`

`color(blue)"cross-multiplying"` gives.

`kx^2=yz`

`rArrk=(yz)/x^2`

To calculate k, substitute the given values for x, y and z

`rArrk=(6xx27)/9^2=162/81=2`

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