Question

Whats the equation of variation where y varies jointly as x and z and inversely as the square of w and y=20 when x= -0.5, z =4, and w = 5?

Answer 1

`y=-(250xz)/w^2`

Explanation:

`"the initial statement is "yprop(xz)/w^2`

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

`rArry=kxx(xz)/w^2=(kxz)/w^2`

`"to find k use the given condition"`

`y=20" when "x=-0.5,z=4" and "w=5`

`y=(kxz)/w^2rArrk=(yxxw^2)/(xz)=(20xx5^2)/(-0.5xx4)=-250`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(y=-(250xz)/w^2)color(white)(2/2)|)))`