Question

Suppose that z varies jointly as u and v and inversely as w, and that z=.8 and when u=8, v=6, w=5. How do you find z when u=3, v=10 and w=5?

Answer 1

`z=4/5`

Explanation:

`"the initial statement is "zprop(uv)/w`

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

`rArrz=(kuv)/w`

`"to find k use the given condition"`

`z=0.8" when "u=8,v=6,w=5`

`z=(kuv)/w`

`rArrk=(wz)/(uv)=(5xx0.8)/(3xx10)=0.8/6=8/60=2/15`

`"equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(z=(2uv)/(15w))color(white)(2/2)|)))`

`"when "u=3,v=10" and "w=5`

`rArrz=(2xx3xx10)/(15xx5)=60/75=4/5`