Question

If r varies jointly as p and q and inversely as t, then how do you find an equation for r if r=6 when p=8, q=−3, and t=3?

Answer 1

`r=-(3pq)/(4t)`

Explanation:

`"the initial statement is "rprop(pq)/t`

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

`rArrr=(kpq)/t`

`"to find k use the given condition"`

`r=6" when "p=8,q=-3" and "t=3`

`r=(kpq)/t`

`rArrkpq=rtlarrcolor(blue)" cross-multiplying"`

`rArrk=(rt)/(pq)=(6xx3)/(8xx-3)=18/(-24)=-3/4`

`rArr" equation is " color(red)(bar(ul(|color(white)(2/2)color(black)(r=-(3pq)/(4t)color(white)(2/2)|)))`