If p varies jointly as t and r and inversely as q, then find an equation for p if p=4 when t=6,r=5 , and q=-5.

Answer 1

"p varies jointly as t and r" means p = k(t)(r) where "k" is the constant of variation.

"p varies inversely as q" means p = k/q

Putting these together:

p = k(t)(r)/(q)

If p = 4 when t = 6, r = 5, and q = -5 then:

p = k(t)(r)/(q) becomes 4 = k(6)(5)/(-5) or 4 = -6k meaning k = -2/3

So the equation is: p = (-2/3)tr/q