Question

find a mathematicl model representing the statement. (Determine the constant of proportionality) v varies jointly as p and q and inversely as the square of s. (v=1.6 when p=4.1, q=7 and s=1.3

Answer 1

Mathematical model =
`v = (0.09422pq)/(s^(2) )`

k = 0.09422

Explanation:

If v varies jointly as p and q, this means that v varies directly as the product of p and q as shown;

`v \alpha pq`

`v = kpq`... 1

k = constant of proportionality

Also v varies inversely as the square of s; mathematically,

`v \alpha (1)/(s^(2) ) \\v = (k)/(s^(2) )... 2`

Equating 1 and 2, we have;

`v = (kpq)/(s^(2) )`

Given v = 1.6, when p=4.1, q=7 and s=1.3

`k = (vs^(2) )/(pq)`

`k = (1.6*1.3^(2) )/(4.1*7)\\k = (2.704)/(28.7)\\ k =0.09422`

The constant of proportionality is 0.09422

The expression therefore becomes
`v = (0.09422pq)/(s^(2) )`