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

Answer:

Mathematical model = $v = \frac{0.09422pq}{s^{2} }$

k = 0.09422

Step-by-step 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,

$v \alpha \frac{1}{s^{2} } \\v = \frac{k}{s^{2} }... 2$

Equating 1 and 2, we have;

$v = \frac{kpq}{s^{2} }$

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

$k = \frac{vs^{2} }{pq}$

$k = \frac{1.6*1.3^{2} }{4.1*7}\\k = \frac{2.704}{28.7}\\ k =0.09422$

The constant of proportionality is 0.09422

The expression therefore becomes $v = \frac{0.09422pq}{s^{2} }$