Question

find the mathematical model for the following statement. remember to use $k$ as the constant of proportionality. $p$ varies jointly as the product of $r$ and $t$ inversely to $v$.

Explanation:

Step1: Recall joint - inverse variation formula

If a variable $y$ varies jointly as $x_1$ and $x_2$ and inversely as $x_3$, the formula is $y = k\frac{x_1x_2}{x_3}$.

Step2: Substitute variables

Here, $p$ is $y$, $R$ and $T$ are $x_1$ and $x_2$, and $V$ is $x_3$. So the formula is $p=k\frac{RT}{V}$.

Answer:

$p = k\frac{RT}{V}$