Writing an equation that models variation Write an equation that expresses the following relationship. \[ p \text { varies jointly with the square of } d \text { and the cube of } u \] In your equation, use \( k \) as the constant of proportionality.

The relationship described can be expressed with the equation: \[ p = k \cdot d^2 \cdot u^3 \] Here, \( p \) varies jointly with the square of \( d \) (denoted as \( d^2 \)) and the cube of \( u \) (denoted as \( u^3 \)), while \( k \) represents the constant of proportionality that will change based on specific conditions or units in your particular context. Understanding variation is not just for academics—it's quite useful in fields like physics and economics. For instance, in a physics scenario, considering how the pressure of a gas varies with respect to volume and temperature could be modeled similarly. These relationships help scientists and engineers predict outcomes in real-world applications!