Questions: Write an equation that expresses the following relationship. u varies directly with p and inversely with d In your equation, use k as the constant of proportionality.

Write an equation that expresses the following relationship. u varies directly with p and inversely with d In your equation, use k as the constant of proportionality.

Transcript text: Write an equation that expresses the following relationship. $u$ varies directly with $p$ and inversely with $d$ In your equation, use $k$ as the constant of proportionality.

Solution

Solution Steps

To express the relationship where $ u $ varies directly with $ p $ and inversely with $ d $, we can use the concept of direct and inverse variation. Direct variation with $ p $ means $ u $ is proportional to $ p $, and inverse variation with $ d $ means $ u $ is inversely proportional to $ d $. Combining these, we get the equation $ u = k \cdot \frac{p}{d} $, where $ k $ is the constant of proportionality.

Step 1: Define the Relationship

Given that $ u $ varies directly with $ p $ and inversely with $ d $, we can express this relationship mathematically as: \[ u = k \cdot \frac{p}{d} \] where $ k $ is the constant of proportionality.

Step 2: Substitute the Values

We are provided with the values: