To express the relationship where $P$ varies directly with $D$ and inversely with $U$, we use the constant of proportionality $K$. The equation can be written as:

$P = K \frac{D}{U}$

In this equation:

• $P$ is directly proportional to $D$, meaning as $D$ increases, $P$ increases.
• $P$ is inversely proportional to $U$, meaning as $U$ increases, $P$ decreases.
• $K$ is the constant of proportionality that relates $P$, $D$, and $U$.

Would you like more details or have any questions?

Here are 5 related questions to further explore this topic:

1. How would you solve for $K$ if $P$, $D$, and $U$ are known?
2. How does the value of $K$ affect the relationship between $P$, $D$, and $U$?
3. What happens to $P$ if both $D$ and $U$ are doubled?
4. Can you give a real-life example where this type of relationship might occur?
5. How would you graph the relationship between $P$ and $D$ for a fixed value of $U$?

Tip: When dealing with direct and inverse variations, always keep in mind how changes in one variable affect the others to understand the overall relationship fully.