https://file.aiquickdraw.com/mathbot/file/1727303275449ly1mzr9a.jpg

To express the relationship where \( w \) varies jointly with \( u \) and \( d \), and inversely with \( p \), we use the following form:

\[ w = k \cdot \frac{u \cdot d}{p} \]

Here, \( k \) is the constant of proportionality.

### Explanation:
- **Joint variation** with \( u \) and \( d \): This means \( w \) is directly proportional to the product of \( u \) and \( d \). This is represented as \( w \propto u \cdot d \).
- **Inverse variation** with \( p \): This means \( w \) is inversely proportional to \( p \), represented as \( w \propto \frac{1}{p} \).

Combining these two variations, we get the equation:

\[ w = k \cdot \frac{u \cdot d}{p} \]

Would you like further details or have any questions?

### Related Questions:
1. What is the value of \( k \) if \( w = 20 \), \( u = 5 \), \( d = 4 \), and \( p = 2 \)?
2. How would the equation change if \( w \) varied directly with \( p \) instead of inversely?
3. If \( u \) is doubled and \( p \) is halved, by what factor will \( w \) change?
4. What happens to \( w \) if both \( u \) and \( d \) are tripled and \( p \) is unchanged?
5. How can we use this relationship to solve practical problems in physics or engineering?

### Tip:
When dealing with joint and inverse variation problems, always identify what the variables are directly or inversely related to in order to set up the correct proportionality.

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

Learn how to express a relationship where w varies jointly with u and d, and inversely with p. This algebraic concept uses proportionality to set up the equation w = k * (u * d) / p, suitable for high school students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation