Math Problem Statement

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

Solution

The equation that expresses the relationship "d varies jointly with w and p and inversely with u" is:

d=kwpud = k \cdot \frac{w \cdot p}{u}

Here:

  • kk is the constant of proportionality,
  • dd varies directly with ww and pp,
  • dd varies inversely with uu.

Would you like more details or have any questions?

Here are some related questions:

  1. How does the value of dd change if uu is doubled?
  2. What happens to dd if both ww and pp are halved?
  3. How can you solve for kk if dd, ww, pp, and uu are known?
  4. What is the effect on dd if only ww increases while pp and uu remain constant?
  5. How would the equation change if dd varied directly with the square of ww instead?

Tip: Remember, when dealing with joint variation, multiple factors directly influence the dependent variable, while inverse variation reduces the influence of other factors.

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Math Problem Analysis

Mathematical Concepts

Variation
Proportionality

Formulas

Joint variation formula
Inverse variation formula

Theorems

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Suitable Grade Level

Grades 10-12