Joint and combined variation - Relations and Functions

Joint and combined variation

Lessons

Notes:

In this lesson, we will learn:

  • Identifying Types of Variations
  • Translating Variation Statements Into Equations
  • Solving Variation Problems
  • Word Problems of Variations

  • Joint variation is a direct variation, but with two or more variables. It has the equation y=kxzy=k \cdot x \cdot z where kk is the constant of variation and k0k \neq 0 .
  • A combined variation is formed when we combine any of the variations together (direct, inverse and joint). In most cases, we combine direct and inverse variations to form a combined variation. i.e. yy varies directly with xx and inversely with zz (y=kxz) (y = k \cdot \frac{x}{z})
  • Steps to solving a variation problem:
    1. Write the general variation formula of the problem.
    2. Find the constant of variation kk.
    3. Rewrite the formula with the value of kk.
    4. Solve the problem by inputting known information.
    • Intro Lesson
      Introduction to joint and combined variation
    • 1.
      Identifying Types of Variations
      Determine whether each equation represents a direct, inverse, joint, or combined variation. Name the constant of variation.
    • 2.
      Translating Variation Statements Into Equations
      Translate the following statements, and then classify the variations.
    • 3.
      Solving Variation Problems
      Find the missing variables.
    • 4.
      Word Problems of Variations
      The volume of a cylinder varies jointly as the height and the square of its radius. A cylinder with an 9 cm height and 6 cm radius has a volume of 1018 cm3.
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    Joint and combined variation

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