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 where is the constant of variation and .
- 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. varies directly with and inversely with
- Steps to solving a variation problem:
- Write the general variation formula of the problem.
- Find the constant of variation .
- Rewrite the formula with the value of .
- Solve the problem by inputting known information.
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Intro Lesson
Introduction to joint and combined variation
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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.
