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 $y=k \cdot x \cdot z$ where $k$ is the constant of variation and $k \neq 0$.
 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. $y$ varies directly with $x$ and inversely with $z$ $(y = k \cdot \frac{x}{z})$
 Steps to solving a variation problem:
 Write the general variation formula of the problem.
 Find the constant of variation $k$.
 Rewrite the formula with the value of $k$.
 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 cm^{3}.