# Joint and combined variation

##### Intros

###### Lessons

##### Examples

###### Lessons

**Identifying Types of Variations**

Determine whether each equation represents a direct, inverse, joint, or combined variation. Name the constant of variation.**Translating Variation Statements Into Equations**

Translate the following statements, and then classify the variations.**Solving Variation Problems**

Find the missing variables.**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}.- The time required to process a shipment at Mamazon varies directly with the number of orders being made and inversely with the number of workers. If 1344 orders can be processed by 7 workers in 12 hours, how long will it take 125 workers to process 20,000 items?

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###### Topic 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.

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