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A combined variation, or combined proportionality, occurs when one variable depends on two or more variables, either directly, inversely, or a combination of both. This means that any joint variation is also a combined variation.
z=kx/y
The variable z varies directly with x and inversely with y, and k is the constant of variation. Therefore, this is a combined variation. Here are some examples.
| Examples of Combined Variation | ||
|---|---|---|
| Example | Rule | Comment |
| Newton's Law of Gravitational Force | F=G m_1 m_2/d^2 | The gravitational force F varies directly as the masses of the objects m_1 and m_2, and inversely as the square of the distance d^2 between the objects. The gravitational constant G is the constant of variation. |
| The Ideal Gas Law | P=nRT/V | The pressure P varies directly as the number of moles n and the temperature T, and inversely as the volume V. The universal gas constant R is the constant of variation. |
Combined variation is closely related to other types of variation.