Revision:Variation

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Proportion

If is proportional to ,

,

and , where is a constant.

The value of will be the same for all values of and .

Example

If , and b = 10 when a = 5, find an equation connecting a and b.

.

Substitute the values of 5 and 10 into the equation to find k:

,

so .

Substitute this into (1):

.

Similarly, if:

,

then:

.

Inverse Proportion

If a and b are inversely proportionally to one another,

,

and

.

In these examples, is known as the constant of variation.

Example

If b is inversely proportional to the square of a, and when a = 3, b = 1, find the constant of variation.

when and ,

,

.

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