Precalculus Examples

Find x Using the Constant of Variation
, ,
Step 1
When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is , where is the constant of variation.
Step 2
Solve the equation for , the constant of variation.
Step 3
Replace the variables and with the actual values.
Step 4
Multiply the numerator by the reciprocal of the denominator.
Step 5
Multiply .
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Step 5.1
Multiply by .
Step 5.2
Multiply by .
Step 6
Use the formula to substitute for and for .
Step 7
Solve for .
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Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 7.3
Remove parentheses.
Step 7.4
Simplify .
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Step 7.4.1
Multiply by .
Step 7.4.2
Cancel the common factor of .
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Step 7.4.2.1
Factor out of .
Step 7.4.2.2
Cancel the common factor.
Step 7.4.2.3
Rewrite the expression.
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