Precalculus Examples

$y = 3$ , $x = 3$ , $z = 7$

Step 1

When three variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other two vary. The formula for direct variation is $y = k x z^{2}$ , where $k$ is the constant of variation.

$y = k x z^{2}$

Step 2

Solve the equation for $k$ , the constant of variation.

$k = \frac{y}{x z^{2}}$

Step 3

Replace the variables $x$ , $y$ , and $z$ with the actual values.

$k = \frac{3}{(3) \cdot {(7)}^{2}}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Cancel the common factor.

$k = \frac{3}{3 \cdot {(7)}^{2}}$

Step 4.2

Rewrite the expression.

$k = \frac{1}{{(7)}^{2}}$

Step 5

Raise $7$ to the power of $2$ .

$k = \frac{1}{49}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{1}{49}$ .

$y = \frac{x z^{2}}{49}$

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