Precalculus Examples

$x = 4$ , $z = 3$ , $y = 5$

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.

$k = \frac{5}{(4) \cdot {(3)}^{2}}$

Step 4

Raise $3$ to the power of $2$ .

$k = \frac{5}{4 \cdot 9}$

Step 5

Multiply $4$ by $9$ .

$k = \frac{5}{36}$

Step 6

Write the equation of variation such that $y = k x z^{2}$ , replacing $k$ with the $\frac{5}{36}$ .

$y = \frac{5 x z^{2}}{36}$

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