Algebra Examples

y = 1.5

$y = 1.5$ ,

x = 5

$x = 5$ ,

z = 7

$z = 7$

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}

$y = k x z^{2}$ , where

k

$k$ is the constant of variation.

y = k x z^{2}

$y = k x z^{2}$

Step 2

Solve the equation for

k

$k$ , the constant of variation.

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

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

Step 3

Replace the variables

x

$x$ ,

y

$y$ , and

z

$z$ with the actual values.

k = \frac{1.5}{(5) \cdot {(7)}^{2}}

$k = \frac{1.5}{(5) \cdot {(7)}^{2}}$

Step 4

Raise

7

$7$ to the power of

2

$2$ .

k = \frac{1.5}{5 \cdot 49}

$k = \frac{1.5}{5 \cdot 49}$

Step 5

Multiply

5

$5$ by

49

$49$ .

k = \frac{1.5}{245}

$k = \frac{1.5}{245}$

Step 6

Divide

1.5

$1.5$ by

245

$245$ .

k = 0.00612244

$k = 0.00612244$

Step 7

Write the equation of variation such that

y = k x z^{2}

$y = k x z^{2}$ , replacing

k

$k$ with the

0.00612244

$0.00612244$ .

y = 0.00612244 x z^{2}

$y = 0.00612244 x z^{2}$

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