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Which equation describes this relationship? Remember to include $k$ , the constant of variation. $\newline$ $z$ varies directly with $w$ and inversely with $x$ and $y$ $\newline$ Choices: $\newline$ (A) $z = \frac{kwy}{x}$ $\newline$ (B) $z = \frac{k}{wxy}$ $\newline$ (C) $z = \frac{kw}{xy}$ $\newline$ (D) $z = \frac{ky}{wx}$

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Write joint and combined variation equations II

Full solution

Q. Which equation describes this relationship? Remember to include

k

, the constant of variation.

\newline

z

varies directly with

w

and inversely with

x

and

y

\newline

Choices:

\newline

(A)

z = \frac{kwy}{x}

\newline

(B)

z = \frac{k}{wxy}

\newline

(C)

z = \frac{kw}{xy}

\newline

(D)

z = \frac{ky}{wx}

Identify Direct Variation: $z$ varies directly with $w$ and inversely with $x$ and $y$ , so the equation should have $w$ in the numerator and $x$ and $y$ in the denominator.
Determine Correct Equation Form: The correct form for the equation of variation is $z = \frac{k(w)}{xy}$ , because $z$ is directly proportional to $w$ and inversely proportional to both $x$ and $y$ .
Match with Choices: Looking at the choices, $(C)z = \frac{k w}{x y}$ matches the form we derived.

More problems from Write joint and combined variation equations II

Question

In a direct variation,

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Question

In an inverse variation,

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\_\_\_\_

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Question

z

varies directly with

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and inversely with

x

y = -12

x = -4

z = -36

. What is the equation of variation? Write your answer in the form

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\frac{A}{B}

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B

are constants or variable expressions. Remember to include the value of

k

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\newline

\ z

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Question

Which equation describes this relationship? Remember to include

k

, the constant of variation.

a

varies directly with

b

and inversely with

c

d

\newline

\newline

\[[A]a = \frac{kb}{cd}\]

\newline

\[[B]a = \frac{kbd}{c}\]

\newline

\[[C]a = \frac{k}{bcd}\]

\newline

\[[D]a = \frac{kd}{bc}\]

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Question

z

varies directly with

y

and inversely with

w

x

y = 12

w = 8

x = –5

z = –3

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k

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\newline

Write your answer in the form

A

\frac {(A)}{(B)}

A

B

are constants or variable expressions.

\newline

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Question

Given the substitutions

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\newline

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Question

Square VWXY is dilated by a scale factor of

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V^{\prime} W^{\prime} X^{\prime} Y^{\prime}

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Question

6

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Question

1

5

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Use the given information to find

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Question

10+7 x=4 x+2+b x

\newline

In the equation shown,

b

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\newline

1

\newline

3

\newline

5

\newline

6

\newline

7

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