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Which equation describes this relationship? Remember to include $k$ , the constant of variation. $a$ varies directly with $b$ and inversely with $c$ and $d$ $\newline$ Choices: $\newline$ \[[A]a = \frac{kb}{cd}\] $\newline$ \[[B]a = \frac{kbd}{c}\] $\newline$ \[[C]a = \frac{k}{bcd}\] $\newline$ \[[D]a = \frac{kd}{bc}\]

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Write joint and combined variation equations I

Full solution

Q. Which equation describes this relationship? Remember to include

k

, the constant of variation.

a

varies directly with

b

and inversely with

c

and

d

\newline

Choices:

\newline

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

\newline

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

\newline

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

\newline

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

Identify direct variation: Identify the direct variation component of the relationship. Since $a$ varies directly with $b$ , the equation should start with $a = kb$ , where $k$ is the constant of variation.
Identify inverse variation: Identify the inverse variation component of the relationship. Since $a$ varies inversely with $c$ and $d$ , this means that $a$ should be divided by the product of $c$ and $d$ . The equation should incorporate $\frac{1}{cd}$ to represent the inverse variation with $c$ and $d$ .
Combine direct and inverse variations: Combine the direct and inverse variations into one equation. Since $a$ varies directly with $b$ and inversely with $c$ and $d$ , the equation should multiply $b$ by the constant of variation $k$ and divide by the product of $c$ and $d$ . The combined equation is $a = \frac{kb}{cd}$ .

More problems from Write joint and combined variation equations I

Question

In a direct variation,

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x=5

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x

y

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Posted 9 months ago

Question

In an inverse variation,

y = 4

x = 6

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x

y

. Write the equation using a decimal or an integer.

\_\_\_\_

Posted 8 months ago

Question

z

varies directly with

y

and inversely with

x

y = -12

x = -4

z = -36

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

A

\frac{A}{B}

A

B

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

k

, the constant of variation, in exact form.

\newline

\ z

Posted 9 months ago

Question

z

varies directly with

y

and inversely with

w

x

y = 12

w = 8

x = –5

z = –3

. What is the value of

k

, the constant of variation?

\newline

Write your answer in the form

A

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

A

B

are constants or variable expressions.

\newline

Posted 9 months ago

Question

Given the substitutions

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\ln 5=c

, find the value of

\ln \left(\frac{e}{3}\right)

a, b

c

\newline

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Question

Square VWXY is dilated by a scale factor of

6

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

. Side W'X' measures

12

. What is the measure of side WX?

\newline

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Question

b

in the proportion.

\newline

\begin{array}{l}\frac{10}{8}=\frac{b}{12} \\b=\square\end{array}

Posted 6 months ago

Question

In a direct variation,

y = 4

x = 2

. Write a direct variation equation that shows the relationship between

x

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

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Question

In a direct variation,

y = 18

x = 2

. Write a direct variation equation that shows the relationship between

x

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

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Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

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