Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

View step-by-step help

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 inversely with

w

,

x

, and

y

\newline

Choices:

\newline

(A)

z = \frac{k}{wxy}

\newline

(B)

z = \frac{ky}{wx}

\newline

(C)

z = \frac{kwy}{x}

\newline

(D)

z = \frac{k}{wxy}

Identify Inverse Variation: $z$ varies inversely with $w$ , $x$ , and $y$ means $z = \frac{k}{wxy}$ , where $k$ is the constant of variation.
Analyze Answer Choices: Looking at the choices, we need to find the one that matches the form $z = \frac{k}{wxy}$ .
Eliminate Incorrect Forms: Choice (A) is z = rac{k w}{x y}, which is not the correct form because it suggests $z$ varies directly with $w$ , which is wrong.
Choose Correct Form: Choice (B) is $z = \frac{k y}{w x}$ , which is also not the correct form because it suggests $z$ varies directly with $y$ , which is wrong.
Choose Correct Form: Choice (B) is $z = \frac{k y}{w x}$ , which is also not the correct form because it suggests $z$ varies directly with $y$ , which is wrong. Choice (C) is $z = \frac{k w y}{x}$ , which is not the correct form because it suggests $z$ varies directly with $w$ and $y$ , which is wrong.
Choose Correct Form: Choice (B) is $z = \frac{k}{y}/wx$ , which is also not the correct form because it suggests $z$ varies directly with $y$ , which is wrong. Choice (C) is $z = \frac{kwy}{x}$ , which is not the correct form because it suggests $z$ varies directly with $w$ and $y$ , which is wrong. Choice (D) is $z = \frac{k}{wxy}$ , which is the correct form because it shows $z$ varies inversely with $w$ , $z$ $0$ , and $y$ .

More problems from Write joint and combined variation equations II

Question

In a direct variation,

y=15

x=5

. Write a direct variation equation that shows the relationship between

x

y

. Write your answer as an equation with

y

first, followed by an equals sign.

Posted 2 months ago

Question

In an inverse variation,

y = 4

x = 6

. Write an inverse variation equation that shows the relationship between

x

y

. Write the equation using a decimal or an integer.

\_\_\_\_

Posted 2 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 2 months ago

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

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

Posted 2 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 2 months ago

Question

Given the substitutions

\ln 2=a, \ln 3=b

\ln 5=c

, find the value of

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

a, b

c

\newline

Posted 2 months ago

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

Posted 2 months ago

Question

6

2

\newline

2

4

2

11

1

2

16

2

\newline

In the system of equations, r is a constant. For what value of r does the system of linear equations have infinitely many solutions?

Posted 2 months ago

Question

1

5

\newline

Use the given information to find

m \angle P Q W

\newline

2

\newline

m \angle P Q W

m \angle W Q R=134 x

m \angle P Q R=169^{\circ}

m \angle P Q W=36 x-1

Posted 2 months ago

Question

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

\newline

In the equation shown,

b

is a constant. For what value of

b

does the equation have no solutions?

\newline

1

\newline

3

\newline

5

\newline

6

\newline

7

Posted 2 months ago