<< Chapter < Page Chapter >> Page >

A quantity y varies inversely with the square of x . If y = 8 when x = 3 , find y when x is 4.

9 2

Got questions? Get instant answers now!

Solving problems involving joint variation

Many situations are more complicated than a basic direct variation or inverse variation model. One variable often depends on multiple other variables. When a variable is dependent on the product or quotient of two or more variables, this is called joint variation    . For example, the cost of busing students for each school trip varies with the number of students attending and the distance from the school. The variable c , cost, varies jointly with the number of students, n , and the distance, d .

Joint variation

Joint variation occurs when a variable varies directly or inversely with multiple variables.

For instance, if x varies directly with both y and z , we have x = k y z . If x varies directly with y and inversely with z , we have x = k y z . Notice that we only use one constant in a joint variation equation.

Solving problems involving joint variation

A quantity x varies directly with the square of y and inversely with the cube root of z . If x = 6 when y = 2 and z = 8 , find x when y = 1 and z = 27.

Begin by writing an equation to show the relationship between the variables.

x = k y 2 z 3

Substitute x = 6 , y = 2 , and z = 8 to find the value of the constant k .

6 = k 2 2 8 3 6 = 4 k 2 3 = k

Now we can substitute the value of the constant into the equation for the relationship.

x = 3 y 2 z 3

To find x when y = 1 and z = 27 , we will substitute values for y and z into our equation.

x = 3 ( 1 ) 2 27 3 = 1
Got questions? Get instant answers now!
Got questions? Get instant answers now!

A quantity x varies directly with the square of y and inversely with z . If x = 40 when y = 4 and z = 2 , find x when y = 10 and z = 25.

x = 20

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with direct and inverse variation.

Visit this website for additional practice questions from Learningpod.

Key equations

Direct variation y = k x n , k  is a nonzero constant .
Inverse variation y = k x n , k  is a nonzero constant .

Key concepts

  • A relationship where one quantity is a constant multiplied by another quantity is called direct variation. See [link] .
  • Two variables that are directly proportional to one another will have a constant ratio.
  • A relationship where one quantity is a constant divided by another quantity is called inverse variation. See [link] .
  • Two variables that are inversely proportional to one another will have a constant multiple. See [link] .
  • In many problems, a variable varies directly or inversely with multiple variables. We call this type of relationship joint variation. See [link] .

Section exercises

Verbal

What is true of the appearance of graphs that reflect a direct variation between two variables?

The graph will have the appearance of a power function.

Got questions? Get instant answers now!

If two variables vary inversely, what will an equation representing their relationship look like?

Got questions? Get instant answers now!

Is there a limit to the number of variables that can vary jointly? Explain.

No. Multiple variables may jointly vary.

Got questions? Get instant answers now!

Algebraic

For the following exercises, write an equation describing the relationship of the given variables.

Questions & Answers

x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
How can I solve for a domain and a codomains in a given function?
Oliver Reply
ranges
EDWIN
Thank you I mean range sir.
Oliver
proof for set theory
Kwesi Reply
don't you know?
Inkoom
find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
Martina Reply
factoring polynomial
Noven Reply
what's your topic about?
Shin Reply
find general solution of the Tanx=-1/root3,secx=2/root3
Nani Reply
find general solution of the following equation
Nani
the value of 2 sin square 60 Cos 60
Sanjay Reply
0.75
Lynne
0.75
Inkoom
when can I use sin, cos tan in a giving question
duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
I want to learn the calculations
Koru Reply
where can I get indices
Kojo Reply
I need matrices
Nasasira
hi
Raihany
Hi
Solomon
need help
Raihany
maybe provide us videos
Nasasira
about complex fraction
Raihany
Hello
Cromwell
a
Amie
What do you mean by a
Cromwell
nothing. I accidentally press it
Amie
you guys know any app with matrices?
Khay
Ok
Cromwell
Solve the x? x=18+(24-3)=72
Leizel Reply
x-39=72 x=111
Suraj
Solve the formula for the indicated variable P=b+4a+2c, for b
Deadra Reply
Need help with this question please
Deadra
b=-4ac-2c+P
Denisse
b=p-4a-2c
Suddhen
b= p - 4a - 2c
Snr
p=2(2a+C)+b
Suraj
b=p-2(2a+c)
Tapiwa
P=4a+b+2C
COLEMAN
b=P-4a-2c
COLEMAN
like Deadra, show me the step by step order of operation to alive for b
John
A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
Practice Key Terms 7

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask