View by Category

Loading...

PPT – Functions and Equations of Two Variables PowerPoint presentation | free to download

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Functions and Equations of Two Variables

- Lesson 6.1

Functions of Two Variables

- Consider a function with two inputs and one

output - Two independentvariables
- One dependant variable
- z f ( x, y )

7

5

f (x, y)

43

Example

- Consider the volume of a cylinder
- Given r 5, h 10
- V p 2510 250p
- Calculator can define such functions

r

h

Solving for One of the Variables

- How high must the cylinder be for
- Radius of 6 inches
- Volume of 230 cubic inches
- Write out the formula
- Substitute in the known quantities
- Solve for the unknown value

6

h

230 in3

Linear Equation in Two Variables

- Format
- Where a, b, and k are constants
- This can also be thought of as a function in two

variables - Example
- Now note that there are many (x, y) ordered pairs

that can be considered solutions

System of Equations

- If we have two equations in two variables it is

possible that one ordered pair is the solution

for both equations - Which of the following ordered pairs are

solutions for the system (3, 2) (3, -4)

(5, 0)

Solving Systems of Equations

- Graphical solution
- Solve each equation for y
- Graph the resulting function
- Note their intersections

Symbolic Solution

- Solve one of the equations for one of the

variables - x y 5
- Substitute the expression in for that variable in

the other equation - 2 ( y 5 ) y 10
- Result is an equation in one variable
- Solve that equation for the variable 3y 0
- Substitute that value back into the other

equation 2x 0 10

Try It Out

- Given
- Part of class determine graphical solution
- Part of class determine symbolic solution by

substitution

Using Calculator

- Calculator can be used to solve systems of

equations - Use solve command
- Note use of
- and
- curly brackets

Systems of Non-Linear Equations

- Consider
- Note one of equations is not linear
- Same types of solutions can often be used
- Symbolic by substitution
- Graphical
- What kind of graphs are demonstrated

Number of Solutions

- System of linear equations
- One solution no solutions many

solutions - For non linear systems
- Depends on the type of the graphs involved
- What different possibilities exist for a line and

a parabola

Try It Out

- Given the system
- Part of class do graphically
- Part of class do symbolically

Assignment

- Lesson 6.1
- Page 460
- Exercises 1 75 EOO

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

«

/ »

Promoted Presentations

Related Presentations

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2014 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Functions and Equations of Two Variables" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Letu University and other schools with their online training by sharing educational presentations for free