1 / 29

Inverse, Joint, and Combined Variation

Inverse, Joint, and Combined Variation. Objective: To find the constant of variation for many types of problems and to solve real world problems. Inverse Variation.

dane-neal
Download Presentation

Inverse, Joint, and Combined Variation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Inverse, Joint, and Combined Variation Objective: To find the constant of variation for many types of problems and to solve real world problems.

  2. Inverse Variation • Two variables, x and y, have an inverse-variation relationship if there is a nonzero number k such that xy = k, y = k/x. The constant of variation is k.

  3. Example 1

  4. Example 1

  5. Example 1

  6. Try This • The variable y varies inversely as x, and y = 120 when x = 6.5. Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

  7. Try This • The variable y varies inversely as x, and y = 120 when x = 6.5. Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

  8. Try This • The variable y varies inversely as x, and y = 120 when x = 6.5. Find the constant of variation and write an equation for the relationship. Then, find y when x is 1.5, 4.5, 8, 12.5, and 14.

  9. Joint Variation • If y = kxz, then y varies jointly as x and z, and the constant of variation is k.

  10. Example 2

  11. Example 2

  12. Squared Variation • If , where k is a nonzero constant, then y varies directly as the square of x. Many geometric relationships involve this type of variation, as show in the next example.

  13. Example 3

  14. Example 3

  15. Example 3

  16. Try This • Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. • Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5.

  17. Try This • Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. • Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5. • The constant of variation is .

  18. Try This • Write the formula for the area A, of a circle whose radius is r. Identify the type of variation and the constant of variation. • Find the area of the circle when r is 1.5, 2.5, 3.5, 4.5. • The constant of variation is .

  19. Combined Variation

  20. Example 4

  21. Example 4

  22. Example 4

  23. Homework • Page 486 • 13-27 odd

More Related