Download
inverse joint and combined variation n.
Skip this Video
Loading SlideShow in 5 Seconds..
Inverse, Joint, and Combined Variation PowerPoint Presentation
Download Presentation
Inverse, Joint, and Combined Variation

Inverse, Joint, and Combined Variation

608 Vues Download Presentation
Télécharger la présentation

Inverse, Joint, and Combined Variation

- - - - - - - - - - - - - - - - - - - - - - - - - - - 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