POWERPOINT IN JOINT & COMBINED VARIATIONS pptx

Joint and Combined Variations

1. JOINT & COMBINED VARIATIONS

2. LEARNING OBJECTIVES Illustrate situations that involve joint and combined variations Translate into joint or combined variation statements a relationship between two quantities.

3. Joint Variations It occurs when one quantity varies directly as the product of two or more other quantities. y varies jointly as x and z if there exists a nonzero number k such that y = kxz , where x ≠ 0 and z ≠ 0.

4. Example #1

5. Example #2

6. Example #3

7. Example #4

8. Example #5

9. Example #1

10. Example #2

11. Example #3

12. Example #4

13. Example #5 The variable z varies directly as x and inversely as y. If z = 7/5 when x = 9 and y = 45, find z when x = and y = 18.  

14. Example #6 The variable z varies jointly as the x and y and inversely as w. If z = 1/4 when x = , y = 3/2 and w = 24, find x when z = 1/4, y = 4/5 and w = 32.  

15. Example #7 The variable z varies directly as y and inversely as w. What will be the change in z if y is squared and w is halved?

16. Example #8 The variable w varies directly as x and inversely as y and z. What happens to w if x is increased by 50% and y and z are each decreased by 20%?