1. Section 9.1 Inverse & Joint Variation p.534

2. Objectives Recall previous knowledge on direct variation. Apply prior knowledge to new situations such as inverse variation and joint variation. Discover when these concepts are actually used. Be super awesome.

3. Just a reminder from chapter 2 Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation.

4. New stuff! Inverse Variation “y varies inversely with x.” k is the constant of variation.

5. Ex: tell whether x & y show direct variation, inverse variation, or neither. a. xy=4.8 b. y=x+4 c. Hint: Solve the equation for y and take notice of the relationship. Inverse Variation Neither Direct Variation

6. Ex: The variables x & y vary inversely, and y=8 when x=3. Write an equation that relates x & y. k=24 Find y when x= -4. y= -6

7. Drum Roll Please …. EXAMPLES!

8. THEY’RE BACK!!! The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=2: x = 5, y = -2 Answer Check: y = -10/x; -5

9. One More … Or is it BRANDON?!?! The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x=2: x = 3/4, y = 3/8 Answer Check: y = 9/32x; 9/64

10. Joint Variation When a quantity varies directly as the product of 2 or more other quantities. For example: if z varies jointly with x & y, then z=kxy. Ex: if y varies inversely with the square of x, then y=k/x 2. Ex: if z varies directly with y and inversely with x, then z=ky/x.

11. Examples: Write an equation. y varies directly with x and inversely with z 2. y varies inversely with x 3. y varies directly with x 2 and inversely with z. z varies jointly with x 2 and y. y varies inversely with x and z.

12. Real World Application Whirlpools: The speed of the current in a whirlpool varies inversely with the distance from the whirlpools center. The Lofoten Maelstrom is a whirlpool located off the coast of norway.

13. Lofoten Maelstrom One of the strongest whirlpools in the world.

14. Lofoten Maelstrom So large it can be seen from outer space.

15. Now for the problem … At a distance of 3 kilometers (3,000 meters) from the center, the speed of the current is about 0.1 meters per second. Describe the change in the speed of the current as you move closer to the whirlpool’s center. For example try 2000 meters, 1,500 meters, 500 meters, 250 meters, 50 meters, etc.

16. Assignment Pg. 537-538 #22-28(evens) #29-34 (all … show all work!) #39-44 (evens … show all work!)