Algebra 3: Week 11. Monday: 2.5 Work Day Tuesday: Exam 2, Review Day 1 Wednesday: Exam 2, Review Day 2 Thursday: Exam 2 Friday: Debrief

Transcription

1 Algebra 3: Week 11 Monday: 2.5 Work Day Tuesday: Exam 2, Review Day 1 Wednesday: Exam 2, Review Day 2 Thursday: Exam 2 Friday: Debrief Next Week: Start Chapter 3 1

2 Monday Mindfulness Training This week: Loving Kindness editation.mp3 2

3 2.5: Variation Goals Direct Variation Models Inverse Variation Models Joint / Combined Variation Models 3

4 Direct Variation Direct Variation when two quantities have a constant (unchanged) ratio. One varies directly with the other. If one increases, the other increases. If one decreases, the other decreases. y=kx, where k is the constant of variation. Or y x = k e.g., x y

5 Variation Recall that we can combine sets of data to test whether or not they are related. One type of relationship is variation. Variation two variables being related to each other by some equation, e.g., the more hours you work earns more money if paid by the hour. 5

6 Example 1 The weekly salary a woman earns, S, varies directly as the number of hours, h, which she works. Express this relation as a formula. If she makes $1200 for 40 hours of work, what is the constant of change? S=hk h=hours worked k=rate per hour 6

7 Example 2 Given that y varies directly as x, with a constant of variation k = 1/3, find y when x = 12. What about when x = 21? 7

8 Example 3 General Procedure: 1. Use the initial x and y variables to solve for k. 2. Write the direct variation equation. 3. Use the equation to finish problem. Given that y varies directly as x, find the constant of variation if y = 24 and x = 3. What is y when x = 10? 8

9 Example 4 Suppose y varies directly as x, and y = 30 when x = 6. What is the value of y when x = 100? 9

10 Note Direct variation vs. equation of line: y=kx versus y=mx+b Direct variation is linear with no y-intercept, i.e., a line that passes through the origin. 10

11 Example 5 While riding a bicycle, the distance you travel varies directly with time. If you travel 5 miles in 30 minutes, how long will it take you to travel 20 miles? 11

12 Inverse Variation Inverse Variation when two quantities have a non-constant (changed) ratio. y=k/x, where k is the constant of variation. Or: k=xy One varies inversely with the other. If one increases, the other decreases. If one decreases, the other increases. A biker traveling at 8 mph can cover 8 miles in 1 hour. If the biker's speed decreases to 4 mph, it will take the biker 2 hours (an increase of one hour), to cover the same distance. 12

13 Example 1 The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 2 hours for a square inch of ice to melt at 65º, find the constant of proportionality. 13

14 Example 2 In a formula, Z varies inversely as p. If Z is 200 when p = 4, find Z when p =

15 Example 3 In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long? 15

16 Varies / Combined Variation Varies Jointly when a variable is proportional to the product of two or more other variables. Combined Variation a combination of direct and/or inverse variation. y = kxz y = kx / z 16

17 Example 1 Suppose y varies jointly as x and z. Find y when x=8 & z=3, if y=105 when x=5 and z=6. 17

18 Example 2 Variable M varies directly as variable t and inversely as variable s. If M = 24 when t = 3 and s = 2, find M when t = 5 and s = 8. 18

19 Example 3 The number of hours h that it takes m men to assemble x machines varies directly as the number of machines and inversely as the number of men. If four men can assemble 12 machines in four hours, how many men are needed to assemble 36 machin es in eight hours? 19

20 2.5 Work Day Day 1 (Last Friday) Day 2 (Today) 2.5, p , p , 21, 22, 24, 28 Show Instructor When Completed 20

21 Tuesday Mindfulness Training This week: Loving Kindness editation.mp3 21

22 Exam 2, Review Day 1 Chapter Review, p. 110 Make Review Sheet Things to Know Equations How To p. 112: 1-38, 42, 43 22

23 Wednesday Mindfulness Training This week: Loving Kindness editation.mp3 23

24 Exam 2, Review Day 2 Chapter Review, p. 110 Make Review Sheet Things to Know Equations How To p. 112: 1-38, 42, 43 24

25 Thursday Mindfulness Training This week: Loving Kindness editation.mp3 25

26 Exam Day 26

27 Friday Mindfulness Training This week: Loving Kindness editation.mp3 Get off the phones Clean up your trash 27

28 Meditation Day Breath Meditation: 28