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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Review Asg #63: Ch. 10, Lesson 1 (pp. 380-384): Set I Exercises 7-11 and 15-17. Set II Exercises 27-30. Lesson: Averages Homework / Questions Clean-up. Averages. For distance: Suppose you drive 1 hour at 50mph and 1 hour at 35mph.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Review Asg #63: Ch. 10, Lesson 1 (pp. 380-384): • Set I Exercises 7-11 and 15-17. • Set II Exercises 27-30. • Lesson: Averages • Homework / Questions • Clean-up

  3. Averages • For distance: • Suppose you drive 1 hour at50mph and 1 hour at 35mph. • 50 mi + 35 mi = 85 mi • Average speed = ? • For interest: • Suppose you start with $1,000and earn 12% over 1 year, then8% over the next year. • ($1,000)(1.12)(1.08) = $1,209.60 • Average rate of earning = ?

  4. Average Problems

  5. Averages: Two Types arithmetic geometric

  6. Geometric Mean • The geometric mean of a and b is c, iff: Contrast: arithmetic mean

  7. Trying again: Geometric Mean • Year 1 Multiplier: 1.12 • Year 2 Multiplier: 1.08 • Average (arithmetic mean) = 1.10 wrong answer! • Geometric mean =  1.12*1.08  1.09981817

  8. Geometric Mean: Example • Find the geometric mean of 10 and 90. • Is it different from the arithmetic mean? • If so, how big is the difference?

  9. Puzzles!

  10. Cube Puzzle: Conclusion • Can we separate the 27 cubes using fewer than six cuts? • No.

  11. Puzzle: Reconstruct the Division Each digit is replaced by “X” American Mathematical Monthly, April 1954. Contributed by P.L. Chessin.

  12. Homework • Asg #64: From Ch. 10 L. 1 (same as today’s): • Set I Exercises 1-6. • Set II Exercises 34-40 (if you prefer visuals)or 41-47 (if you prefer music). • Bonus:Both 34-40 and 41-47. • Due Wednesday, 4/10.

  13. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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