Int Math 2 Section 6-9 1011
- 1. Section 6-9 Inverse Variation
- 2. Essential Question How do you solve problems involving inverse variation and inverse square variation functions? Where you’ll see this: Music, physics, industry, travel
- 3. Vocabulary 1. Inverse Variation: 2. Inverse Square Variation:
- 4. Vocabulary 1. Inverse Variation: A variation situation where when one variable gets larger, the other gets smaller 2. Inverse Square Variation:
- 5. Vocabulary 1. Inverse Variation: A variation situation where when one variable gets larger, the other gets smaller 2. Inverse Square Variation: An inverse variation situation where the independent variable is squared
- 6. Inverse Variation Function: Inverse Square Variation Function:
- 7. Inverse Variation Function: k y= x Inverse Square Variation Function:
- 8. Inverse Variation Function: k y= x k ≠ 0, x ≠ 0 Inverse Square Variation Function:
- 9. Inverse Variation Function: k y= x k ≠ 0, x ≠ 0 Inverse Square Variation Function: k y= 2 x
- 10. Inverse Variation Function: k y= x k ≠ 0, x ≠ 0 Inverse Square Variation Function: k y= 2 x k ≠ 0, x ≠ 0
- 11. Example 1 The force of gravitational attraction between two objects varies inversely as the distance between them. If two objects have a gravitational force of 550 newtons (N) when they are 2200 m apart, how far apart are they when their gravitational force is 665.5 N?
- 12. Example 1 The force of gravitational attraction between two objects varies inversely as the distance between them. If two objects have a gravitational force of 550 newtons (N) when they are 2200 m apart, how far apart are they when their gravitational force is 665.5 N?
- 13. Example 1 The force of gravitational attraction between two objects varies inversely as the distance between them. If two objects have a gravitational force of 550 newtons (N) when they are 2200 m apart, how far apart are they when their gravitational force is 665.5 N? force distance
- 14. Example 1 The force of gravitational attraction between two objects varies inversely as the distance between them. If two objects have a gravitational force of 550 newtons (N) when they are 2200 m apart, how far apart are they when their gravitational force is 665.5 N? y = force x = distance
- 15. Example 1 The force of gravitational attraction between two objects varies inversely as the distance between them. If two objects have a gravitational force of 550 newtons (N) when they are 2200 m apart, how far apart are they when their gravitational force is 665.5 N? y = force x = distance k y= x
- 16. Example 1 y = force x = distance k y= x
- 17. Example 1 y = force x = distance k y= x k 550 = 2200
- 18. Example 1 y = force x = distance k y= x k 550 = 2200 k = 1210000
- 19. Example 1 y = force x = distance k 1210000 y= y= x x k 550 = 2200 k = 1210000
- 20. Example 1 y = force x = distance k 1210000 y= y= x x k 1210000 550 = 665.5 = 2200 x k = 1210000
- 21. Example 1 y = force x = distance k 1210000 y= y= x x k 1210000 550 = 665.5 = 2200 x k = 1210000 665.5x = 1210000
- 22. Example 1 y = force x = distance k 1210000 y= y= x x k 1210000 550 = 665.5 = 2200 x k = 1210000 665.5x = 1210000 2 x = 1818 11
- 23. Example 1 y = force x = distance k 1210000 y= y= x x k 1210000 550 = 665.5 = 2200 x k = 1210000 665.5x = 1210000 2 x = 1818 m 11
- 24. Example 2 The weight of a body is inversely proportional to the square of its distance from the center of the Earth. If a man weighs 147 lb on Earth’s surface, what will he weight 200 miles above Earth? (Assume Earth’s radius to be 4000 mi.)
- 25. Example 2 The weight of a body is inversely proportional to the square of its distance from the center of the Earth. If a man weighs 147 lb on Earth’s surface, what will he weight 200 miles above Earth? (Assume Earth’s radius to be 4000 mi.)
- 26. Example 2 The weight of a body is inversely proportional to the square of its distance from the center of the Earth. If a man weighs 147 lb on Earth’s surface, what will he weight 200 miles above Earth? (Assume Earth’s radius to be 4000 mi.) weight distance
- 27. Example 2 The weight of a body is inversely proportional to the square of its distance from the center of the Earth. If a man weighs 147 lb on Earth’s surface, what will he weight 200 miles above Earth? (Assume Earth’s radius to be 4000 mi.) y = weight x = distance
- 28. Example 2 The weight of a body is inversely proportional to the square of its distance from the center of the Earth. If a man weighs 147 lb on Earth’s surface, what will he weight 200 miles above Earth? (Assume Earth’s radius to be 4000 mi.) y = weight x = distance k y= 2 x
- 29. Example 2 y = weight x = distance k y= 2 x
- 30. Example 2 y = weight x = distance k y= 2 x k 147 = 2 4000
- 31. Example 2 y = weight x = distance k y= 2 x k 147 = 2 4000 k 147 = 16000000
- 32. Example 2 y = weight x = distance k y= 2 x k 147 = 2 4000 k 147 = 16000000 k = 2352000000
- 33. Example 2 y = weight x = distance k 2352000000 y= 2 y= 2 x x k 147 = 2 4000 k 147 = 16000000 k = 2352000000
- 34. Example 2 y = weight x = distance k 2352000000 y= 2 y= 2 x x k 1210000 147 = 2 y= 2 4000 4200 k 147 = 16000000 k = 2352000000
- 35. Example 2 y = weight x = distance k 2352000000 y= 2 y= 2 x x k 1210000 147 = 2 y= 2 4000 4200 k 2352000000 147 = y= 16000000 17640000 k = 2352000000
- 36. Example 2 y = weight x = distance k 2352000000 y= 2 y= 2 x x k 1210000 147 = 2 y= 2 4000 4200 k 2352000000 147 = y= 16000000 17640000 k = 2352000000 1 y = 133 3
- 37. Example 2 y = weight x = distance k 2352000000 y= 2 y= 2 x x k 1210000 147 = 2 y= 2 4000 4200 k 2352000000 147 = y= 16000000 17640000 k = 2352000000 1 y = 133 lb 3
- 38. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5.
- 39. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k y= x
- 40. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k y= x k 15 = 10
- 41. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k y= x k 15 = 10 k = 150
- 42. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k 150 y= y= x x k 15 = 10 k = 150
- 43. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k 150 y= y= x x k 150 15 = y= 10 5 k = 150
- 44. Example 3 Assume y varies inversely as x. a. When x = 10, y = 15. Find y when x = 5. k 150 y= y= x x k 150 15 = y= 10 5 k = 150 y = 30
- 45. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40.
- 46. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k y= x
- 47. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k y= x k 10 = 2
- 48. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k y= x k 10 = 2 k = 20
- 49. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k 20 y= y= x x k 10 = 2 k = 20
- 50. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k 20 y= y= x x k 20 10 = y= 2 40 k = 20
- 51. Example 3 Assume y varies inversely as x. b. When x = 2, y = 10. Find y when x = 40. k 20 y= y= x x k 20 10 = y= 2 40 k = 20 1 y= 2
- 52. Problem Set
- 53. Problem Set p. 284 #1 - 21 odd "If people only knew how hard I work to gain my mastery, it wouldn't seem so wonderful at all." - Michelangelo Buonarroti
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