1. The document discusses inverse and inverse square variation functions and how to solve problems involving them. 2. Inverse variation occurs when one variable gets larger as the other gets smaller. Inverse square variation is when the independent variable is squared. 3. The inverse variation function is y = k/x and the inverse square variation function is y = k/x^2, where k is the constant of variation. 4. Two examples are provided to demonstrate solving inverse variation and inverse square variation word problems.

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. Homework

53. Homework
p. 284 #1 -21 odd
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