## anonymous one year ago @robtobey A geometric sequence is obtained by placing five terms between 10 and 640. What is the common ratio equal to ?

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1. jim_thompson5910

If r is the common ratio, then what is the next term right after 10?

2. anonymous

nothing the question was just like this

3. jim_thompson5910

do you agree that it would be 10*r or 10r ?

4. jim_thompson5910

since to get the next term, you multiply the last term by r hopefully that makes sense

5. anonymous

nope mate the answer will be 4 2 3 5 or 6

6. jim_thompson5910

7. anonymous

ok

8. anonymous

11

9. jim_thompson5910

idk what you mean the term that comes after 10 is 10r the term after 10r is 10r*r = 10r^2 etc etc until you get to 640

10. jim_thompson5910

you should get this sequence: 10, 10r, 10r^2, 10r^3, 10r^4, 10r^5, 640

11. anonymous

ok

12. jim_thompson5910

the next term after 10r^5 is 10r^6 therefore, 10r^6 = 640

13. jim_thompson5910

14. anonymous

which is 4

15. zzr0ck3r

I agree, to see an example look at 1,2,4,8,16,32,64 64/1=2^6

16. jim_thompson5910

r = 4 is false

17. anonymous

sorry it will be 2

18. jim_thompson5910

r = 2 is true

19. anonymous

thanks man can I ask 1 more question

20. jim_thompson5910

sure

21. anonymous

thank you then now I am writing

22. anonymous

|dw:1439165401472:dw|

23. anonymous

Did you get the question because my drawing is not good enough ?

24. jim_thompson5910

what is the area of the circle given

25. jim_thompson5910

hint: use A = pi*r^2

26. anonymous

it has given no area

27. jim_thompson5910

use that formula I gave to compute the area

28. jim_thompson5910

r = 5 in this case

29. anonymous

ok but how

30. jim_thompson5910

A = pi*r^2 A = pi*5^2 A = ???

31. anonymous

25pi then wat will happen

32. jim_thompson5910

now we will have another circle with the same center at point A this new circle will have radius 3 |dw:1439165882115:dw|

33. anonymous

ok

34. jim_thompson5910

the goal is to find the area of this shaded region and divide it by the 25pi found earlier |dw:1439165892979:dw|

35. jim_thompson5910

what is the area of the smaller circle?

36. anonymous

9pi

37. anonymous

but the answer is not 9/25 mate

38. jim_thompson5910

it would be 9pi/25pi = 9/25 IF we wanted to land inside the inner circle but we want to land in that ring I shaded above

39. jim_thompson5910

area of ring = (area of larger circle) - (area of smaller circle)

40. jim_thompson5910

answer = (area of ring)/(area of larger circle)

41. anonymous

yes which will be 16/25

42. jim_thompson5910

good

43. anonymous

44. jim_thompson5910

one last one

45. anonymous

ok

46. anonymous

47. jim_thompson5910

which one?

48. anonymous

10

49. anonymous

if you can all of them :D

50. jim_thompson5910

are you able to compute f ' (x) ?

51. anonymous

not at all

52. jim_thompson5910

|dw:1439166519002:dw|

53. jim_thompson5910

what is the derivative of sin(x) ?

54. anonymous

cosx

55. jim_thompson5910

so we just derive the outer function sin(...) to get cos(...) |dw:1439166578842:dw|

56. jim_thompson5910

then we use the chain rule to derive cos(x) to get -sin(x) so derive cos(...) to get -sin(...) that gets multiplied to what we have |dw:1439166647000:dw|

57. jim_thompson5910

we then go in further derive 5x to get 5 that gets tacked on too |dw:1439166679192:dw| I placed it up front

58. anonymous

ok

59. jim_thompson5910

so $\Large f \ ' (x) = 5\cos(\cos(5x))*(-\sin(5x))$

60. jim_thompson5910

now just replace every x with pi/10 and evaluate

61. anonymous

ok

62. anonymous

the answer I think will be -5

63. jim_thompson5910

yep it's -5

64. anonymous

65. anonymous

just one more and thats it

66. anonymous

thank you

67. anonymous

68. anonymous

57

69. anonymous

did you find the answer mate

70. anonymous

Recall that $$sec^2(x) - tan^2(x) =1$$ $$cos^2(x) - cos(x)sin(x) = cos^2(x)[1 - tanx] = \frac{1}{sec^2(x)}[1-tanx] = \frac{1}{1+tan^2(x)}[1-tan(x)]$$ Now put the value of tan(x) that's given.

71. anonymous

ok carry on

72. anonymous

* $$\frac{1}{1+tan^2(x)}[1-tan(x)]$$

73. anonymous

yeah but thats not my answer

74. anonymous

Substitute the tan(x)= 2 and get the answer.

75. anonymous

wat you think will be the answer