## ganeshie8 3 years ago ...

1. mlb004

2. ganeshie8

look at the model

3. ganeshie8

its height is just 2 feet, whereas the actual ramp was 12feet.

4. ganeshie8

so the model is 6 times smaller than the actual ramp

5. ganeshie8

look at the grid now

6. ganeshie8

can you tell me the length of JL ?

7. ganeshie8

@mlb004 still there :)

8. mlb004

yes sorry

9. ganeshie8

np, take ur time :) see if u can find the length of JL

10. mlb004

Ok I am looking at the grid nd trying to figure it out.

11. ganeshie8

if you see, both J and L are at same height (60)

12. ganeshie8

J is on left side at 10 L is on right side at 34

13. mlb004

yes

14. ganeshie8

so length of JL = distance between JL= 34-10 = 24

15. mlb004

ok

16. ganeshie8

so we now knw two lengths of actual ramp. JK = 12 feet JL = 24 feet

17. mlb004

yes ok

18. ganeshie8

we need to figure out where R goes

19. mlb004

ok

20. ganeshie8

look at the ramps, JL of actual ramp is represented by PR in model, right ?

21. mlb004

yes it is

22. ganeshie8

now this is the key :- since the model is 6 times smaller than actual ramp, PR will also be 6 times smaller than JL

23. ganeshie8

so, PR = JL/6 = 24/6 = 4

24. mlb004

Yes that makes sense

25. ganeshie8

good :) so what does that mean ?

26. ganeshie8

it means, we need to pick R such that it is 4 feet away from P

27. ganeshie8

look at grid now

28. ganeshie8

P is located at (30, 20)

29. mlb004

yes

30. ganeshie8

can we say R can be at (30+4, 20) = (34, 20)

31. ganeshie8

?

32. mlb004

yes

33. ganeshie8

thats it ! point R has to be at (34, 20)

34. mlb004

And we explain this usuing reasoning because of all of the above notes?

35. ganeshie8

you can compress it :-

36. mlb004

ok

37. ganeshie8

Since QP(2feet) in model is smaller than JK(12feet) in actual ramp by 12 times, all dimensions in model have to be smaller than actual ramp by 6 times. From the grid, length of JL = 24. JL is represented in model as PR. Since PR has to be 6 times smaller than JL. so PR = 24/6 = 4 feet. Since P is fixed in grid at (30, 20), R point which is 4feet from P can be at (30+4, 20) = (34, 20).

38. mlb004

oh ok, thank you so much. :)

39. ganeshie8

np :)

40. mlb004

What is the sum of the first 12 terms in the Fibonacci Sequence? Term - 1,2,3,4,5,6,7,8,9 Febonacci Number - 1,1,2,3,5,8,13,21,34 Numberical number? _________

41. ganeshie8

use this :- sum of first n numbers = (n+2)th numeber - 1

42. ganeshie8

since you want to knw suermnsm of first 12 terms, you need to look for (12+2) = 14th number

43. mlb004

ok

44. ganeshie8

google and tell me, whats the 14th number in fibonacci sequence

45. mlb004

Ok, I am doing it now.

46. mlb004

It is 377

47. ganeshie8

correct! thats the 14th number. subtract 1 to get the sum of first 12 numbers

48. mlb004

49. ganeshie8

sum of first 12 numbers = (12+2)the number - 1 = 14th number - 1 = 377 - 1 = 376

50. ganeshie8

yes thats the answer. you can confirm it by adding manually all 12 numbers !

51. ganeshie8
52. mlb004

So is the Fibonacci Sequence always the same?

53. ganeshie8

Yes

54. mlb004

Ok so if it asks what the 13th term in the Fibonacci Sequence is then it would be 233?

55. ganeshie8

you're tossing, whether to call 233 ias 13th number or 14th number ?

56. mlb004

It asked me : What is the 13th term in the Fibonacci Sequence?

57. mlb004

That is a 2nd question, I got and understand the first question.

58. ganeshie8

cuz if u start from 0,1 then 14th number wud be 233 if u start from 1,1 then 13th number wud be 233

59. ganeshie8

You have posted this :- What is the sum of the first 12 terms in the Fibonacci Sequence? Term - 1,2,3,4,5,6,7,8,9 Febonacci Number - 1,1,2,3,5,8,13,21,34 Numberical number? _________

60. ganeshie8

Is this what they gave you to use ?

61. mlb004

My chart starts with 1 so I was saying the correct answer would be 233, correct?

62. ganeshie8

here it starts from 1,1..

63. ganeshie8

yes, if you start from 1,1, then, 13th number is 233

64. mlb004

Yes starts 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. Ok that is what I thought. And one more question please.

65. ganeshie8

but actual fibonacci sequence starts from 0,1... but you should use what ur chart shows :)

66. ganeshie8

yea sure

67. mlb004

Using the same chart starting at 1,1 What is the ratio between 14th and 13th terms in the Fibonacci sequence? Round your answer to five decimal places.

68. ganeshie8

14th number : ? 13th number : ?

69. ganeshie8

377 233

70. mlb004

So you just subtract correct

71. ganeshie8

ratio between 14th and 13th terms = $$\large \frac{377}{233}$$

72. ganeshie8

ratio means division !

73. mlb004

1.6180258

74. ganeshie8

dont forget to round it to 5 decimal places

75. mlb004

Since it says round to 5 decimal places it would be 1.61803 is that correct?

76. ganeshie8

correct

77. mlb004

Oh I did it. Thank you so much for explaining that, that actually helped me with 3 problems.

78. ganeshie8

np :) btw this 1.61803 is called Golden ratio. it was used in Greek architectures like parthenon building and all... u may google "Golden ratio" if u have interest u wil get to know cool things