## anonymous one year ago Currently have the first 3 answers here to start us off, not sure where to go from here, please help! (problems: http://imgur.com/Eo8fZIR,mJ2vS04,3ys9vme,xyjbOve ) here's what i've got: * A=40 * B=20 * C=12 hour period

1. anonymous

What exactly is the question?

2. anonymous

There's multiple questions, would you like me to type them out for you? I don't mind.

3. anonymous

Are there more than the 3 in the link? Or are you just asking if those answers are correct?

4. anonymous

There are more than 3, I have the first 3 which I listed and I need assistance with the rest, I believe the answers for the first 3 that I got are vital to answering the rest.

5. anonymous

There are 5 more questions, 2 bonus questions but i'm not too worried about them.

6. anonymous

ok. I didn't see the links to the other questions before

7. anonymous

Oh it's alright, you've got it or do I need to type them?

8. anonymous

I see them.

9. anonymous

For part d, a is the amplitude and b is 2π divided by the period The y = cos x parent function has a maximum on the y-axis. Your function has the minimum there, so make "a" negative

10. anonymous

so for A, the amplitude was either 40 or 20 from the previous questions, correct?

11. anonymous

The amplitude is 20, the answer from B

12. anonymous

I didn't have my work pulled up sorry about that, so it's y=20 cos 2pi x?

13. anonymous

Wait! I read you wrong, a=20 and b=2pi/the period?

14. anonymous

close. you need to divide 2π by the period of 12 and make the amplitude negative to account for the reflection $y=-20\cos \frac{ 2\pi }{ 12 }x$

15. anonymous

Am I going to need to get this down to one number for the answer to "a=" or will it be an equation?

16. anonymous

Or will this be for both a= and b=

17. anonymous

oh you're right. They are asking for a and b separately

18. anonymous

so a will be -20 and b will be π/6

19. anonymous

Does that make sense?

20. anonymous

That does, I was wondering when the negative 20 would come in as I looked around online and saw that it would turn out like that, now the next question is to "sketch" and label a graph, Seeing as we can't really do that here, what would I put into my graphing calculator to figure this out?

21. anonymous

Not sure if the draw option is any use, im new here

22. anonymous

We could use this: https://www.desmos.com/calculator

23. anonymous

ok

24. anonymous

so you want to enter the equation we found above. and set your window to show 1 period at least

25. anonymous

so your horizontal axis should be from 0 to 12. and vertical from -20 to 20

26. anonymous

y=-20 cos 2pi/12x is the equation I want to put in?

27. anonymous

Reduce the 2π/12 to π/6 and use parentheses to avoid ambiguity y=-20 cos (pi/6)x

28. anonymous

Hold up, put everything after cos in (). y=-20 cos ((pi/6)x)

29. anonymous

Have this so far, should I fix it with the ()'s? http://imgur.com/ptftpkN

30. anonymous

Yes

31. anonymous

If I add the extra parenthesis it makes two lines, like this: http://imgur.com/KM6VOZB

32. anonymous

Is that what we want?

33. anonymous

yes. If you zoom out you'll see the waves

34. anonymous

Yes! alright so that's all that was? we're done graphing?

35. anonymous

yes.

36. anonymous

Mind sticking around and helping with the rest? I'll give you medals or whatever the currency on here is.

37. anonymous

oh yeah. I just meant we were done with that question

38. anonymous

Alright so F, how do we find the average water levels?

39. anonymous

Just the top of the waves?

40. anonymous

It's the average of the maximum and minimum, which I think was 32 and 12. I need to go back to the beginning to check

41. anonymous

52 and 12 I believe

42. anonymous

you're right

43. anonymous

So what can we do with those to find the average? Divide?

44. anonymous

Add them and then divide (52+12)/2 = 22

45. anonymous

Crazy how complicated they make it sound and then it's that easy! This next one may be a bit of a challenge

46. anonymous

I have the graph on hand, how do I determine where the times are?

47. anonymous

That's where the first column comes in. 11:15 is 2 hours after 9:15, so you want to find y when x = 2.

48. anonymous

will finding y give the water level?

49. anonymous

correct!

50. anonymous

not sure how to find it with just x, walk me through it?

51. anonymous

yes. It might actually be easier to do this on a calculator than to use the graph. For the first one, plug in 2 for x. y = -20 cos ((π/6)*2) http://www.wolframalpha.com/input/?i=-20+cos+%28%28%CF%80%2F6%29*x%29+at+x+%3D+2

52. anonymous

so for each one we just plug in the hours and we get the level, for this it's -10?

53. anonymous

right

54. anonymous

3:45pm is 7 hours, right?

55. anonymous

6.5 hrs

56. anonymous

19.31?

57. anonymous

yes

58. anonymous

and then 6:15 is 9 hours? I'm in high school I should really be able to tell time at this point but it's hard without a clock to look at.

59. anonymous

lol. It is 9. I'm just as pathetic. I have to count it on my fingers

60. anonymous

wolfram just gave me the answer as "true", that cant be right

61. anonymous

62. anonymous
63. anonymous

Just take out the y= so it will evaluate the expression

64. anonymous

0?

65. anonymous

yep

66. anonymous

for the next one it's looking like we're working backwards, it gives us the water level but not the time, how do we manage this?

67. anonymous

Use 7 for y and solve for x. 7 = -20 cos ((π/6)*x)

68. anonymous
69. anonymous

8.5 hours?

70. anonymous

or 7.5

71. anonymous
72. anonymous

sorry about that. You have to restrict the domain to just the period, or it will give all possilbe answers

73. anonymous

this is looking like jibberish to me, is it 12? i'm seeing 12 a lot in there

74. anonymous

hold up. can we go back to part c for a second?

75. anonymous

the 12 hour period, yes

76. anonymous

The period is actually 24. (9:15 to 3:15 is only half the period)

77. anonymous

9:15 to 3:15 is a six hour gap. so six hours from low to high plus 6 hours from high back to low is a 12 hour period, right?

78. anonymous

ok. yes. massive brain fart

79. anonymous

so is H a 12 hour period as well?

80. anonymous

yes, so there will be two solutions over the 12 hour period

81. anonymous

Ignore all the "alternate form" gibberish and scroll down to where it says "solutions" You may have to click on the "approximate form" box http://www.wolframalpha.com/input/?i=7+%3D+-20+cos+%28%28%CF%80%2F6%29*x%29%2C+0%3Cx%3C12

82. anonymous

Do you see x = 8.32 and x = 3.68?

83. anonymous

I see them now yep, what do they have to do with it?

84. anonymous

that equals 12?

85. anonymous

no, they are the x values where the water level is 7

86. anonymous

and they helped us determine that it's a 12 hour period in some way I guess?

87. anonymous

The other way around. The equation 7 = -20 cos ((π/6)*x) has infinitely many solutions. We used the 12 hour period to restrict the amount of solutions the equation would give us. That's why the 0<x<12 is in there

88. anonymous

got it!

89. anonymous

So to find the times for H, add 3.68 hrs and 8.32 hrs to 9:15.

90. anonymous

20.115

91. anonymous

not sure how to add .___ in time

92. anonymous

9:15 is 9.25 hours 9.25 hrs + 3.68 hrs = 12.93 hr (pm) convert 0.93 hrs to minutes by multiplying by 60 → 55.8 minutes First time 12:56 pm

93. anonymous

wait a minute are we still on H or have we moved onto the bonus questions? I'm getting lost in all these times here as I know 9am is involved in both

94. anonymous

I thought we were still on H

95. anonymous

No this is still H

96. anonymous

I was showing you how to add the times.

97. anonymous

The first time we got for H was 3.68 hours. We need to add that to 9:15 to get the time of day the question is asking for

98. anonymous

that makes much more sense, and when you did that you got 12.93, correct? should we round this?

99. anonymous

With 12.93, we have to convert the decimal part to minutes, because there's no 12:93 on a clock. That's why I multiplied 0.93 by 60 to get 55.8, and I rounded that to 56 minutes

100. anonymous

So it's only a 56 minute period?

101. anonymous

no

102. anonymous

12 hours 56 minutes

103. anonymous

12:56 is the time at which the water level is 7

104. anonymous

got it now, thanks for the description, it's okay if you dont want to do the bonus questions but if you're up for the challenge I am as well

105. anonymous

give me a sec.

106. anonymous

sure

107. anonymous

If the low tide repeats every 12 hours, there will be 3 in a 24 hour period, inclusive. |dw:1433136689393:dw|

108. anonymous

and 2 high tides

109. anonymous

and you can go off that same chart to get both? I'd think so since high and low are both on there

110. anonymous

yes you can

111. anonymous

Well I gave you best response which I guess gave medals, is there anything else I can give you? very thankful you stuck around to help

112. anonymous

No I think that's it :)