Question

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

Answer 1

What exactly is the question?

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

I see them.

Answer 9

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

Answer 10

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

Answer 11

The amplitude is 20, the answer from B

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Or will this be for both a= and b=

Answer 17

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

Answer 18

so a will be -20 and b will be π/6

Answer 19

Does that make sense?

Answer 20

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?

Answer 21

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

Answer 22

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

Answer 23

ok

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

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

Answer 30

Yes

Answer 31

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

Answer 32

Is that what we want?

Answer 33

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

Answer 34

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

Answer 35

yes.

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

Just the top of the waves?

Answer 40

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

Answer 41

52 and 12 I believe

Answer 42

you're right

Answer 43

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

Answer 44

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

Answer 45

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

Answer 46

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

Answer 47

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.

Answer 48

will finding y give the water level?

Answer 49

correct!

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

right

Answer 54

3:45pm is 7 hours, right?

Answer 55

6.5 hrs

Answer 56

19.31?

Answer 57

yes

Answer 58

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.

Answer 59

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

Answer 60

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

Answer 61

copy your link here

Answer 62

http://www.wolframalpha.com/input/?i=y+%3D+-20+cos+%28%28%CF%80%2F6%29*9%29

Answer 63

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

Answer 64

0?

Answer 65

yep

Answer 66

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?

Answer 67

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

Answer 68

http://www.wolframalpha.com/input/?i=7+%3D+-20+cos+%28%28%CF%80%2F6%29*x%29?

Answer 69

8.5 hours?

Answer 70

or 7.5

Answer 71

http://www.wolframalpha.com/input/?i=7+%3D+-20+cos+%28%28%CF%80%2F6%29*x%29%2C+0%3Cx%3C12

Answer 72

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

Answer 73

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

Answer 74

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

Answer 75

the 12 hour period, yes

Answer 76

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

Answer 77

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?

Answer 78

ok. yes. massive brain fart

Answer 79

so is H a 12 hour period as well?

Answer 80

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

Answer 81

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

Answer 82

Do you see x = 8.32 and x = 3.68?

Answer 83

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

Answer 84

that equals 12?

Answer 85

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

Answer 86

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

Answer 87

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

Answer 88

got it!

Answer 89

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

Answer 90

20.115

Answer 91

not sure how to add .___ in time

Answer 92

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

Answer 93

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

Answer 94

I thought we were still on H

Answer 95

No this is still H

Answer 96

I was showing you how to add the times.

Answer 97

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

Answer 98

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