chaotic_butterflies
  • chaotic_butterflies
Please help - In Panama City in January, high tide was at midnight. The water level at high tide was 9 feet and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and that the height of the water can be modeled by a cosine curve, find an equation for water level in January for Panama City as a function of time (t). I don't know what the formula for a cosine curve is, nor am I aware of the meanings of each part. Multiple choice answers are below:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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chaotic_butterflies
  • chaotic_butterflies
1 Attachment
anonymous
  • anonymous
@SithsAndGiggles
anonymous
  • anonymous
@ybarrap

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chaotic_butterflies
  • chaotic_butterflies
You know they're not online right? @MLG360GABEN
anonymous
  • anonymous
ybarrap is
Afrodiddle
  • Afrodiddle
I wish that question had an oxford comma in it... I had to read one of the sentences like 5 times. lol
chaotic_butterflies
  • chaotic_butterflies
You have no idea how confusing all these questions are... virtual school goes nuts making up scenarios and barely spends any time on teaching the content >~<
ybarrap
  • ybarrap
You know that the peak is 9 feet and the low point is 1 foot. What is the most that cos (x) can be ? What is the smallest cos(x) can be? That is a huge hint. Answer this and we'll go forward.
ybarrap
  • ybarrap
?
ybarrap
  • ybarrap
|dw:1433619049716:dw|
chaotic_butterflies
  • chaotic_butterflies
Sorry I was afk
ybarrap
  • ybarrap
This means that maximum that 4 cos (x) can be is 4 and the smallest it can be is -4. This means that maximum that 5 cos (x) can be is 5 and the smallest it can be is -5. Next look at the offsets. Your options are either 5 or 4. This will tell you which 2 of the 4 options to eliminate. That the maximum of the cosine term and add to this offset and it should equal 9. Take the minimum of the cosine term and add to this offset and it should be 1.
ybarrap
  • ybarrap
|dw:1433619397690:dw|
imqwerty
  • imqwerty
The equation we want is h(t) = a*cos((2pi/P)*t) + b, where a is the amplitude of motion, P is the period and b is the vertical displacement. Now a = [(max. height) - (min. height)]/2 = (9 - 1)/2 = 4, and b = [(max. height) + (min. height)]/2 = (9 + 1) / 2 = 5. The period is given as P = 12 hours, so the equation is h(t) = 4*cos((2pi/12)*t) + 5 = 4*cos((pi/6)*t) + 5.
ybarrap
  • ybarrap
Once you figure out which of the two to eliminate, then figure out the current frequency: \(\pi/2\) or \(\pi/6\)
ybarrap
  • ybarrap
|dw:1433619618409:dw|
ybarrap
  • ybarrap
For \(\pi/6\), after 12 hours, you get back to your starting point. This will help eliminate one of the two remaining options.
imqwerty
  • imqwerty
@chaotic_butterflies did u got the answer??
chaotic_butterflies
  • chaotic_butterflies
I haven't taken it yet because I'm failing to understand the process - but I appreciated both @imqwerty and @ybarrap 's willingness to help.
ybarrap
  • ybarrap
Say you did not have he cosine term. You just had the constant. How much would you need to add to either 5 or 4 to each to get 9? This is what I'm saying. Take the last option $$ 4\cos \cfrac{\pi t}{6}+5 $$ What if you just had $$ 5 $$ What do you need to add to this to get 9?
chaotic_butterflies
  • chaotic_butterflies
well 4 of course
ybarrap
  • ybarrap
Ok. So if we had 4 that would be great because that would match the peak. Next, what do we need to add to $$ 5 $$ to get 1?
ybarrap
  • ybarrap
That's the low point
chaotic_butterflies
  • chaotic_butterflies
-4
chaotic_butterflies
  • chaotic_butterflies
I suppose it wouldn't work...
chaotic_butterflies
  • chaotic_butterflies
add 5
chaotic_butterflies
  • chaotic_butterflies
-3
chaotic_butterflies
  • chaotic_butterflies
But the minimum is -4
ybarrap
  • ybarrap
Back to the last option $$ 4\cos \cfrac{\pi t}{6} + 5 $$ We have the cosine term having a max of 4 and a min of -4. When we add the max to 5 we get 9 and when we add the min we get 1. That's exactly what we want. You agree?
ybarrap
  • ybarrap
|dw:1433620878420:dw|
ybarrap
  • ybarrap
|dw:1433620951827:dw|
chaotic_butterflies
  • chaotic_butterflies
I see it now
ybarrap
  • ybarrap
Great!
chaotic_butterflies
  • chaotic_butterflies
Sorry for not replying, someone came to my door.
chaotic_butterflies
  • chaotic_butterflies
Thank you so much!
ybarrap
  • ybarrap
you're welcome
chaotic_butterflies
  • chaotic_butterflies
Thank you @imqwerty too, I wish I could also give you a metal :c
imqwerty
  • imqwerty
:) its ok @chaotic_butterflies btw @ybarrap really deservs the medal ;)

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