Asked by steve
The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 am. High tide occurs at 3:30 pm. What is a cosine function that models the variation in inches above and below the water level as a function of time and hours since 9:15 am?
My answer ism 20cos(x-3.5)+32
My answer ism 20cos(x-3.5)+32
Answers
Answered by
Reiny
Your amplitude and vertical shift are ok
but your period is not taken care of
period:
time between 9:15 am and 3:30 pm
= 6:15 = 6.25 hrs
so the period is 12.5 hrs
2π/k = 12.5
k = 2π/12.5 = 4π/25
height = 20 cos ( (4π/25)(x + d) ) + 32
we want 3:15 am ---> x = 0
12 = 20cos( 4π/25 d) + 32
-1 = cos( 4π/25 d)
I know cos π = -1
so 4π/25 d = π
d = 25/4 =6.25
I get
height = 20 cos ( (4π/25)(x + 6.25) ) + 32
check:
when t=0 ,
height = 20cos( (4π/25)(6.25)) + 32
= 20cos π + 32 = -20+32 = 12 , good!
when t= 6.25
height = 20 cos( (4π/25)(6.25+6.25)) + 32
= 20 cos 2π + 32 = 20+32 = 52, good!
but your period is not taken care of
period:
time between 9:15 am and 3:30 pm
= 6:15 = 6.25 hrs
so the period is 12.5 hrs
2π/k = 12.5
k = 2π/12.5 = 4π/25
height = 20 cos ( (4π/25)(x + d) ) + 32
we want 3:15 am ---> x = 0
12 = 20cos( 4π/25 d) + 32
-1 = cos( 4π/25 d)
I know cos π = -1
so 4π/25 d = π
d = 25/4 =6.25
I get
height = 20 cos ( (4π/25)(x + 6.25) ) + 32
check:
when t=0 ,
height = 20cos( (4π/25)(6.25)) + 32
= 20cos π + 32 = -20+32 = 12 , good!
when t= 6.25
height = 20 cos( (4π/25)(6.25+6.25)) + 32
= 20 cos 2π + 32 = 20+32 = 52, good!
Answered by
steve
Thank you
Answered by
Jacob
My dogs laying on my bed
Answered by
Daniel J. D'arby
Nice dog, what breed?
Answered by
Trying to understand
How did you get 4pi/25? Is it multiplying by 2? Besides, Is your answer 100% correct?
Answered by
Welp
Dog is more important
Answered by
bruh
more details about the dog, please.
Answered by
jacob's dog
bark