Question

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

Answer 1

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!

Answer 2

Thank you

Answer 3

My dogs laying on my bed

Answer 4

Nice dog, what breed?

Answer 5

How did you get 4pi/25? Is it multiplying by 2? Besides, Is your answer 100% correct?

Answer 6

Dog is more important

Answer 7

more details about the dog, please.

Answer 8

bark