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
    
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