1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elina [12.6K]
3 years ago
12

The tides around Cherokee Bay range between a low of 1 foot to a high of 5 feet. The tide is at its lowest point when time, t, i

s 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon?

Mathematics
1 answer:
Eddi Din [679]3 years ago
6 0
Given:
Low tide height = 1 ft
High tide height = 5 ft
Tide period, T = 24  houts

Let the height of the tide be modeled by the expression
h(t) = K + A cos(bt)
Because the period is 24, therefore
b = (2π)/24 = π/12

That is,
h(t) = K + Acos[(πt)/12]

When r=0, h = 1, therefore
K + A cos(0) = 1, ot
 K + A = 1             (1)
When t = 12 (half cycle), h = 5, therefore
K + A cos(π) = 5, or
K - A = 5             (2)

Add (1) and (2):
2K = 6
K = 3
From(1), obtain
A = 1 - 3 = - 2

Answer:
The required function is h(t) = 3  - 2 cos[(πt)/12]
The amplitude is 2 feet
The period is 24 hours
The midline of the function is h = 3 feet
A graph of the function is shown below.

You might be interested in
The point (- square-root 2/2, square-root2/2 is the point at which the terminal ray of angle theta intersects the unit circle. W
Rufina [12.5K]

Answer: The value of cosine is \frac{-\sqrt{2}} {2} and the value of cotangent is -1.

Explanation:

The given point is (\frac{-\sqrt{2}} {2}},\frac{\sqrt{2}} {2}).

Since the x coordinate is negative and y coordinate is positive so the point must be lies in second quadrant.

The distance of the point from the origin is,

r=\sqrt{(\frac{-\sqrt{2}} {2}-0)^2+(\frac{\sqrt{2}} {2}-0)^2}

r=\sqrt{ \frac{2}{4}+\frac{2}{4}}

r=1

The given point is in the form of (a,b). So we get,

a=\frac{-\sqrt{2}} {2}

b=\frac{\sqrt{2}} {2}

The formula for cosine,

\cos \theta =\frac{a}{r}

\cos \theta =\frac{\frac{-\sqrt{2}} {2}}{1}}

\cos \theta =\frac{-\sqrt{2}} {2}}

The formula for cotangent,

\cot \theta =\frac{a}{b}

\cos \theta=\frac{\frac{-\sqrt{2}} {2}}{\frac{\sqrt{2}} {2}}

\cos \theta=-1

Therefore, the value of cosine is \frac{-\sqrt{2}} {2} and the value of cotangent is -1.

7 0
3 years ago
Read 2 more answers
What is the product of 28×32
yKpoI14uk [10]
28×32 = 896 you just multiply them together

7 0
3 years ago
Read 2 more answers
Using y=-16x²+100x what is the highest point of the golf ball​
Westkost [7]

Answer:

156.25

Step-by-step explanation:

5 0
3 years ago
Let U1, U2, and U3
lukranit [14]

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

3 0
3 years ago
Can someone please help me this i will mark u as BRAINLIEST ANSWER ​
VLD [36.1K]

Answer:

12,21

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • Carlo works as a waiter. he works double shifts 6 days a week. the lunch shift is 3 hours and the dinner shift is 5 hours. find
    6·1 answer
  • F(x)=4x^2+1 and g(x)=x^2-5 fins (f+g)(x)
    8·2 answers
  • What is sin45 degrees divided by 20
    12·2 answers
  • Need help on 4,5 pleasesss
    9·1 answer
  • 5.
    14·1 answer
  • A or D im not sure if the variable should be negative.​
    9·2 answers
  • Consider two competing firms in a declining industry that cannot support both firms profitably. Each firm has three possible cho
    9·1 answer
  • Write the relation as a set of ordered pairs.
    15·1 answer
  • Solve the equation, Write one solution, No solution, Infinitely Many Solution
    15·2 answers
  • Kyla has the number of cherries that Denise has. If Kyla has 46 cherries, how many cherries do they have altogether?​
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!