Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Question
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Chapter 9.6, Problem 31E

a.

To determine

To find: A sinusoidal model for the tide depth d (in feet) as a function of time t (in hours).

a.

Expert Solution
Check Mark

Answer to Problem 31E

  y=6.5cos(π6t)+10 where t=0 represents midnight.

Explanation of Solution

Given information:

The low tide occurs at midnight and is at 3.5 feet. After 6 hours high tide occurs which is at 16.5 feet.

Calculation:

As per the given information −

The low tide occurs at midnight and is at 3.5 feet. After 6 hours high tide occurs which is at 16.5 feet.

Step 1: Find the maximum and minimum value.

Here, maximum value is 16.5 and minimum value is 3.5 .

Step 2: Identify the vertical shift k .

The value of k is the mean of maximum and minimum value, i.e.

  k=16.5+3.52=10

Step 3: Find the amplitude and period.

Function goes from minimum to maximum in 6 hours and then again maximum to minimum in next 6 hours. So, period would be 12 hours.

  i.e12=2πbb=π6

Also at t=0 , function would be at its minimum value. So, cosine function reflected across x axis can be taken as model.

  |a|=Maximum valueMinimum value2=16.53.52=6.5Since graph is a reflection, a>0a=6.5

Step 5 : The function graph would be given as −

  y=6.5cos(π6t)+10

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 31E , additional homework tip  1

Hence, desired model function is y=6.5cos(π6t)+10 where t=0 represents midnight.

b.

To determine

To find: All the time when low and high tide occurs in 24 hour period.

b.

Expert Solution
Check Mark

Answer to Problem 31E

Low tide occurs at midnight, 12 noon and again at midnight.

Similarly, high tide occurs at 6 AM, 6 PM.

Explanation of Solution

Given information:

Same as part a of this exercise.

Calculation:

From part a of this exercise the model function would be given as −

  y=6.5cos(π6t)+10 where t=0 represents midnight.

Below is the function graph for a 24 hour period.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 31E , additional homework tip  2

From above graph it can be observed that low tide occurs at midnight, 12 noon and again at midnight.

Similarly, high tide occurs at 6 AM, 6 PM.

c.

To determine

To find: The relationship between graph from part b and graph of tide depth t hours after 3:00 AM.

c.

Expert Solution
Check Mark

Explanation of Solution

Given information:

Same as part a of this exercise.

Calculation:

From part a of this exercise the model function would be given as −

  y=6.5cos(π6t)+10 where t=0 represents midnight.

Below is the function graph for a 24 hour period.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 31E , additional homework tip  3

When t=0 is at 3:00 AM. Tide depth is halfway through maximum. So, a sine function can be modeled.

  y=6.5sin(π6t)+10 where t=0 represents 3:00 AM.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 9.6, Problem 31E , additional homework tip  4

Chapter 9 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Prob. 58ECh. 9.1 - Prob. 59ECh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - 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