Holt Mcdougal Larson Algebra 2: Student Edition 2012
Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
Expert Solution & Answer
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Chapter 10.2, Problem 54PS
Solution

a.

To determine the ratio of population of rabbits to coyotes when t=0,6,12 and 18 months.

The ratio of population of rabbits to coyotes when t=0,6,12 and 18 months are RC=289,53,43 and103 respectively.

Given:

The given functions are:

  C=9000+3000sinπ12t

and

  R=20000+8000cosπ12t

where

  C= The population of coyotesR= The population of rabbitst= time in months

Calculation:

When t=0 , the population of coyotes is:

  C=9000+3000sinπ12tC=9000+3000sinπ120C=9000

Now when t=0 , the population of rabbits is:

  R=20000+8000cosπ12tR=20000+8000cosπ120R=20000+8000×1R=28000

So, the ratio of population of rabbits to coyotes is:

  RC=280009000RC=289

Next when t=6 , the population of coyotes is:

  C=9000+3000sinπ126C=9000+3000sinπ2C=9000+3000×1C=12000

And when t=6 , the population of rabbits is:

  R=20000+8000cosπ126R=20000+8000cosπ2R=20000+8000×0R=20000

So, the ratio of population of rabbits to coyotes is:

  RC=2000012000RC=53

Next when t=12 , the population of coyotes is:

  C=9000+3000sinπ1212C=9000+3000sinπC=9000+3000×0C=9000

And when t=12 , the population of rabbits is:

  R=20000+8000cosπ1212R=20000+8000cosπR=20000−8000R=12000

So, the ratio of population of rabbits to coyotes is:

  RC=120009000RC=43

Next when t=18 , population of coyotes is:

  C=9000+3000sinπ1218C=9000+3000sin3π2C=9000−3000C=6000

And when t=18 , the population of rabbits is:

  R=20000+8000cosπ1218R=20000+8000cos3π2R=20000+8000×0R=20000

So, the ratio of population of rabbits to coyotes is:

  RC=200006000RC=103

b.

To draw the graph for both functions in the same coordinate plane.

Given:

The given functions are:

  C=9000+3000sinπ12t

and

  R=20000+8000cosπ12t

where

  C= The population of coyotesR= The population of rabbitst= time in months

Graph:

The graph for both functions is shown below:

  Holt Mcdougal Larson Algebra 2: Student Edition 2012, Chapter 10.2, Problem 54PS

c.

To explain how the changes in the two populations appear to be related.

Interpretation:

From the graph, the population of the rabbits are always higher than the population of coyotes. The variations in the populations of rabbits and coyotes are oscillatory. Although the population of rabbits undergo a higher amplitude oscillation, i.e. the population of rabbits increases by a higher number and then decreases by a higher number compared to the population of coyotes. Also, the variations in the population of rabbits is ahead of the population of coyotes by a phase difference of π2 or a time difference of 6 months.

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Chapter 10.2, Problem 53PS
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Chapter 10.2, Problem 55PS

Chapter 10 Solutions

Holt Mcdougal Larson Algebra 2: Student Edition 2012

Ch. 10.1 - Prob. 1GPCh. 10.1 - Prob. 2GPCh. 10.1 - Prob. 3GPCh. 10.1 - Prob. 4GPCh. 10.1 - Prob. 5GPCh. 10.1 - Prob. 6GPCh. 10.1 - Prob. 7GPCh. 10.1 - Prob. 8GPCh. 10.1 - Prob. 9GPCh. 10.1 - Prob. 10GP
Ch. 10.1 - Prob. 11GPCh. 10.1 - Prob. 12GPCh. 10.1 - Prob. 13GPCh. 10.1 - Prob. 1ECh. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Prob. 4ECh. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29PSCh. 10.1 - Prob. 30PSCh. 10.1 - Prob. 31PSCh. 10.1 - Prob. 32PSCh. 10.1 - Prob. 33PSCh. 10.2 - Prob. 1GPCh. 10.2 - Prob. 2GPCh. 10.2 - Prob. 3GPCh. 10.2 - Prob. 4GPCh. 10.2 - Prob. 5GPCh. 10.2 - Prob. 6GPCh. 10.2 - Prob. 7GPCh. 10.2 - Prob. 1ECh. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Prob. 10ECh. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Prob. 14ECh. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Prob. 19ECh. 10.2 - Prob. 20ECh. 10.2 - Prob. 21ECh. 10.2 - Prob. 22ECh. 10.2 - Prob. 23ECh. 10.2 - Prob. 24ECh. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Prob. 41ECh. 10.2 - Prob. 42ECh. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Prob. 47ECh. 10.2 - Prob. 48ECh. 10.2 - Prob. 49ECh. 10.2 - Prob. 50PSCh. 10.2 - Prob. 51PSCh. 10.2 - Prob. 52PSCh. 10.2 - Prob. 53PSCh. 10.2 - Prob. 54PSCh. 10.2 - Prob. 55PSCh. 10.2 - Prob. 1QCh. 10.2 - Prob. 2QCh. 10.2 - Prob. 3QCh. 10.2 - Prob. 4QCh. 10.2 - Prob. 5QCh. 10.2 - Prob. 6QCh. 10.2 - Prob. 7QCh. 10.2 - Prob. 8QCh. 10.2 - Prob. 9QCh. 10.2 - Prob. 10QCh. 10.2 - Prob. 11QCh. 10.2 - Prob. 12QCh. 10.2 - Prob. 13QCh. 10.2 - Prob. 1DCCh. 10.2 - Prob. 2DCCh. 10.2 - Prob. 3DCCh. 10.2 - Prob. 4DCCh. 10.2 - Prob. 5DCCh. 10.2 - Prob. 6DCCh. 10.2 - Prob. 7DCCh. 10.2 - Prob. 8DCCh. 10.2 - Prob. 9DCCh. 10.2 - Prob. 10DCCh. 10.3 - Prob. 1GPCh. 10.3 - Prob. 2GPCh. 10.3 - Prob. 3GPCh. 10.3 - Prob. 4GPCh. 10.3 - Prob. 5GPCh. 10.3 - Prob. 6GPCh. 10.3 - Prob. 7GPCh. 10.3 - Prob. 8GPCh. 10.3 - Prob. 9GPCh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Prob. 3ECh. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - Prob. 8ECh. 10.3 - Prob. 9ECh. 10.3 - Prob. 10ECh. 10.3 - Prob. 11ECh. 10.3 - Prob. 12ECh. 10.3 - Prob. 13ECh. 10.3 - Prob. 14ECh. 10.3 - Prob. 15ECh. 10.3 - Prob. 16ECh. 10.3 - Prob. 17ECh. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Prob. 21ECh. 10.3 - Prob. 22ECh. 10.3 - Prob. 23ECh. 10.3 - Prob. 24ECh. 10.3 - Prob. 25ECh. 10.3 - Prob. 26ECh. 10.3 - Prob. 27ECh. 10.3 - Prob. 28ECh. 10.3 - Prob. 29ECh. 10.3 - Prob. 30ECh. 10.3 - Prob. 31ECh. 10.3 - Prob. 32ECh. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - Prob. 35ECh. 10.3 - Prob. 36ECh. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39PSCh. 10.3 - Prob. 40PSCh. 10.3 - Prob. 41PSCh. 10.3 - Prob. 42PSCh. 10.3 - Prob. 43PSCh. 10.3 - Prob. 44PSCh. 10.3 - Prob. 45PSCh. 10.4 - Prob. 1GPCh. 10.4 - Prob. 2GPCh. 10.4 - Prob. 3GPCh. 10.4 - Prob. 4GPCh. 10.4 - Prob. 5GPCh. 10.4 - Prob. 6GPCh. 10.4 - Prob. 7GPCh. 10.4 - Prob. 1ECh. 10.4 - Prob. 2ECh. 10.4 - Prob. 3ECh. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Prob. 9ECh. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - Prob. 12ECh. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Prob. 20ECh. 10.4 - Prob. 21ECh. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Prob. 34ECh. 10.4 - Prob. 35ECh. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41PSCh. 10.4 - Prob. 42PSCh. 10.4 - Prob. 43PSCh. 10.4 - Prob. 44PSCh. 10.4 - Prob. 45PSCh. 10.4 - Prob. 1PCh. 10.4 - Prob. 2PCh. 10.4 - Prob. 3PCh. 10.4 - Prob. 4PCh. 10.4 - Prob. 5PCh. 10.4 - Prob. 6PCh. 10.4 - Prob. 7PCh. 10.4 - Prob. 8PCh. 10.4 - Prob. 9PCh. 10.4 - Prob. 1MRPSCh. 10.4 - Prob. 2MRPSCh. 10.4 - Prob. 3MRPSCh. 10.4 - Prob. 4MRPSCh. 10.4 - Prob. 5MRPSCh. 10.4 - Prob. 6MRPSCh. 10.4 - Prob. 7MRPSCh. 10.5 - Prob. 1GPCh. 10.5 - Prob. 2GPCh. 10.5 - Prob. 3GPCh. 10.5 - Prob. 4GPCh. 10.5 - Prob. 1ECh. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - Prob. 9ECh. 10.5 - Prob. 10ECh. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 - Prob. 21ECh. 10.5 - Prob. 22ECh. 10.5 - Prob. 23PSCh. 10.5 - Prob. 24PSCh. 10.5 - Prob. 25PSCh. 10.5 - Prob. 26PSCh. 10.5 - Prob. 27PSCh. 10.5 - Prob. 28PSCh. 10.5 - Prob. 29PSCh. 10.5 - Prob. 1QCh. 10.5 - Prob. 2QCh. 10.5 - Prob. 3QCh. 10.5 - Prob. 4QCh. 10.5 - Prob. 5QCh. 10.5 - Prob. 6QCh. 10.5 - Prob. 7QCh. 10.5 - Prob. 8QCh. 10.5 - Prob. 9QCh. 10.5 - Prob. 10QCh. 10.5 - Prob. 11QCh. 10.5 - Prob. 12QCh. 10.5 - Prob. 3DCCh. 10.5 - Prob. 4DCCh. 10.6 - Prob. 1GPCh. 10.6 - Prob. 2GPCh. 10.6 - Prob. 3GPCh. 10.6 - Prob. 4GPCh. 10.6 - Prob. 5GPCh. 10.6 - Prob. 6GPCh. 10.6 - Prob. 7GPCh. 10.6 - Prob. 8GPCh. 10.6 - Prob. 9GPCh. 10.6 - Prob. 1ECh. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Prob. 4ECh. 10.6 - Prob. 5ECh. 10.6 - Prob. 6ECh. 10.6 - Prob. 7ECh. 10.6 - Prob. 8ECh. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - Prob. 11ECh. 10.6 - Prob. 12ECh. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - Prob. 16ECh. 10.6 - Prob. 17ECh. 10.6 - Prob. 18ECh. 10.6 - Prob. 19ECh. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - Prob. 23ECh. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - Prob. 37ECh. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - Prob. 40PSCh. 10.6 - Prob. 41PSCh. 10.6 - Prob. 42PSCh. 10.6 - Prob. 43PSCh. 10.6 - Prob. 44PSCh. 10.6 - Prob. 45PSCh. 10.7 - Prob. 1GPCh. 10.7 - Prob. 2GPCh. 10.7 - Prob. 3GPCh. 10.7 - Prob. 4GPCh. 10.7 - Prob. 5GPCh. 10.7 - Prob. 6GPCh. 10.7 - Prob. 7GPCh. 10.7 - Prob. 8GPCh. 10.7 - Prob. 9GPCh. 10.7 - Prob. 10GPCh. 10.7 - Prob. 11GPCh. 10.7 - Prob. 12GPCh. 10.7 - Prob. 13GPCh. 10.7 - Prob. 14GPCh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Prob. 7ECh. 10.7 - Prob. 8ECh. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Prob. 11ECh. 10.7 - Prob. 12ECh. 10.7 - Prob. 13ECh. 10.7 - Prob. 14ECh. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10.7 - Prob. 17ECh. 10.7 - Prob. 18ECh. 10.7 - Prob. 19ECh. 10.7 - Prob. 20ECh. 10.7 - Prob. 21ECh. 10.7 - Prob. 22ECh. 10.7 - Prob. 23ECh. 10.7 - Prob. 24ECh. 10.7 - Prob. 25ECh. 10.7 - Prob. 26ECh. 10.7 - Prob. 27ECh. 10.7 - Prob. 28ECh. 10.7 - Prob. 29ECh. 10.7 - Prob. 30ECh. 10.7 - Prob. 31ECh. 10.7 - Prob. 32ECh. 10.7 - Prob. 33ECh. 10.7 - Prob. 34ECh. 10.7 - Prob. 35ECh. 10.7 - Prob. 36ECh. 10.7 - Prob. 37ECh. 10.7 - Prob. 38ECh. 10.7 - Prob. 39ECh. 10.7 - Prob. 40ECh. 10.7 - Prob. 41ECh. 10.7 - Prob. 42ECh. 10.7 - Prob. 43ECh. 10.7 - Prob. 44ECh. 10.7 - Prob. 45ECh. 10.7 - Prob. 46ECh. 10.7 - Prob. 47ECh. 10.7 - Prob. 48ECh. 10.7 - Prob. 49ECh. 10.7 - Prob. 50PSCh. 10.7 - Prob. 51PSCh. 10.7 - Prob. 52PSCh. 10.7 - Prob. 53PSCh. 10.7 - Prob. 54PSCh. 10.7 - Prob. 55PSCh. 10.7 - Prob. 56PSCh. 10.7 - Prob. 1QCh. 10.7 - Prob. 2QCh. 10.7 - Prob. 3QCh. 10.7 - Prob. 4QCh. 10.7 - Prob. 5QCh. 10.7 - Prob. 6QCh. 10.7 - Prob. 7QCh. 10.7 - Prob. 8QCh. 10.7 - Prob. 9QCh. 10.7 - Prob. 1MRPSCh. 10.7 - Prob. 2MRPSCh. 10.7 - Prob. 3MRPSCh. 10.7 - Prob. 4MRPSCh. 10.7 - Prob. 5MRPSCh. 10 - Prob. 1VECh. 10 - Prob. 2VECh. 10 - Prob. 3VECh. 10 - Prob. 4VECh. 10 - Prob. 5VECh. 10 - Prob. 6REAECh. 10 - Prob. 7REAECh. 10 - Prob. 8REAECh. 10 - Prob. 9REAECh. 10 - Prob. 10REAECh. 10 - Prob. 11REAECh. 10 - Prob. 12REAECh. 10 - Prob. 13REAECh. 10 - Prob. 14REAECh. 10 - Prob. 15REAECh. 10 - Prob. 16REAECh. 10 - Prob. 17REAECh. 10 - Prob. 18REAECh. 10 - Prob. 19REAECh. 10 - Prob. 20REAECh. 10 - Prob. 21REAECh. 10 - Prob. 22REAECh. 10 - Prob. 23REAECh. 10 - Prob. 24REAECh. 10 - Prob. 25REAECh. 10 - Prob. 26REAECh. 10 - Prob. 27REAECh. 10 - Prob. 28REAECh. 10 - Prob. 29REAECh. 10 - Prob. 30REAECh. 10 - Prob. 31REAECh. 10 - Prob. 32REAECh. 10 - Prob. 33REAECh. 10 - Prob. 34REAECh. 10 - Prob. 35REAECh. 10 - Prob. 1TCh. 10 - Prob. 2TCh. 10 - Prob. 3TCh. 10 - Prob. 4TCh. 10 - Prob. 5TCh. 10 - Prob. 6TCh. 10 - Prob. 7TCh. 10 - Prob. 8TCh. 10 - Prob. 9TCh. 10 - Prob. 10TCh. 10 - Prob. 11TCh. 10 - Prob. 12TCh. 10 - Prob. 13TCh. 10 - Prob. 14TCh. 10 - Prob. 15TCh. 10 - Prob. 16TCh. 10 - Prob. 17TCh. 10 - Prob. 18TCh. 10 - Prob. 19TCh. 10 - Prob. 20TCh. 10 - Prob. 21TCh. 10 - Prob. 22TCh. 10 - Prob. 23TCh. 10 - Prob. 24TCh. 10 - Prob. 1PCh. 10 - Prob. 1TPCh. 10 - Prob. 2TPCh. 10 - Prob. 3TPCh. 10 - Prob. 4TPCh. 10 - Prob. 5TPCh. 10 - Prob. 6TPCh. 10 - Prob. 7TPCh. 10 - Prob. 8TPCh. 10 - Prob. 9TPCh. 10 - Prob. 10TPCh. 10 - Prob. 11TPCh. 10 - Prob. 12TPCh. 10 - Prob. 13TP
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