Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 2.4, Problem 31E
To determine

To find: the coordinates of the car located at the loading platform, and then find its location at Rot90,Rot180 and Rot270 .

Expert Solution & Answer
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Answer to Problem 31E

  (0,−125),(125,0),(0,125),(−125,0)

  Location at Rot90=[1250−1125−125    0−1−125]Location at Rot180=[0125−125    0    0−125125  0]Location at Rot270=[−125    0    0−125125  0 0125]

Explanation of Solution

Given information:

The diameter of wheel =250 ft

Axle length = 45 ft

Assume that axle is fitted at the origin of wheel.

  R180=[−100−1]

Calculation:

The radius of wheel can be evaluated as follows:

  Radius=Diameter2=2502 ft=125 ft

Since we have to assume that axle is fitted at the origin of wheel i.e. (0,0) , so the coordinates of the car located at the loading platform will be (0,−125),(125,0),(0,125),(−125,0) .

Now use the x and y coordinates to write the rows of the vertex matrix as follows:

  Vertex matrix=[   0−125125  0  0125−125    0]

Multiply the vertex matrix by each rotation matrix as follows:

  (R90)⋅(Vertex matrix)=[01−1 0]⋅[   0−125125  0  0125−125    0]=[1250−1125−125    0−1−125]

  (R180)⋅(Vertex matrix)=[−100−1]⋅[   0−125125  0  0125−125    0]=[0125−125    0    0−125125  0]

  (R270)⋅(Vertex matrix)=[0−110]⋅[   0−125125  0  0125−125    0]=[−125    0    0−125125  0 0125]

Thus, the location of the car at Rot90,Rot180 and Rot270 is as follows:

  Location at Rot90=[1250−1125−125    0−1−125]Location at Rot180=[0125−125    0    0−125125  0]Location at Rot270=[−125    0    0−125125  0 0125]

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Chapter 2.4, Problem 30E
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Chapter 2.4, Problem 32E

Chapter 2 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 2.1 - Prob. 1CFUCh. 2.1 - Prob. 2CFUCh. 2.1 - Prob. 3CFUCh. 2.1 - Prob. 4CFUCh. 2.1 - Prob. 5CFUCh. 2.1 - Prob. 6CFUCh. 2.1 - Prob. 7CFUCh. 2.1 - Prob. 8CFUCh. 2.1 - Prob. 9CFUCh. 2.1 - Prob. 10CFU
Ch. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.2 - Prob. 1CFUCh. 2.2 - Prob. 2CFUCh. 2.2 - Prob. 3CFUCh. 2.2 - Prob. 4CFUCh. 2.2 - Prob. 5CFUCh. 2.2 - Prob. 6CFUCh. 2.2 - Prob. 7CFUCh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.3 - Prob. 1CFUCh. 2.3 - Prob. 2CFUCh. 2.3 - Prob. 3CFUCh. 2.3 - Prob. 4CFUCh. 2.3 - Prob. 5CFUCh. 2.3 - Prob. 6CFUCh. 2.3 - Prob. 7CFUCh. 2.3 - Prob. 8CFUCh. 2.3 - Prob. 9CFUCh. 2.3 - Prob. 10CFUCh. 2.3 - Prob. 11CFUCh. 2.3 - Prob. 12CFUCh. 2.3 - Prob. 13CFUCh. 2.3 - Prob. 14CFUCh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59ECh. 2.3 - Prob. 60ECh. 2.3 - Prob. 61ECh. 2.3 - Prob. 62ECh. 2.3 - Prob. 63ECh. 2.3 - Prob. 64ECh. 2.4A - Prob. 1GCECh. 2.4A - Prob. 2GCECh. 2.4A - Prob. 3GCECh. 2.4A - Prob. 4GCECh. 2.4A - Prob. 1MCQCh. 2.4A - Prob. 2MCQCh. 2.4A - Prob. 3MCQCh. 2.4A - Prob. 4MCQCh. 2.4A - Prob. 5MCQCh. 2.4A - Prob. 6MCQCh. 2.4A - Prob. 7MCQCh. 2.4A - Prob. 8MCQCh. 2.4A - Prob. 9MCQCh. 2.4A - Prob. 10MCQCh. 2.4 - Prob. 1CFUCh. 2.4 - Prob. 2CFUCh. 2.4 - Prob. 3CFUCh. 2.4 - Prob. 4CFUCh. 2.4 - Prob. 5CFUCh. 2.4 - Prob. 6CFUCh. 2.4 - Prob. 7CFUCh. 2.4 - Prob. 8CFUCh. 2.4 - Prob. 9CFUCh. 2.4 - Prob. 10CFUCh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.5 - Prob. 1CFUCh. 2.5 - Prob. 2CFUCh. 2.5 - Prob. 3CFUCh. 2.5 - Prob. 4CFUCh. 2.5 - Prob. 5CFUCh. 2.5 - Prob. 6CFUCh. 2.5 - Prob. 7CFUCh. 2.5 - Prob. 8CFUCh. 2.5 - Prob. 9CFUCh. 2.5 - Prob. 10CFUCh. 2.5 - Prob. 11CFUCh. 2.5 - Prob. 12CFUCh. 2.5 - Prob. 13CFUCh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - Prob. 49ECh. 2.5 - Prob. 50ECh. 2.5 - Prob. 51ECh. 2.5 - Prob. 52ECh. 2.5 - Prob. 53ECh. 2.5 - Prob. 54ECh. 2.5 - Prob. 55ECh. 2.5 - Prob. 56ECh. 2.5 - Prob. 57ECh. 2.5 - Prob. 58ECh. 2.5 - Prob. 59ECh. 2.5 - Prob. 60ECh. 2.5 - Prob. 61ECh. 2.5 - Prob. 62ECh. 2.5B - Prob. 1GCECh. 2.5B - Prob. 2GCECh. 2.5B - Prob. 3GCECh. 2.5B - Prob. 4GCECh. 2.5B - Prob. 5GCECh. 2.6 - Prob. 1CFUCh. 2.6 - Prob. 2CFUCh. 2.6 - Prob. 3CFUCh. 2.6 - Prob. 4CFUCh. 2.6 - Prob. 5CFUCh. 2.6 - Prob. 6CFUCh. 2.6 - Prob. 7CFUCh. 2.6 - Prob. 8CFUCh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.7 - Prob. 1CFUCh. 2.7 - Prob. 2CFUCh. 2.7 - Prob. 3CFUCh. 2.7 - Prob. 4CFUCh. 2.7 - Prob. 5CFUCh. 2.7 - Prob. 6CFUCh. 2.7 - Prob. 7CFUCh. 2.7 - Prob. 8CFUCh. 2.7 - Prob. 9ECh. 2.7 - Prob. 10ECh. 2.7 - Prob. 11ECh. 2.7 - Prob. 12ECh. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2 - Prob. 1SGACh. 2 - Prob. 2SGACh. 2 - Prob. 3SGACh. 2 - Prob. 4SGACh. 2 - Prob. 5SGACh. 2 - Prob. 6SGACh. 2 - Prob. 7SGACh. 2 - Prob. 8SGACh. 2 - Prob. 9SGACh. 2 - Prob. 10SGA

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