PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
8th Edition
ISBN: 9781337904285
Author: Larson
Publisher: CENGAGE L
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Question
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Chapter 5.5, Problem 124E

(a)

To determine

To calculate: The angle θ that corresponds to a given Mach number.

(a)

Expert Solution
Check Mark

Answer to Problem 124E

The angle θ that corresponds to a given Mach number is 180° .

Explanation of Solution

Given information:

The following relation:

  sinθ2=1M

Where M correspond to Mach number and M=1

Calculation:

The angle θ that corresponds to the given Mach number is as follows:

  sinθ2=1M         [Given]sinθ2=11   [Substitute]sinθ2=1   [Simplify]θ2=arcsin(1)     [Inverse trigonometric function]θ2=90°  [Value of inverse]θ=180°  [Multiply both sides by 2]

(b)

To determine

To calculate: The angle θ that corresponds to a given Mach number.

(b)

Expert Solution
Check Mark

Answer to Problem 124E

The angle θ that corresponds to a given Mach number is 25.68° .

Explanation of Solution

Given information:

The following relation:

  sinθ2=1M

Where M correspond to Mach number and M=4.5

Calculation:

The angle θ that corresponds to the given Mach number is as follows:

  sinθ2=1M              [Given]sinθ2=14.5        [Substitute]θ2=arcsin(14.5)     [Inverse trigonometric function]θ2=12.84°         [Value of inverse]θ=25.68°         [Multiply both sides by 2]

(c)

To determine

To calculate: The speed of an object having the Mach numbers in part(a) and (b).

(c)

Expert Solution
Check Mark

Answer to Problem 124E

For M=1 , speed of object is 760 miles per hour .

For M=4.5 , speed of object is 3240 miles per hour .

Explanation of Solution

Given information:

The Mach number M of an airplane is the ratio of its speed to the speed of sound.

Speed of sound in air = 760 miles per hour .

The following relation:

  sinθ2=1M

Where M correspond to Mach number.

Calculation:

As given,

  M=VoVs

Where Vo is the speed of object and Vs is the speed of sound.

For M=1 , speed of object is calculated as:

  M=V0Vs                            [Given]1=V0760                             [Substitute]V0=760 miles per hour    [Simplify] 

For M=4.5 , speed of object is calculated as:

  M=V0Vs                               [Given]4.5=V0760                            [Substitute]V0=3420 miles per hour     [Simplify] 

(d)

To determine

To write: The given equation as a trigonometric function of θ .

(d)

Expert Solution
Check Mark

Answer to Problem 124E

The given equation as a trigonometric function of θ can be written as cosθ=1−2M2 .

Explanation of Solution

Given information:

The following relation:

  sinθ2=1M

Where M correspond to Mach number.

Formula used:

The following half angle formula:

  sinu2=±1−cosu2

Calculation:

The given trigonometric equation as a function of θ can be written as:

  sinθ2=1M                [Given]±1−cosθ2=1M      [Half angle formula]1−cosθ2= 1M2       [Square both sides]1−cosθ=2M2         [Multiply both sides by 2]cosθ=1−2M2         [Simplify]

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Chapter 5.5, Problem 123E
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Chapter 5.5, Problem 125E

Chapter 5 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.1 - Prob. 31ECh. 5.1 - Prob. 32ECh. 5.1 - Prob. 33ECh. 5.1 - Prob. 34ECh. 5.1 - Prob. 35ECh. 5.1 - Prob. 36ECh. 5.1 - Prob. 37ECh. 5.1 - Prob. 38ECh. 5.1 - Prob. 39ECh. 5.1 - Prob. 40ECh. 5.1 - Prob. 41ECh. 5.1 - Prob. 42ECh. 5.1 - Prob. 43ECh. 5.1 - Prob. 44ECh. 5.1 - Prob. 45ECh. 5.1 - Prob. 46ECh. 5.1 - Prob. 47ECh. 5.1 - Prob. 48ECh. 5.1 - Prob. 49ECh. 5.1 - Prob. 50ECh. 5.1 - Prob. 51ECh. 5.1 - Prob. 52ECh. 5.1 - Prob. 53ECh. 5.1 - Prob. 54ECh. 5.1 - Prob. 55ECh. 5.1 - Prob. 56ECh. 5.1 - Prob. 57ECh. 5.1 - Prob. 58ECh. 5.1 - Prob. 59ECh. 5.1 - Prob. 60ECh. 5.1 - Prob. 61ECh. 5.1 - Prob. 62ECh. 5.1 - Prob. 63ECh. 5.1 - 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Prob. 12CRCh. 5 - Prob. 13CRCh. 5 - Prob. 14CRCh. 5 - Prob. 15CRCh. 5 - Prob. 16CRCh. 5 - Prob. 17CRCh. 5 - Prob. 18CRCh. 5 - Prob. 19CRCh. 5 - Prob. 20CRCh. 5 - Prob. 21CRCh. 5 - Prob. 22CRCh. 5 - Prob. 23CRCh. 5 - Prob. 24CRCh. 5 - Prob. 25CRCh. 5 - Prob. 26CRCh. 5 - Prob. 27CRCh. 5 - Prob. 28CRCh. 5 - Prob. 29CRCh. 5 - Prob. 30CRCh. 5 - Prob. 31CRCh. 5 - Prob. 32CRCh. 5 - Prob. 33CRCh. 5 - Prob. 34CRCh. 5 - Prob. 35CRCh. 5 - Prob. 36CRCh. 5 - Prob. 37CRCh. 5 - Prob. 38CRCh. 5 - Prob. 39CRCh. 5 - Prob. 40CRCh. 5 - Prob. 41CRCh. 5 - Prob. 42CRCh. 5 - Prob. 43CRCh. 5 - Prob. 44CRCh. 5 - Prob. 45CRCh. 5 - Prob. 46CRCh. 5 - Prob. 47CRCh. 5 - Prob. 48CRCh. 5 - Prob. 49CRCh. 5 - Prob. 50CRCh. 5 - Prob. 51CRCh. 5 - Prob. 52CRCh. 5 - Prob. 53CRCh. 5 - Prob. 54CRCh. 5 - Prob. 55CRCh. 5 - Prob. 56CRCh. 5 - Prob. 57CRCh. 5 - Prob. 58CRCh. 5 - Prob. 59CRCh. 5 - Prob. 60CRCh. 5 - Prob. 61CRCh. 5 - Prob. 62CRCh. 5 - Prob. 63CRCh. 5 - Prob. 64CRCh. 5 - Prob. 65CRCh. 5 - Prob. 66CRCh. 5 - Prob. 67CRCh. 5 - Prob. 68CRCh. 5 - Prob. 69CRCh. 5 - Prob. 70CRCh. 5 - Prob. 71CRCh. 5 - Prob. 72CRCh. 5 - Prob. 73CRCh. 5 - Prob. 74CRCh. 5 - Prob. 75CRCh. 5 - Prob. 76CRCh. 5 - Prob. 77CRCh. 5 - Prob. 78CRCh. 5 - Prob. 79CRCh. 5 - Prob. 80CRCh. 5 - Prob. 81CRCh. 5 - Prob. 82CRCh. 5 - Prob. 83CRCh. 5 - Prob. 84CRCh. 5 - Prob. 85CRCh. 5 - Prob. 86CRCh. 5 - Prob. 87CRCh. 5 - Prob. 88CRCh. 5 - Prob. 89CRCh. 5 - Prob. 90CRCh. 5 - Prob. 91CRCh. 5 - Prob. 92CRCh. 5 - Prob. 93CRCh. 5 - Prob. 94CRCh. 5 - Prob. 95CRCh. 5 - Prob. 96CRCh. 5 - Prob. 97CRCh. 5 - Prob. 98CRCh. 5 - Prob. 99CRCh. 5 - Prob. 100CRCh. 5 - Prob. 101CRCh. 5 - Prob. 102CRCh. 5 - Prob. 103CRCh. 5 - Prob. 104CRCh. 5 - Prob. 105CRCh. 5 - Prob. 106CRCh. 5 - Prob. 107CRCh. 5 - Prob. 108CRCh. 5 - Prob. 109CRCh. 5 - Prob. 110CRCh. 5 - Prob. 111CRCh. 5 - Prob. 112CRCh. 5 - Prob. 113CRCh. 5 - Prob. 114CRCh. 5 - Prob. 115CRCh. 5 - Prob. 116CRCh. 5 - Prob. 117CRCh. 5 - Prob. 118CRCh. 5 - Prob. 119CRCh. 5 - Prob. 120CRCh. 5 - Prob. 121CRCh. 5 - Prob. 122CRCh. 5 - Prob. 123CRCh. 5 - Prob. 124CRCh. 5 - Prob. 125CRCh. 5 - Prob. 126CRCh. 5 - Prob. 127CRCh. 5 - Prob. 128CRCh. 5 - Prob. 129CRCh. 5 - Prob. 130CRCh. 5 - Prob. 131CRCh. 5 - Prob. 132CRCh. 5 - Prob. 1CTCh. 5 - Prob. 2CTCh. 5 - Prob. 3CTCh. 5 - Prob. 4CTCh. 5 - Prob. 5CTCh. 5 - Prob. 6CTCh. 5 - Prob. 7CTCh. 5 - Prob. 8CTCh. 5 - Prob. 9CTCh. 5 - Prob. 10CTCh. 5 - Prob. 11CTCh. 5 - Prob. 12CTCh. 5 - Prob. 13CTCh. 5 - Prob. 14CTCh. 5 - Prob. 15CTCh. 5 - Prob. 16CTCh. 5 - Prob. 17CTCh. 5 - Prob. 18CTCh. 5 - Prob. 19CTCh. 5 - Prob. 20CTCh. 5 - Prob. 21CTCh. 5 - Prob. 22CTCh. 5 - Prob. 23CTCh. 5 - Prob. 24CTCh. 5 - Prob. 25CT
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