EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
Expert Solution & Answer
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Chapter 9.5, Problem 49PS
Solution

To find: The distance between the Earth and Mercury planet.

On that certain day the distance between the Earth and the Mercury is nearly 161 miles.

Given data:

The distance between the Sun and the Mercury is 37millionmiles and between the Sun and the Earth 93millionmiles . At a certain day angle between the Sun and the Mercury measured from the Earth is 22° .

Method/Formula used:

  EBK ALGEBRA 2, Chapter 9.5, Problem 49PS , additional homework tip  1

The ‘Law of Cosines’ states for a triangle ABC , Fig. 1:

  cosA=b2+c2a22bc

The solution of quadratic equation, x2bx+c=0 is

  x=b±b24c2 … (1)

Calculations:

The positions of the Sun, the Earth, and the Mercury with the triangle EMS is shown in Fig.2.

  EBK ALGEBRA 2, Chapter 9.5, Problem 49PS , additional homework tip  2

Here, the distance between the Sun and the Mercury ( SM ) is 37millionmiles and between the Sun and the Earth ( ES ) 93millionmiles . At a certain day angle between the Sun and the Mercury measured from the Earth is 22° .

Using ‘Law of Cosine’ in triangle EMS,

  cosE=EM2+ES2MS22EMES

Substitute, 22° for E , 37 for SM , and 93 for ES ,

  cos22°=EM2+9323722EM93cos22°=0.92720.9272=EM2+7280186EMEM2+7280=172.46EM0=EM2172.46EM+7280

Substitute x for EM , get quadratic equation

  x2172.46x+7280=0 ... (2)

  x=172.46±172.462472802=172.46±149.862=172.46+149.862172.46149.862161.36,11.3

The distance cannot be negative, therefore, on that certain day the distance between the Earth and the Mercury is nearly 161 miles.

Chapter 9 Solutions

EBK ALGEBRA 2

Ch. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - Prob. 5ECh. 9.1 - Prob. 6ECh. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Prob. 9ECh. 9.1 - Prob. 10ECh. 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. 30PSCh. 9.1 - Prob. 31PSCh. 9.1 - Prob. 32PSCh. 9.1 - Prob. 33PSCh. 9.1 - Prob. 34PSCh. 9.1 - Prob. 35PSCh. 9.1 - Prob. 36PSCh. 9.1 - Prob. 37PSCh. 9.2 - Prob. 1GPCh. 9.2 - Prob. 2GPCh. 9.2 - Prob. 3GPCh. 9.2 - Prob. 4GPCh. 9.2 - Prob. 5GPCh. 9.2 - Prob. 6GPCh. 9.2 - Prob. 7GPCh. 9.2 - Prob. 8GPCh. 9.2 - Prob. 9GPCh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48PSCh. 9.2 - Prob. 49PSCh. 9.2 - Prob. 50PSCh. 9.2 - Prob. 51PSCh. 9.2 - Prob. 52PSCh. 9.2 - Prob. 53PSCh. 9.2 - Prob. 54PSCh. 9.2 - Prob. 1QCh. 9.2 - Prob. 2QCh. 9.2 - Prob. 3QCh. 9.2 - Prob. 4QCh. 9.2 - Prob. 5QCh. 9.2 - Prob. 6QCh. 9.2 - Prob. 7QCh. 9.2 - Prob. 8QCh. 9.2 - Prob. 9QCh. 9.2 - Prob. 10QCh. 9.2 - Prob. 11QCh. 9.2 - Prob. 12QCh. 9.3 - Prob. 1GPCh. 9.3 - Prob. 2GPCh. 9.3 - Prob. 3GPCh. 9.3 - Prob. 4GPCh. 9.3 - Prob. 5GPCh. 9.3 - Prob. 6GPCh. 9.3 - Prob. 7GPCh. 9.3 - Prob. 8GPCh. 9.3 - Prob. 9GPCh. 9.3 - Prob. 10GPCh. 9.3 - Prob. 11GPCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35PSCh. 9.3 - Prob. 36PSCh. 9.3 - Prob. 37PSCh. 9.3 - Prob. 38PSCh. 9.3 - Prob. 39PSCh. 9.3 - Prob. 40PSCh. 9.3 - Prob. 1MRPSCh. 9.3 - Prob. 2MRPSCh. 9.3 - Prob. 3MRPSCh. 9.3 - Prob. 4MRPSCh. 9.3 - Prob. 5MRPSCh. 9.3 - Prob. 6MRPSCh. 9.3 - Prob. 7MRPSCh. 9.3 - Prob. 1DCCh. 9.3 - Prob. 2DCCh. 9.3 - Prob. 3DCCh. 9.4 - Prob. 1GPCh. 9.4 - Prob. 2GPCh. 9.4 - Prob. 3GPCh. 9.4 - Prob. 4GPCh. 9.4 - Prob. 5GPCh. 9.4 - Prob. 6GPCh. 9.4 - Prob. 7GPCh. 9.4 - Prob. 8GPCh. 9.4 - Prob. 9GPCh. 9.4 - Prob. 10GPCh. 9.4 - Prob. 11GPCh. 9.4 - Prob. 12GPCh. 9.4 - Prob. 13GPCh. 9.4 - Prob. 14GPCh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - 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Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43PSCh. 9.5 - Prob. 44PSCh. 9.5 - Prob. 45PSCh. 9.5 - Prob. 46PSCh. 9.5 - Prob. 47PSCh. 9.5 - Prob. 48PSCh. 9.5 - Prob. 49PSCh. 9.6 - Prob. 1GPCh. 9.6 - Prob. 2GPCh. 9.6 - Prob. 3GPCh. 9.6 - Prob. 4GPCh. 9.6 - Prob. 5GPCh. 9.6 - Prob. 6GPCh. 9.6 - Prob. 1ECh. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - Prob. 15ECh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Prob. 32ECh. 9.6 - Prob. 33ECh. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Prob. 39ECh. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43PSCh. 9.6 - Prob. 44PSCh. 9.6 - Prob. 45PSCh. 9.6 - Prob. 46PSCh. 9.6 - Prob. 47PSCh. 9.6 - Prob. 48PSCh. 9.6 - Prob. 1QCh. 9.6 - Prob. 2QCh. 9.6 - Prob. 3QCh. 9.6 - Prob. 4QCh. 9.6 - Prob. 5QCh. 9.6 - Prob. 6QCh. 9.6 - Prob. 7QCh. 9.6 - Prob. 8QCh. 9.6 - Prob. 9QCh. 9.6 - Prob. 10QCh. 9.6 - Prob. 11QCh. 9.6 - Prob. 12QCh. 9.6 - Prob. 13QCh. 9.6 - Prob. 14QCh. 9.6 - Prob. 15QCh. 9.6 - Prob. 1PCh. 9.6 - Prob. 2PCh. 9.6 - Prob. 3PCh. 9.6 - Prob. 4PCh. 9.6 - Prob. 5PCh. 9.6 - Prob. 1MRPSCh. 9.6 - Prob. 2MRPSCh. 9.6 - Prob. 3MRPSCh. 9.6 - Prob. 4MRPSCh. 9.6 - Prob. 5MRPSCh. 9.6 - Prob. 6MRPSCh. 9.6 - Prob. 7MRPSCh. 9 - Prob. 1VECh. 9 - Prob. 2VECh. 9 - Prob. 3VECh. 9 - Prob. 4VECh. 9 - Prob. 5VECh. 9 - Prob. 6REAECh. 9 - Prob. 7REAECh. 9 - Prob. 8REAECh. 9 - Prob. 9REAECh. 9 - Prob. 10REAECh. 9 - Prob. 11REAECh. 9 - Prob. 12REAECh. 9 - Prob. 13REAECh. 9 - Prob. 14REAECh. 9 - Prob. 15REAECh. 9 - Prob. 16REAECh. 9 - Prob. 17REAECh. 9 - Prob. 18REAECh. 9 - Prob. 19REAECh. 9 - Prob. 20REAECh. 9 - Prob. 21REAECh. 9 - Prob. 22REAECh. 9 - Prob. 23REAECh. 9 - Prob. 24REAECh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Prob. 9TCh. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Prob. 13TCh. 9 - Prob. 14TCh. 9 - Prob. 15TCh. 9 - Prob. 16TCh. 9 - Prob. 17TCh. 9 - Prob. 18TCh. 9 - Prob. 19TCh. 9 - Prob. 20TCh. 9 - Prob. 21TCh. 9 - Prob. 22TCh. 9 - Prob. 23TCh. 9 - Prob. 24TCh. 9 - Prob. 25TCh. 9 - Prob. 26TCh. 9 - Prob. 27TCh. 9 - Prob. 28TCh. 9 - Prob. 29TCh. 9 - Prob. 30TCh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 1TPCh. 9 - Prob. 2TPCh. 9 - Prob. 3TPCh. 9 - Prob. 4TPCh. 9 - Prob. 5TPCh. 9 - Prob. 6TPCh. 9 - Prob. 7TPCh. 9 - Prob. 8TPCh. 9 - Prob. 9TPCh. 9 - Prob. 10TPCh. 9 - Prob. 11TPCh. 9 - Prob. 12TPCh. 9 - Prob. 13TPCh. 9 - Prob. 14TPCh. 9 - Prob. 15TPCh. 9 - Prob. 16TPCh. 9 - Prob. 17TPCh. 9 - Prob. 18TPCh. 9 - Prob. 19TP
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