EBK ALGEBRA 2
EBK ALGEBRA 2
11th Edition
ISBN: 9780544714304
Author: Larson
Publisher: HMH PUB
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Chapter 3.2, Problem 87PS
Solution

(a)

How many times fainter is Altair than Vega?

  1.98 times fainter

Given:

The apparent magnitude of a star is a number that indicates how faint the star is in relation to the other stars. The expression 2.512m12.512m2 tells how many times fainter a star with magnitude m1 is than a star with magnitude m2 .

  EBK ALGEBRA 2, Chapter 3.2, Problem 87PS , additional homework tip 1

Concept Used:

  • Power of a power property: xab=xa⋅b
  • Product of power property: am⋅an=am+n
  • Quotient of power property: aman=am−n
  • Product property of radicals: an⋅bn=a⋅bn
  • Quotient property of radicals: anbn=abn
  • The exponent form of the nth root of a number a is given by an=a1n

Calculation:

In order to find how many times fainter is Altair than Vega, substitute m1=0.77 and m2=0.03 into the given expression and simplify further as shown below,

  2.512m12.512m2=2.5120.772.5120.03=2.5120.77−0.03=2.5120.74≈1.98

Therefore, Altair is about 1.98 times fainter than Vega.

(b)

How many times fainter is Deneb than Altair?

  1.56 times fainter

Given:

The apparent magnitude of a star is a number that indicates how faint the star is in relation to the other stars. The expression 2.512m12.512m2 tells how many times fainter a star with magnitude m1 is than a star with magnitude m2 .

  EBK ALGEBRA 2, Chapter 3.2, Problem 87PS , additional homework tip 2

Concept Used:

  • Power of a power property: xab=xa⋅b
  • Product of power property: am⋅an=am+n
  • Quotient of power property: aman=am−n
  • Product property of radicals: an⋅bn=a⋅bn
  • Quotient property of radicals: anbn=abn
  • The exponent form of the nth root of a number a is given by an=a1n

Calculation:

In order to find how many times fainter is Deneb than Altair, substitute m1=1.25 and m2=0.77 into the given expression and simplify further as shown below,

  2.512m12.512m2=2.5121.252.5120.77=2.5121.25−0.77=2.5120.48≈1.56

Therefore, Deneb is about 1.56 times fainter than Altair.

(c)

How many times fainter is Deneb than Vega?

  3.08 times fainter

Given:

The apparent magnitude of a star is a number that indicates how faint the star is in relation to the other stars. The expression 2.512m12.512m2 tells how many times fainter a star with magnitude m1 is than a star with magnitude m2 .

  EBK ALGEBRA 2, Chapter 3.2, Problem 87PS , additional homework tip 3

Concept Used:

  • Power of a power property: xab=xa⋅b
  • Product of power property: am⋅an=am+n
  • Quotient of power property: aman=am−n
  • Product property of radicals: an⋅bn=a⋅bn
  • Quotient property of radicals: anbn=abn
  • The exponent form of the nth root of a number a is given by an=a1n

Calculation:

In order to find how many times fainter is Deneb than Vega, substitute m1=1.25 and m2=0.03 into the given expression and simplify further as shown below,

  2.512m12.512m2=2.5121.252.5120.03=2.5121.25−0.03=2.5121.22≈3.08

Therefore, Deneb is about 3.08 times fainter than Vega.

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Chapter 3.2, Problem 86PS
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Chapter 3.2, Problem 88PS

Chapter 3 Solutions

EBK ALGEBRA 2

Ch. 3.1 - Prob. 1GPCh. 3.1 - Prob. 2GPCh. 3.1 - Prob. 3GPCh. 3.1 - Prob. 4GPCh. 3.1 - Prob. 5GPCh. 3.1 - Prob. 6GPCh. 3.1 - Prob. 7GPCh. 3.1 - Prob. 8GPCh. 3.1 - Prob. 9GPCh. 3.1 - Prob. 10GP
Ch. 3.1 - Prob. 11GPCh. 3.1 - Prob. 12GPCh. 3.1 - Prob. 13GPCh. 3.1 - Prob. 14GPCh. 3.1 - Prob. 15GPCh. 3.1 - Prob. 16GPCh. 3.1 - Prob. 17GPCh. 3.1 - Prob. 18GPCh. 3.1 - Prob. 19GPCh. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10ECh. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Prob. 24ECh. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Prob. 30ECh. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - Prob. 37ECh. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Prob. 44ECh. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.1 - Prob. 49ECh. 3.1 - Prob. 50ECh. 3.1 - Prob. 51ECh. 3.1 - Prob. 52ECh. 3.1 - Prob. 53ECh. 3.1 - Prob. 54ECh. 3.1 - Prob. 55ECh. 3.1 - Prob. 56ECh. 3.1 - Prob. 57ECh. 3.1 - Prob. 58ECh. 3.1 - Prob. 59ECh. 3.1 - Prob. 60PSCh. 3.1 - Prob. 61PSCh. 3.1 - Prob. 62PSCh. 3.1 - Prob. 63PSCh. 3.1 - Prob. 64PSCh. 3.1 - Prob. 65PSCh. 3.1 - Prob. 66PSCh. 3.2 - Prob. 1GPCh. 3.2 - Prob. 2GPCh. 3.2 - Prob. 3GPCh. 3.2 - Prob. 4GPCh. 3.2 - Prob. 5GPCh. 3.2 - Prob. 6GPCh. 3.2 - Prob. 7GPCh. 3.2 - Prob. 8GPCh. 3.2 - Prob. 9GPCh. 3.2 - Prob. 10GPCh. 3.2 - Prob. 11GPCh. 3.2 - Prob. 12GPCh. 3.2 - Prob. 13GPCh. 3.2 - Prob. 1ECh. 3.2 - Prob. 2ECh. 3.2 - Prob. 3ECh. 3.2 - Prob. 4ECh. 3.2 - Prob. 5ECh. 3.2 - Prob. 6ECh. 3.2 - Prob. 7ECh. 3.2 - Prob. 8ECh. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - Prob. 12ECh. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - Prob. 16ECh. 3.2 - Prob. 17ECh. 3.2 - Prob. 18ECh. 3.2 - Prob. 19ECh. 3.2 - Prob. 20ECh. 3.2 - Prob. 21ECh. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 67ECh. 3.2 - Prob. 68ECh. 3.2 - Prob. 69ECh. 3.2 - Prob. 70ECh. 3.2 - Prob. 71ECh. 3.2 - Prob. 72ECh. 3.2 - Prob. 73ECh. 3.2 - Prob. 74ECh. 3.2 - Prob. 75ECh. 3.2 - Prob. 76ECh. 3.2 - Prob. 77ECh. 3.2 - Prob. 78ECh. 3.2 - Prob. 79ECh. 3.2 - Prob. 80ECh. 3.2 - Prob. 81ECh. 3.2 - Prob. 82ECh. 3.2 - Prob. 83PSCh. 3.2 - Prob. 84PSCh. 3.2 - Prob. 85PSCh. 3.2 - Prob. 86PSCh. 3.2 - Prob. 87PSCh. 3.2 - Prob. 88PSCh. 3.2 - Prob. 89PSCh. 3.2 - Prob. 90PSCh. 3.2 - Prob. 1QCh. 3.2 - Prob. 2QCh. 3.2 - Prob. 3QCh. 3.2 - Prob. 4QCh. 3.2 - Prob. 5QCh. 3.2 - Prob. 6QCh. 3.2 - Prob. 7QCh. 3.2 - Prob. 8QCh. 3.2 - Prob. 9QCh. 3.2 - Prob. 10QCh. 3.2 - Prob. 11QCh. 3.2 - Prob. 12QCh. 3.2 - Prob. 13QCh. 3.2 - Prob. 14QCh. 3.2 - Prob. 15QCh. 3.3 - Prob. 1GPCh. 3.3 - Prob. 2GPCh. 3.3 - Prob. 3GPCh. 3.3 - Prob. 4GPCh. 3.3 - Prob. 5GPCh. 3.3 - Prob. 6GPCh. 3.3 - Prob. 7GPCh. 3.3 - Prob. 8GPCh. 3.3 - Prob. 9GPCh. 3.3 - Prob. 10GPCh. 3.3 - Prob. 11GPCh. 3.3 - Prob. 12GPCh. 3.3 - Prob. 13GPCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43PSCh. 3.3 - Prob. 44PSCh. 3.3 - Prob. 45PSCh. 3.3 - Prob. 46PSCh. 3.3 - Prob. 47PSCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - Prob. 3PCh. 3.3 - Prob. 4PCh. 3.3 - Prob. 1MRPSCh. 3.3 - Prob. 2MRPSCh. 3.3 - Prob. 3MRPSCh. 3.3 - Prob. 4MRPSCh. 3.3 - Prob. 5MRPSCh. 3.3 - Prob. 6MRPSCh. 3.3 - Prob. 7MRPSCh. 3.3 - Prob. 1DCCh. 3.3 - Prob. 2DCCh. 3.3 - Prob. 3DCCh. 3.4 - Prob. 1GPCh. 3.4 - Prob. 2GPCh. 3.4 - Prob. 3GPCh. 3.4 - Prob. 4GPCh. 3.4 - Prob. 5GPCh. 3.4 - Prob. 6GPCh. 3.4 - Prob. 7GPCh. 3.4 - Prob. 8GPCh. 3.4 - Prob. 9GPCh. 3.4 - Prob. 10GPCh. 3.4 - Prob. 11GPCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Prob. 28ECh. 3.4 - Prob. 29ECh. 3.4 - Prob. 30ECh. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Prob. 33ECh. 3.4 - Prob. 34ECh. 3.4 - Prob. 35ECh. 3.4 - Prob. 36ECh. 3.4 - Prob. 37ECh. 3.4 - Prob. 38ECh. 3.4 - Prob. 39ECh. 3.4 - Prob. 40ECh. 3.4 - Prob. 41ECh. 3.4 - Prob. 42ECh. 3.4 - Prob. 43ECh. 3.4 - Prob. 44ECh. 3.4 - Prob. 45ECh. 3.4 - Prob. 46PSCh. 3.4 - Prob. 47PSCh. 3.4 - Prob. 48PSCh. 3.4 - Prob. 49PSCh. 3.4 - Prob. 50PSCh. 3.4 - Prob. 51PSCh. 3.4 - Prob. 1QCh. 3.4 - Prob. 2QCh. 3.4 - Prob. 3QCh. 3.4 - Prob. 4QCh. 3.4 - Prob. 5QCh. 3.4 - Prob. 6QCh. 3.4 - Prob. 7QCh. 3.4 - Prob. 8QCh. 3.4 - Prob. 9QCh. 3.4 - Prob. 10QCh. 3.4 - Prob. 11QCh. 3.4 - Prob. 12QCh. 3.4 - Prob. 13QCh. 3.4 - Prob. 14QCh. 3.4 - Prob. 15QCh. 3.4 - Prob. 16QCh. 3.4 - Prob. 17QCh. 3.4 - Prob. 18QCh. 3.4 - Prob. 19QCh. 3.5 - Prob. 1GPCh. 3.5 - Prob. 2GPCh. 3.5 - Prob. 3GPCh. 3.5 - Prob. 4GPCh. 3.5 - Prob. 5GPCh. 3.5 - Prob. 6GPCh. 3.5 - Prob. 7GPCh. 3.5 - Prob. 8GPCh. 3.5 - Prob. 9GPCh. 3.5 - Prob. 10GPCh. 3.5 - Prob. 11GPCh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 5ECh. 3.5 - Prob. 6ECh. 3.5 - Prob. 7ECh. 3.5 - Prob. 8ECh. 3.5 - Prob. 9ECh. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35PSCh. 3.5 - Prob. 36PSCh. 3.5 - Prob. 37PSCh. 3.5 - Prob. 38PSCh. 3.5 - Prob. 39PSCh. 3.5 - Prob. 40PSCh. 3.6 - Prob. 1GPCh. 3.6 - Prob. 2GPCh. 3.6 - Prob. 3GPCh. 3.6 - Prob. 4GPCh. 3.6 - Prob. 5GPCh. 3.6 - Prob. 6GPCh. 3.6 - Prob. 7GPCh. 3.6 - Prob. 8GPCh. 3.6 - Prob. 9GPCh. 3.6 - Prob. 10GPCh. 3.6 - Prob. 11GPCh. 3.6 - Prob. 12GPCh. 3.6 - Prob. 13GPCh. 3.6 - Prob. 14GPCh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Prob. 52ECh. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56PSCh. 3.6 - Prob. 57PSCh. 3.6 - Prob. 58PSCh. 3.6 - Prob. 59PSCh. 3.6 - Prob. 60PSCh. 3.6 - Prob. 61PSCh. 3.6 - Prob. 62PSCh. 3.6 - Prob. 1QCh. 3.6 - Prob. 2QCh. 3.6 - Prob. 3QCh. 3.6 - Prob. 4QCh. 3.6 - Prob. 5QCh. 3.6 - Prob. 6QCh. 3.6 - Prob. 7QCh. 3.6 - Prob. 8QCh. 3.6 - Prob. 9QCh. 3.6 - Prob. 10QCh. 3.6 - Prob. 11QCh. 3.6 - Prob. 12QCh. 3.6 - Prob. 13QCh. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.6 - Prob. 6PCh. 3.6 - Prob. 7PCh. 3.6 - Prob. 1.1PCh. 3.6 - Prob. 1.2PCh. 3.6 - Prob. 1.3PCh. 3.6 - Prob. 1.4PCh. 3.6 - Prob. 1.5PCh. 3.6 - Prob. 1.6PCh. 3.6 - Prob. 1.7PCh. 3.6 - Prob. 1.8PCh. 3.6 - Prob. 1.9PCh. 3.6 - Prob. 1.10PCh. 3.6 - Prob. 1.11PCh. 3.6 - Prob. 1.12PCh. 3.6 - Prob. 1.13PCh. 3.6 - Prob. 1MRPSCh. 3.6 - Prob. 2MRPSCh. 3.6 - Prob. 3MRPSCh. 3.6 - Prob. 4MRPSCh. 3.6 - Prob. 5MRPSCh. 3.6 - Prob. 6MRPSCh. 3.6 - Prob. 7MRPSCh. 3.6 - Prob. 8MRPSCh. 3.6 - Prob. 9MRPSCh. 3 - Prob. 1VECh. 3 - Prob. 2VECh. 3 - Prob. 3VECh. 3 - Prob. 4VECh. 3 - Prob. 5VECh. 3 - Prob. 6VECh. 3 - Prob. 7VECh. 3 - Prob. 8REAECh. 3 - Prob. 9REAECh. 3 - Prob. 10REAECh. 3 - Prob. 11REAECh. 3 - Prob. 12REAECh. 3 - Prob. 13REAECh. 3 - Prob. 14REAECh. 3 - Prob. 15REAECh. 3 - Prob. 16REAECh. 3 - Prob. 17REAECh. 3 - Prob. 18REAECh. 3 - Prob. 19REAECh. 3 - Prob. 20REAECh. 3 - Prob. 21REAECh. 3 - Prob. 22REAECh. 3 - Prob. 23REAECh. 3 - Prob. 24REAECh. 3 - Prob. 25REAECh. 3 - Prob. 26REAECh. 3 - Prob. 27REAECh. 3 - Prob. 28REAECh. 3 - Prob. 29REAECh. 3 - Prob. 30REAECh. 3 - Prob. 31REAECh. 3 - Prob. 32REAECh. 3 - Prob. 1TCh. 3 - Prob. 2TCh. 3 - Prob. 3TCh. 3 - Prob. 4TCh. 3 - Prob. 5TCh. 3 - Prob. 6TCh. 3 - Prob. 7TCh. 3 - Prob. 8TCh. 3 - Prob. 9TCh. 3 - Prob. 10TCh. 3 - Prob. 11TCh. 3 - Prob. 12TCh. 3 - Prob. 13TCh. 3 - Prob. 14TCh. 3 - Prob. 15TCh. 3 - Prob. 16TCh. 3 - Prob. 17TCh. 3 - Prob. 18TCh. 3 - Prob. 19TCh. 3 - Prob. 20TCh. 3 - Prob. 21TCh. 3 - Prob. 22TCh. 3 - Prob. 23TCh. 3 - Prob. 24TCh. 3 - Prob. 25TCh. 3 - Prob. 26TCh. 3 - Prob. 27TCh. 3 - Prob. 28TCh. 3 - Prob. 29TCh. 3 - Prob. 30TCh. 3 - Prob. 31TCh. 3 - Prob. 32TCh. 3 - Prob. 33TCh. 3 - Prob. 34TCh. 3 - Prob. 35TCh. 3 - Prob. 36TCh. 3 - Prob. 37TCh. 3 - Prob. 38TCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 1TPCh. 3 - Prob. 2TPCh. 3 - Prob. 3TPCh. 3 - Prob. 4TPCh. 3 - Prob. 5TPCh. 3 - Prob. 6TPCh. 3 - Prob. 7TPCh. 3 - Prob. 8TPCh. 3 - Prob. 9TPCh. 3 - Prob. 10TPCh. 3 - Prob. 11TPCh. 3 - Prob. 12TPCh. 3 - Prob. 13TPCh. 3 - Prob. 14TPCh. 3 - Prob. 15TPCh. 3 - Prob. 16TPCh. 3 - Prob. 17TPCh. 3 - Prob. 18TPCh. 3 - Prob. 19TPCh. 3 - Prob. 20TP
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