Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Minimization
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Maxima and Minima
The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.
Derivatives
A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …
Concavity
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Question
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Chapter 2.1, Problem 34PPS

a.

To determine

Graph each function on separate screen.

a.

Expert Solution
Check Mark

Answer to Problem 34PPS

  f(x)=x2 

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 1

  g(x)=2x

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 2

  h(x)=x3−3x2−5x+6

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 3

  j(x)=x3

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 4

Explanation of Solution

Given information:

  f(x)=x2       g(x)=2x          h(x)=x3−3x2−5x+6      j(x)=x3

Calculation:

Consider the given one by one,

Use TI−83 calculator to graph the function, f(x)=x2 

Step 1. Press Y= and put the function on Y1

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 5

Step2.Press GRAPH and TRACE button,

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 6

Use TI−83 calculator to graph the function, g(x)=2x

Step 1. Press Y= and put the function on Y1

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 7

Step 2. Press GRAPH and TRACE button,

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 8

Use TI−83 calculator to graph the function, h(x)=x3−3x2−5x+6

Step 1. Press Y= and put the function on Y1

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 9

Step 2. Press GRAPH and TRACE button,

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 10

Use TI−83 calculator to graph the function, j(x)=x3

Step 1. Press Y= and put the function on Y1

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 11

Step 2. Press GRAPH and TRACE button,

  Algebra 2, Chapter 2.1, Problem 34PPS , additional homework tip 12

b.

To determine

Tabulate the graph of each function to show intersection point on horizontal line.

b.

Expert Solution
Check Mark

Answer to Problem 34PPS

  FunctionPossible  intersection  pointsf(x)=x20,1,2g(x)=2x0,1h(x)=x3−3x2−5x+61,2,3j(x)=x31

Explanation of Solution

Given information:

Graphs shown in part (a)

Calculation:

Consider the graphs of part (a) ,

  FunctionPossible  intersection  pointsf(x)=x20,1,2g(x)=2x0,1h(x)=x3−3x2−5x+61,2,3j(x)=x31

c.

To determine

Identify the function for given condition.

c.

Expert Solution
Check Mark

Answer to Problem 34PPS

  g(x) and j(x) are one-to −one function.

  f(x) and h(x) are not one-to −one function.

Explanation of Solution

Given information:

For a function to be one-to-one, a horizontal line can intersect the function at most once.

Calculation:

It is not easy to check the function of all graphs, introduce a pencil on all graph if it is parallel to the x−axis and then move the pencil up and down then check for the graph lines intersect with the pencil , if they intersect then graph is one-to-one.

  g(x) and j(x) meet the pencil line one time, therefore they are one-to −one,

  f(x) and h(x) functions are one-to −one.

Hence, g(x) and j(x) are one-to −one, f(x) and h(x) functions are one-to −one.

d.

To determine

Identify the function for given condition.

d.

Expert Solution
Check Mark

Answer to Problem 34PPS

  h(x) and j(x) are onto functions,

  f(x) and g(x) are not onto functions.

Explanation of Solution

Given information:

For a function to be onto, a horizontal line can intersect the function at least once.

Calculation:

A parallel line on the graph of h(x) and j(x) will cross over the graph lines more than one at a time therefore they are onto functions, f(x) and g(x) does not intersect the graph lines. They are not onto functions.

e.

To determine

Create the table of given functions.

e.

Expert Solution
Check Mark

Answer to Problem 34PPS

  Functionsone−to−oneOntof(x)=x2NoNog(x)=2x YesNoh(x)=x3−3x2−5x+6  NoYesj(x)=x3YesYes

Explanation of Solution

Given information:

One-to one function and onto function.

Calculation:

  Functionsone−to−oneOntof(x)=x2NoNog(x)=2x YesNoh(x)=x3−3x2−5x+6  NoYesj(x)=x3YesYes

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Chapter 2.1, Problem 33PPS
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Chapter 2.1, Problem 35HP

Chapter 2 Solutions

Algebra 2

Ch. 2.1 - Prob. 1ACYPCh. 2.1 - Prob. 1BCYPCh. 2.1 - Prob. 2CYPCh. 2.1 - Prob. 3CYPCh. 2.1 - Prob. 4ACYPCh. 2.1 - Prob. 4BCYPCh. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYUCh. 2.1 - Prob. 4CYU
Ch. 2.1 - Prob. 5CYUCh. 2.1 - Prob. 6CYUCh. 2.1 - Prob. 7CYUCh. 2.1 - Prob. 8CYUCh. 2.1 - Prob. 9CYUCh. 2.1 - Prob. 10CYUCh. 2.1 - Prob. 11PPSCh. 2.1 - Prob. 12PPSCh. 2.1 - Prob. 13PPSCh. 2.1 - Prob. 14PPSCh. 2.1 - Prob. 15PPSCh. 2.1 - Prob. 16PPSCh. 2.1 - Prob. 17PPSCh. 2.1 - Prob. 18PPSCh. 2.1 - Prob. 19PPSCh. 2.1 - Prob. 20PPSCh. 2.1 - Prob. 21PPSCh. 2.1 - Prob. 22PPSCh. 2.1 - Prob. 23PPSCh. 2.1 - Prob. 24PPSCh. 2.1 - Prob. 25PPSCh. 2.1 - Prob. 26PPSCh. 2.1 - Prob. 27PPSCh. 2.1 - Prob. 28PPSCh. 2.1 - Prob. 29PPSCh. 2.1 - Prob. 30PPSCh. 2.1 - Prob. 31PPSCh. 2.1 - Prob. 32PPSCh. 2.1 - Prob. 33PPSCh. 2.1 - Prob. 34PPSCh. 2.1 - Prob. 35HPCh. 2.1 - Prob. 36HPCh. 2.1 - Prob. 37HPCh. 2.1 - Prob. 38HPCh. 2.1 - Prob. 39HPCh. 2.1 - Prob. 40HPCh. 2.1 - Prob. 41HPCh. 2.1 - Prob. 42HPCh. 2.1 - Prob. 43HPCh. 2.1 - Prob. 44HPCh. 2.1 - Prob. 45STPCh. 2.1 - Prob. 46STPCh. 2.1 - Prob. 47STPCh. 2.1 - Prob. 48STPCh. 2.1 - Prob. 49STPCh. 2.1 - Prob. 50STPCh. 2.1 - Prob. 51STPCh. 2.1 - Prob. 52STPCh. 2.1 - 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Prob. 76SCh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.3 - Prob. 1CYPCh. 2.3 - Prob. 2CYPCh. 2.3 - Prob. 3ACYPCh. 2.3 - Prob. 3BCYPCh. 2.3 - Prob. 4ACYPCh. 2.3 - Prob. 4BCYPCh. 2.3 - Prob. 1CYUCh. 2.3 - Prob. 2CYUCh. 2.3 - Prob. 3CYUCh. 2.3 - Prob. 4CYUCh. 2.3 - Prob. 5CYUCh. 2.3 - Prob. 6CYUCh. 2.3 - Prob. 7CYUCh. 2.3 - Prob. 8CYUCh. 2.3 - Prob. 9PPSCh. 2.3 - Prob. 10PPSCh. 2.3 - Prob. 11PPSCh. 2.3 - Prob. 12PPSCh. 2.3 - Prob. 13PPSCh. 2.3 - Prob. 14PPSCh. 2.3 - Prob. 15PPSCh. 2.3 - Prob. 16PPSCh. 2.3 - Prob. 17PPSCh. 2.3 - Prob. 18PPSCh. 2.3 - Prob. 19PPSCh. 2.3 - Prob. 20PPSCh. 2.3 - Prob. 21PPSCh. 2.3 - Prob. 22PPSCh. 2.3 - Prob. 23PPSCh. 2.3 - Prob. 24PPSCh. 2.3 - Prob. 25PPSCh. 2.3 - Prob. 26PPSCh. 2.3 - Prob. 27PPSCh. 2.3 - Prob. 28PPSCh. 2.3 - Prob. 29PPSCh. 2.3 - Prob. 30PPSCh. 2.3 - Prob. 31PPSCh. 2.3 - Prob. 32PPSCh. 2.3 - Prob. 33PPSCh. 2.3 - Prob. 34PPSCh. 2.3 - Prob. 35PPSCh. 2.3 - Prob. 36HPCh. 2.3 - Prob. 37HPCh. 2.3 - 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Prob. 24PPSCh. 2.4 - Prob. 25PPSCh. 2.4 - Prob. 26PPSCh. 2.4 - Prob. 27PPSCh. 2.4 - Prob. 28PPSCh. 2.4 - Prob. 29PPSCh. 2.4 - Prob. 30PPSCh. 2.4 - Prob. 31PPSCh. 2.4 - Prob. 32PPSCh. 2.4 - Prob. 33PPSCh. 2.4 - Prob. 34PPSCh. 2.4 - Prob. 35PPSCh. 2.4 - Prob. 36PPSCh. 2.4 - Prob. 37HPCh. 2.4 - Prob. 38HPCh. 2.4 - Prob. 39HPCh. 2.4 - Prob. 40HPCh. 2.4 - Prob. 41HPCh. 2.4 - Prob. 42HPCh. 2.4 - Prob. 43HPCh. 2.4 - Prob. 44HPCh. 2.4 - Prob. 45HPCh. 2.4 - Prob. 46HPCh. 2.4 - Prob. 47STPCh. 2.4 - Prob. 48STPCh. 2.4 - Prob. 49STPCh. 2.4 - Prob. 50STPCh. 2.4 - Prob. 51STPCh. 2.4 - Prob. 52STPCh. 2.4 - Prob. 53STPCh. 2.4 - Prob. 54STPCh. 2.4 - Prob. 55STPCh. 2.4 - Prob. 56STPCh. 2.4 - Prob. 57STPCh. 2.4 - Prob. 58STPCh. 2.4 - Prob. 59STPCh. 2.4 - Prob. 60SCh. 2.4 - Prob. 61SCh. 2.4 - Prob. 62SCh. 2.4 - Prob. 63SCh. 2.4 - Prob. 64SCh. 2.4 - Prob. 65SCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.5 - Prob. 1CYPCh. 2.5 - Prob. 2CYPCh. 2.5 - Prob. 1CYUCh. 2.5 - Prob. 2CYUCh. 2.5 - Prob. 3PPSCh. 2.5 - Prob. 4PPSCh. 2.5 - Prob. 5PPSCh. 2.5 - Prob. 6PPSCh. 2.5 - Prob. 7PPSCh. 2.5 - Prob. 8PPSCh. 2.5 - Prob. 9PPSCh. 2.5 - Prob. 10PPSCh. 2.5 - Prob. 11PPSCh. 2.5 - Prob. 12HPCh. 2.5 - Prob. 13HPCh. 2.5 - Prob. 14HPCh. 2.5 - Prob. 15HPCh. 2.5 - Prob. 16HPCh. 2.5 - Prob. 17HPCh. 2.5 - Prob. 18HPCh. 2.5 - Prob. 19HPCh. 2.5 - Prob. 20HPCh. 2.5 - Prob. 21STPCh. 2.5 - Prob. 22STPCh. 2.5 - Prob. 23STPCh. 2.5 - Prob. 24STPCh. 2.5 - Prob. 25STPCh. 2.5 - Prob. 26STPCh. 2.5 - Prob. 27STPCh. 2.5 - Prob. 28STPCh. 2.5 - Prob. 29STPCh. 2.5 - Prob. 30SCh. 2.5 - Prob. 31SCh. 2.5 - Prob. 32SCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.6 - Prob. 1CYPCh. 2.6 - Prob. 2ACYPCh. 2.6 - Prob. 2BCYPCh. 2.6 - Prob. 3CYPCh. 2.6 - Prob. 4ACYPCh. 2.6 - Prob. 4BCYPCh. 2.6 - Prob. 1CYUCh. 2.6 - Prob. 2CYUCh. 2.6 - Prob. 3CYUCh. 2.6 - Prob. 4CYUCh. 2.6 - Prob. 5CYUCh. 2.6 - Prob. 6CYUCh. 2.6 - Prob. 7CYUCh. 2.6 - Prob. 8CYUCh. 2.6 - Prob. 9CYUCh. 2.6 - Prob. 10CYUCh. 2.6 - Prob. 11CYUCh. 2.6 - Prob. 12PPSCh. 2.6 - 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Prob. 2ACYPCh. 2.7 - Prob. 2BCYPCh. 2.7 - Prob. 3ACYPCh. 2.7 - Prob. 3BCYPCh. 2.7 - Prob. 4ACYPCh. 2.7 - Prob. 4BCYPCh. 2.7 - Prob. 5CYPCh. 2.7 - Prob. 1CYUCh. 2.7 - Prob. 2CYUCh. 2.7 - Prob. 3CYUCh. 2.7 - Prob. 4CYUCh. 2.7 - Prob. 5CYUCh. 2.7 - Prob. 6CYUCh. 2.7 - Prob. 7CYUCh. 2.7 - Prob. 8CYUCh. 2.7 - Prob. 9CYUCh. 2.7 - Prob. 10PPSCh. 2.7 - Prob. 11PPSCh. 2.7 - Prob. 12PPSCh. 2.7 - Prob. 13PPSCh. 2.7 - Prob. 14PPSCh. 2.7 - Prob. 15PPSCh. 2.7 - Prob. 16PPSCh. 2.7 - Prob. 17PPSCh. 2.7 - Prob. 18PPSCh. 2.7 - Prob. 19PPSCh. 2.7 - Prob. 20PPSCh. 2.7 - Prob. 21PPSCh. 2.7 - Prob. 22PPSCh. 2.7 - Prob. 23PPSCh. 2.7 - Prob. 24PPSCh. 2.7 - Prob. 25PPSCh. 2.7 - Prob. 26PPSCh. 2.7 - Prob. 27PPSCh. 2.7 - Prob. 28PPSCh. 2.7 - Prob. 29PPSCh. 2.7 - Prob. 30PPSCh. 2.7 - Prob. 31PPSCh. 2.7 - Prob. 32PPSCh. 2.7 - Prob. 33PPSCh. 2.7 - Prob. 34PPSCh. 2.7 - Prob. 35PPSCh. 2.7 - Prob. 36PPSCh. 2.7 - Prob. 37PPSCh. 2.7 - Prob. 38PPSCh. 2.7 - Prob. 39PPSCh. 2.7 - Prob. 40PPSCh. 2.7 - Prob. 41PPSCh. 2.7 - Prob. 42PPSCh. 2.7 - Prob. 43HPCh. 2.7 - Prob. 44HPCh. 2.7 - Prob. 45HPCh. 2.7 - Prob. 46HPCh. 2.7 - Prob. 47HPCh. 2.7 - Prob. 48HPCh. 2.7 - Prob. 49HPCh. 2.7 - Prob. 50HPCh. 2.7 - Prob. 51HPCh. 2.7 - Prob. 52STPCh. 2.7 - Prob. 53STPCh. 2.7 - Prob. 54STPCh. 2.7 - Prob. 55STPCh. 2.7 - Prob. 56STPCh. 2.7 - Prob. 57STPCh. 2.7 - Prob. 58STPCh. 2.7 - Prob. 59STPCh. 2.7 - Prob. 60STPCh. 2.7 - Prob. 61STPCh. 2.7 - Prob. 62STPCh. 2.7 - Prob. 63SCh. 2.7 - Prob. 64SCh. 2.7 - Prob. 65SCh. 2.8 - Prob. 1ACYPCh. 2.8 - Prob. 1BCYPCh. 2.8 - Prob. 2CYPCh. 2.8 - Prob. 3ACYPCh. 2.8 - Prob. 3BCYPCh. 2.8 - Prob. 1CYUCh. 2.8 - Prob. 2CYUCh. 2.8 - Prob. 3CYUCh. 2.8 - Prob. 4CYUCh. 2.8 - Prob. 5CYUCh. 2.8 - Prob. 6CYUCh. 2.8 - Prob. 7CYUCh. 2.8 - Prob. 8PPSCh. 2.8 - Prob. 9PPSCh. 2.8 - Prob. 10PPSCh. 2.8 - Prob. 11PPSCh. 2.8 - Prob. 12PPSCh. 2.8 - Prob. 13PPSCh. 2.8 - Prob. 14PPSCh. 2.8 - Prob. 15PPSCh. 2.8 - Prob. 16PPSCh. 2.8 - Prob. 17PPSCh. 2.8 - Prob. 18PPSCh. 2.8 - Prob. 19PPSCh. 2.8 - Prob. 20PPSCh. 2.8 - Prob. 21PPSCh. 2.8 - Prob. 22PPSCh. 2.8 - Prob. 23PPSCh. 2.8 - Prob. 24PPSCh. 2.8 - Prob. 25PPSCh. 2.8 - Prob. 26PPSCh. 2.8 - Prob. 27PPSCh. 2.8 - Prob. 28PPSCh. 2.8 - Prob. 29PPSCh. 2.8 - Prob. 30PPSCh. 2.8 - Prob. 31PPSCh. 2.8 - Prob. 32PPSCh. 2.8 - Prob. 33HPCh. 2.8 - Prob. 34HPCh. 2.8 - Prob. 35HPCh. 2.8 - Prob. 36HPCh. 2.8 - Prob. 37HPCh. 2.8 - Prob. 38HPCh. 2.8 - Prob. 39HPCh. 2.8 - Prob. 40HPCh. 2.8 - Prob. 41HPCh. 2.8 - Prob. 42STPCh. 2.8 - Prob. 43STPCh. 2.8 - Prob. 44STPCh. 2.8 - Prob. 45STPCh. 2.8 - Prob. 46STPCh. 2.8 - Prob. 47STPCh. 2.8 - Prob. 48STPCh. 2.8 - Prob. 49STPCh. 2.8 - Prob. 50STPCh. 2.8 - Prob. 51STPCh. 2.8 - Prob. 52STPCh. 2.8 - Prob. 53STPCh. 2.8 - Prob. 54STPCh. 2.8 - Prob. 55SCh. 2.8 - Prob. 56SCh. 2.8 - Prob. 57SCh. 2 - Prob. 1QCCh. 2 - Prob. 2QCCh. 2 - Prob. 3QCCh. 2 - Prob. 4QCCh. 2 - Prob. 5QCCh. 2 - Prob. 6QCCh. 2 - Prob. 7QCCh. 2 - Prob. 8QCCh. 2 - Prob. 9QCCh. 2 - Prob. 10QCCh. 2 - Prob. 11QCCh. 2 - Prob. 12QCCh. 2 - Prob. 13QCCh. 2 - Prob. 14QCCh. 2 - Prob. 15QCCh. 2 - Prob. 16QCCh. 2 - Prob. 1MCQCh. 2 - Prob. 2MCQCh. 2 - Prob. 3MCQCh. 2 - Prob. 4MCQCh. 2 - Prob. 5MCQCh. 2 - Prob. 6MCQCh. 2 - Prob. 7MCQCh. 2 - Prob. 8MCQCh. 2 - Prob. 9MCQCh. 2 - Prob. 10MCQCh. 2 - Prob. 11MCQCh. 2 - Prob. 12MCQCh. 2 - Prob. 13MCQCh. 2 - Prob. 14MCQCh. 2 - Prob. 15MCQCh. 2 - Prob. 16MCQCh. 2 - Prob. 17MCQCh. 2 - Prob. 18MCQCh. 2 - Prob. 19MCQCh. 2 - Prob. 20MCQCh. 2 - Prob. 21MCQCh. 2 - Prob. 22MCQCh. 2 - Prob. 23MCQCh. 2 - Prob. 24MCQCh. 2 - Prob. 25MCQCh. 2 - Prob. 1SGRCh. 2 - Prob. 2SGRCh. 2 - Prob. 3SGRCh. 2 - Prob. 4SGRCh. 2 - Prob. 5SGRCh. 2 - Prob. 6SGRCh. 2 - Prob. 7SGRCh. 2 - Prob. 8SGRCh. 2 - Prob. 9SGRCh. 2 - Prob. 10SGRCh. 2 - Prob. 11SGRCh. 2 - Prob. 12SGRCh. 2 - Prob. 13SGRCh. 2 - Prob. 14SGRCh. 2 - Prob. 15SGRCh. 2 - Prob. 16SGRCh. 2 - Prob. 17SGRCh. 2 - Prob. 18SGRCh. 2 - Prob. 19SGRCh. 2 - Prob. 20SGRCh. 2 - Prob. 21SGRCh. 2 - Prob. 22SGRCh. 2 - Prob. 23SGRCh. 2 - Prob. 24SGRCh. 2 - Prob. 25SGRCh. 2 - Prob. 26SGRCh. 2 - Prob. 27SGRCh. 2 - Prob. 28SGRCh. 2 - Prob. 29SGRCh. 2 - Prob. 30SGRCh. 2 - Prob. 31SGRCh. 2 - Prob. 32SGRCh. 2 - Prob. 33SGRCh. 2 - Prob. 34SGRCh. 2 - Prob. 35SGRCh. 2 - Prob. 36SGRCh. 2 - Prob. 37SGRCh. 2 - Prob. 38SGRCh. 2 - Prob. 39SGRCh. 2 - Prob. 40SGRCh. 2 - Prob. 41SGRCh. 2 - Prob. 42SGRCh. 2 - Prob. 43SGRCh. 2 - Prob. 44SGRCh. 2 - Prob. 45SGRCh. 2 - Prob. 46SGRCh. 2 - Prob. 47SGRCh. 2 - Prob. 48SGRCh. 2 - Prob. 49SGRCh. 2 - Prob. 50SGRCh. 2 - Prob. 51SGRCh. 2 - Prob. 52SGRCh. 2 - Prob. 53SGRCh. 2 - Prob. 54SGRCh. 2 - Prob. 55SGRCh. 2 - Prob. 56SGRCh. 2 - Prob. 57SGRCh. 2 - Prob. 58SGRCh. 2 - Prob. 59SGRCh. 2 - Prob. 60SGRCh. 2 - Prob. 61SGRCh. 2 - Prob. 62SGRCh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Prob. 8PTCh. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PTCh. 2 - Prob. 15PTCh. 2 - Prob. 16PTCh. 2 - Prob. 17PTCh. 2 - Prob. 18PTCh. 2 - Prob. 19PTCh. 2 - Prob. 20PTCh. 2 - Prob. 1ECh. 2 - Prob. 2ECh. 2 - Prob. 1STPCh. 2 - Prob. 2STPCh. 2 - Prob. 3STPCh. 2 - Prob. 4STPCh. 2 - Prob. 5STPCh. 2 - Prob. 6STPCh. 2 - Prob. 7STPCh. 2 - Prob. 8STPCh. 2 - Prob. 9STPCh. 2 - Prob. 10STPCh. 2 - Prob. 11STPCh. 2 - Prob. 12STP

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