Geometry, Student Edition
Geometry, Student Edition
1st Edition
ISBN: 9780078884849
Author: McGraw-Hill, McGraw Hill
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Question
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Chapter 7.1, Problem 39PPS

(a)

To determine

To find: Whether the triangle is golden triangle and then find the length of diagonal.

(a)

Expert Solution
Check Mark

Answer to Problem 39PPS

The rectangle is a golden rectangle and the length of diagonal is 22.83 ft .

Explanation of Solution

The ratio of length to width is,

  lw=19.4212.01=1.617

The ratio is a golden ratio.

Hence the rectangle is golden rectangle.

The diagonal is calculated as,

  d=19.422+12.012=377.14+144.24=521.3765=22.83 ft

Therefore, the rectangle is a golden rectangle and the length of diagonal is 22.83 ft .

(b)

To determine

To find: Whether the standard screen and the high definition television is a golden rectangle.

(b)

Expert Solution
Check Mark

Answer to Problem 39PPS

The high definition TV is near to the golden rectangle.

Explanation of Solution

The standard television screen has an aspect ratio 4:3 , it means the ratio of the width and height.

This ratio is equal to 1.33, which is not about 1.68 So the standard television is not golden rectangle.

The high definition television screen has an aspect ratio of 16:9 , it means the ratio of the width and height.

The ratio is equal to 1.78 , it is nearer to golden ratio, hence the high definition television is near to golden rectangle.

Therefore, the high definition TV is near to the golden rectangle.

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Chapter 7.1, Problem 38PPS
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Chapter 7.1, Problem 40PPS

Chapter 7 Solutions

Geometry, Student Edition

Ch. 7.1 - Prob. 1ACYPCh. 7.1 - Prob. 2CYPCh. 7.1 - Prob. 3ACYPCh. 7.1 - Prob. 3BCYPCh. 7.1 - Prob. 3CCYPCh. 7.1 - Prob. 4CYPCh. 7.1 - Prob. 1CYUCh. 7.1 - Prob. 2CYUCh. 7.1 - Prob. 3CYUCh. 7.1 - Prob. 4CYU
Ch. 7.1 - Prob. 5CYUCh. 7.1 - Prob. 6CYUCh. 7.1 - Prob. 7CYUCh. 7.1 - Prob. 8CYUCh. 7.1 - Prob. 9CYUCh. 7.1 - Prob. 10PPSCh. 7.1 - Prob. 11PPSCh. 7.1 - Prob. 12PPSCh. 7.1 - Prob. 13PPSCh. 7.1 - Prob. 14PPSCh. 7.1 - Prob. 15PPSCh. 7.1 - Prob. 16PPSCh. 7.1 - Prob. 17PPSCh. 7.1 - Prob. 18PPSCh. 7.1 - Prob. 19PPSCh. 7.1 - Prob. 20PPSCh. 7.1 - Prob. 21PPSCh. 7.1 - Prob. 22PPSCh. 7.1 - Prob. 23PPSCh. 7.1 - Prob. 24PPSCh. 7.1 - Prob. 25PPSCh. 7.1 - Prob. 26PPSCh. 7.1 - Prob. 27PPSCh. 7.1 - Prob. 28PPSCh. 7.1 - Prob. 29PPSCh. 7.1 - Prob. 30PPSCh. 7.1 - Prob. 31PPSCh. 7.1 - Prob. 32PPSCh. 7.1 - Prob. 33PPSCh. 7.1 - Prob. 34PPSCh. 7.1 - Prob. 35PPSCh. 7.1 - Prob. 36PPSCh. 7.1 - Prob. 37PPSCh. 7.1 - Prob. 38PPSCh. 7.1 - Prob. 39PPSCh. 7.1 - Prob. 40PPSCh. 7.1 - Prob. 41PPSCh. 7.1 - Prob. 42PPSCh. 7.1 - Prob. 43PPSCh. 7.1 - Prob. 44HPCh. 7.1 - Prob. 45HPCh. 7.1 - Prob. 46HPCh. 7.1 - Prob. 47HPCh. 7.1 - Prob. 48HPCh. 7.1 - Prob. 49HPCh. 7.1 - Prob. 50STPCh. 7.1 - Prob. 51STPCh. 7.1 - Prob. 52STPCh. 7.1 - Prob. 53STPCh. 7.1 - Prob. 54SPRCh. 7.1 - Prob. 55SPRCh. 7.1 - Prob. 56SPRCh. 7.1 - Prob. 57SPRCh. 7.1 - Prob. 58SPRCh. 7.1 - Prob. 59SPRCh. 7.1 - Prob. 60SPRCh. 7.1 - Prob. 61SPRCh. 7.1 - Prob. 62SPRCh. 7.1 - Prob. 63SPRCh. 7.1 - Prob. 64SPRCh. 7.1 - Prob. 65SRCh. 7.2 - Prob. 1CYPCh. 7.2 - Prob. 2CYPCh. 7.2 - Prob. 3ACYPCh. 7.2 - Prob. 3BCYPCh. 7.2 - Prob. 4CYPCh. 7.2 - Prob. 1CYUCh. 7.2 - Prob. 2CYUCh. 7.2 - Prob. 3CYUCh. 7.2 - Prob. 4CYUCh. 7.2 - Prob. 5CYUCh. 7.2 - Prob. 6CYUCh. 7.2 - Prob. 7CYUCh. 7.2 - Prob. 8PPSCh. 7.2 - Prob. 9PPSCh. 7.2 - Prob. 10PPSCh. 7.2 - Prob. 11PPSCh. 7.2 - Prob. 12PPSCh. 7.2 - Prob. 13PPSCh. 7.2 - Prob. 14PPSCh. 7.2 - Prob. 15PPSCh. 7.2 - Prob. 16PPSCh. 7.2 - Prob. 17PPSCh. 7.2 - Prob. 18PPSCh. 7.2 - Prob. 19PPSCh. 7.2 - Prob. 20PPSCh. 7.2 - Prob. 21PPSCh. 7.2 - Prob. 22PPSCh. 7.2 - Prob. 23PPSCh. 7.2 - Prob. 24PPSCh. 7.2 - Prob. 25PPSCh. 7.2 - Prob. 26PPSCh. 7.2 - Prob. 27PPSCh. 7.2 - Prob. 28PPSCh. 7.2 - Prob. 29PPSCh. 7.2 - Prob. 30PPSCh. 7.2 - Prob. 31PPSCh. 7.2 - Prob. 32PPSCh. 7.2 - Prob. 33PPSCh. 7.2 - Prob. 34PPSCh. 7.2 - Prob. 35PPSCh. 7.2 - Prob. 36PPSCh. 7.2 - Prob. 37PPSCh. 7.2 - Prob. 38PPSCh. 7.2 - Prob. 39PPSCh. 7.2 - Prob. 40PPSCh. 7.2 - Prob. 41PPSCh. 7.2 - Prob. 42PPSCh. 7.2 - Prob. 43PPSCh. 7.2 - Prob. 44PPSCh. 7.2 - Prob. 45PPSCh. 7.2 - Prob. 46PPSCh. 7.2 - Prob. 47PPSCh. 7.2 - Prob. 48PPSCh. 7.2 - Prob. 49PPSCh. 7.2 - Prob. 50PPSCh. 7.2 - Prob. 51HPCh. 7.2 - Prob. 52HPCh. 7.2 - Prob. 53HPCh. 7.2 - Prob. 54HPCh. 7.2 - Prob. 55HPCh. 7.2 - Prob. 56STPCh. 7.2 - Prob. 57STPCh. 7.2 - Prob. 58STPCh. 7.2 - Prob. 59STPCh. 7.2 - Prob. 60SPRCh. 7.2 - Prob. 61SPRCh. 7.2 - Prob. 62SPRCh. 7.2 - Prob. 63SPRCh. 7.2 - Prob. 64SPRCh. 7.2 - Prob. 65SPRCh. 7.2 - Prob. 66SPRCh. 7.2 - Prob. 67SPRCh. 7.2 - Prob. 68SPRCh. 7.2 - Prob. 69SPRCh. 7.2 - Prob. 70SRCh. 7.2 - Prob. 71SRCh. 7.2 - Prob. 72SRCh. 7.3 - Prob. 1ACYPCh. 7.3 - Prob. 1BCYPCh. 7.3 - Prob. 2ACYPCh. 7.3 - Prob. 2BCYPCh. 7.3 - Prob. 3CYPCh. 7.3 - Prob. 4ACYPCh. 7.3 - Prob. 4BCYPCh. 7.3 - Prob. 5CYPCh. 7.3 - Prob. 1CYUCh. 7.3 - Prob. 2CYUCh. 7.3 - Prob. 3CYUCh. 7.3 - Prob. 4CYUCh. 7.3 - Prob. 5CYUCh. 7.3 - Prob. 6CYUCh. 7.3 - Prob. 7CYUCh. 7.3 - Prob. 8CYUCh. 7.3 - Prob. 9PPSCh. 7.3 - Prob. 10PPSCh. 7.3 - Prob. 11PPSCh. 7.3 - Prob. 12PPSCh. 7.3 - Prob. 13PPSCh. 7.3 - Prob. 14PPSCh. 7.3 - Prob. 15PPSCh. 7.3 - Prob. 16PPSCh. 7.3 - Prob. 17PPSCh. 7.3 - Prob. 18PPSCh. 7.3 - Prob. 19PPSCh. 7.3 - Prob. 20PPSCh. 7.3 - Prob. 21PPSCh. 7.3 - Prob. 22PPSCh. 7.3 - Prob. 23PPSCh. 7.3 - Prob. 24PPSCh. 7.3 - Prob. 25PPSCh. 7.3 - Prob. 26PPSCh. 7.3 - Prob. 27PPSCh. 7.3 - Prob. 28PPSCh. 7.3 - Prob. 29PPSCh. 7.3 - Prob. 30PPSCh. 7.3 - Prob. 31PPSCh. 7.3 - Prob. 32PPSCh. 7.3 - Prob. 33PPSCh. 7.3 - Prob. 34PPSCh. 7.3 - Prob. 35PPSCh. 7.3 - Prob. 36PPSCh. 7.3 - Prob. 37HPCh. 7.3 - Prob. 38HPCh. 7.3 - Prob. 39HPCh. 7.3 - Prob. 40HPCh. 7.3 - Prob. 41HPCh. 7.3 - Prob. 42STPCh. 7.3 - Prob. 43STPCh. 7.3 - Prob. 44STPCh. 7.3 - Prob. 45STPCh. 7.3 - Prob. 46SPRCh. 7.3 - Prob. 47SPRCh. 7.3 - Prob. 48SPRCh. 7.3 - Prob. 49SPRCh. 7.3 - Prob. 50SPRCh. 7.3 - Prob. 51SPRCh. 7.3 - Prob. 52SPRCh. 7.3 - Prob. 53SPRCh. 7.3 - Prob. 54SPRCh. 7.3 - Prob. 55SPRCh. 7.3 - Prob. 56SPRCh. 7.3 - Prob. 57SRCh. 7.4 - Prob. 1CYPCh. 7.4 - Prob. 2CYPCh. 7.4 - Prob. 3ACYPCh. 7.4 - Prob. 3BCYPCh. 7.4 - Prob. 3CCYPCh. 7.4 - Prob. 4CYPCh. 7.4 - Prob. 5ACYPCh. 7.4 - Prob. 5BCYPCh. 7.4 - Prob. 1CYUCh. 7.4 - Prob. 2CYUCh. 7.4 - Prob. 3CYUCh. 7.4 - Prob. 4CYUCh. 7.4 - Prob. 5CYUCh. 7.4 - Prob. 6CYUCh. 7.4 - Prob. 7CYUCh. 7.4 - Prob. 8CYUCh. 7.4 - Prob. 9CYUCh. 7.4 - Prob. 10PPSCh. 7.4 - Prob. 11PPSCh. 7.4 - Prob. 12PPSCh. 7.4 - Prob. 13PPSCh. 7.4 - Prob. 14PPSCh. 7.4 - Prob. 15PPSCh. 7.4 - Prob. 16PPSCh. 7.4 - Prob. 17PPSCh. 7.4 - Prob. 18PPSCh. 7.4 - Prob. 19PPSCh. 7.4 - Prob. 20PPSCh. 7.4 - Prob. 21PPSCh. 7.4 - Prob. 22PPSCh. 7.4 - Prob. 23PPSCh. 7.4 - Prob. 24PPSCh. 7.4 - Prob. 25PPSCh. 7.4 - Prob. 26PPSCh. 7.4 - Prob. 27PPSCh. 7.4 - Prob. 28PPSCh. 7.4 - Prob. 29PPSCh. 7.4 - Prob. 30PPSCh. 7.4 - Prob. 31PPSCh. 7.4 - Prob. 32PPSCh. 7.4 - Prob. 33PPSCh. 7.4 - Prob. 34PPSCh. 7.4 - Prob. 35PPSCh. 7.4 - Prob. 36PPSCh. 7.4 - Prob. 37PPSCh. 7.4 - Prob. 38PPSCh. 7.4 - Prob. 39PPSCh. 7.4 - Prob. 40PPSCh. 7.4 - Prob. 41PPSCh. 7.4 - Prob. 42PPSCh. 7.4 - Prob. 43PPSCh. 7.4 - Prob. 44PPSCh. 7.4 - Prob. 45PPSCh. 7.4 - Prob. 46PPSCh. 7.4 - Prob. 47PPSCh. 7.4 - Prob. 48HPCh. 7.4 - Prob. 49HPCh. 7.4 - Prob. 50HPCh. 7.4 - Prob. 51HPCh. 7.4 - Prob. 52HPCh. 7.4 - Prob. 53STPCh. 7.4 - Prob. 54STPCh. 7.4 - Prob. 55STPCh. 7.4 - Prob. 56STPCh. 7.4 - Prob. 57SPRCh. 7.4 - Prob. 58SPRCh. 7.4 - Prob. 59SPRCh. 7.4 - Prob. 60SPRCh. 7.4 - Prob. 61SPRCh. 7.4 - Prob. 62SPRCh. 7.4 - Prob. 63SPRCh. 7.4 - Prob. 64SPRCh. 7.4 - Prob. 65SPRCh. 7.4 - Prob. 66SPRCh. 7.4 - Prob. 67SRCh. 7.4 - Prob. 68SRCh. 7.4 - Prob. 69SRCh. 7.4 - Prob. 70SRCh. 7.4 - Prob. 71SRCh. 7.5 - Prob. 1ACYPCh. 7.5 - Prob. 1BCYPCh. 7.5 - Prob. 2CYPCh. 7.5 - Prob. 3ACYPCh. 7.5 - Prob. 3BCYPCh. 7.5 - Prob. 1CYUCh. 7.5 - Prob. 2CYUCh. 7.5 - Prob. 3CYUCh. 7.5 - Prob. 4CYUCh. 7.5 - Prob. 5CYUCh. 7.5 - Prob. 6PPSCh. 7.5 - Prob. 7PPSCh. 7.5 - Prob. 8PPSCh. 7.5 - Prob. 9PPSCh. 7.5 - Prob. 10PPSCh. 7.5 - Prob. 11PPSCh. 7.5 - Prob. 12PPSCh. 7.5 - Prob. 13PPSCh. 7.5 - Prob. 14PPSCh. 7.5 - Prob. 15PPSCh. 7.5 - Prob. 16PPSCh. 7.5 - Prob. 17PPSCh. 7.5 - Prob. 18PPSCh. 7.5 - Prob. 19PPSCh. 7.5 - Prob. 20PPSCh. 7.5 - Prob. 21PPSCh. 7.5 - Prob. 22PPSCh. 7.5 - Prob. 23PPSCh. 7.5 - Prob. 24PPSCh. 7.5 - Prob. 25PPSCh. 7.5 - Prob. 26PPSCh. 7.5 - Prob. 27PPSCh. 7.5 - Prob. 28PPSCh. 7.5 - Prob. 29PPSCh. 7.5 - Prob. 30PPSCh. 7.5 - Prob. 31HPCh. 7.5 - Prob. 32HPCh. 7.5 - Prob. 33HPCh. 7.5 - Prob. 34HPCh. 7.5 - Prob. 35HPCh. 7.5 - Prob. 36STPCh. 7.5 - Prob. 37STPCh. 7.5 - Prob. 38STPCh. 7.5 - Prob. 39STPCh. 7.5 - Prob. 40SPRCh. 7.5 - Prob. 41SPRCh. 7.5 - Prob. 42SPRCh. 7.5 - Prob. 43SPRCh. 7.5 - Prob. 44SPRCh. 7.5 - Prob. 45SPRCh. 7.5 - Prob. 46SRCh. 7.5 - Prob. 47SRCh. 7.5 - Prob. 48SRCh. 7.5 - Prob. 49SRCh. 7.5 - Prob. 50SRCh. 7.5 - Prob. 51SRCh. 7.6 - Prob. 1ACYPCh. 7.6 - Prob. 1BCYPCh. 7.6 - Prob. 2CYPCh. 7.6 - Prob. 3ACYPCh. 7.6 - Prob. 3BCYPCh. 7.6 - Prob. 1CYUCh. 7.6 - Prob. 2CYUCh. 7.6 - Prob. 3CYUCh. 7.6 - Prob. 4CYUCh. 7.6 - Prob. 5CYUCh. 7.6 - Prob. 6PPSCh. 7.6 - Prob. 7PPSCh. 7.6 - Prob. 8PPSCh. 7.6 - Prob. 9PPSCh. 7.6 - Prob. 10PPSCh. 7.6 - Prob. 11PPSCh. 7.6 - Prob. 12PPSCh. 7.6 - Prob. 13PPSCh. 7.6 - Prob. 14PPSCh. 7.6 - Prob. 15PPSCh. 7.6 - Prob. 16PPSCh. 7.6 - Prob. 17PPSCh. 7.6 - Prob. 18PPSCh. 7.6 - Prob. 19PPSCh. 7.6 - Prob. 20PPSCh. 7.6 - Prob. 21PPSCh. 7.6 - Prob. 22HPCh. 7.6 - Prob. 23HPCh. 7.6 - Prob. 24HPCh. 7.6 - Prob. 25HPCh. 7.6 - Prob. 26HPCh. 7.6 - Prob. 27HPCh. 7.6 - Prob. 28STPCh. 7.6 - Prob. 29STPCh. 7.6 - Prob. 30STPCh. 7.6 - Prob. 31STPCh. 7.6 - Prob. 32SPRCh. 7.6 - Prob. 33SPRCh. 7.6 - Prob. 34SPRCh. 7.6 - Prob. 35SPRCh. 7.6 - Prob. 36SPRCh. 7.6 - Prob. 37SPRCh. 7.6 - Prob. 38SPRCh. 7.6 - Prob. 39SPRCh. 7.6 - Prob. 40SRCh. 7.6 - Prob. 41SRCh. 7.6 - Prob. 42SRCh. 7.6 - Prob. 43SRCh. 7.6 - Prob. 44SRCh. 7.6 - Prob. 45SRCh. 7.7 - Prob. 1CYPCh. 7.7 - Prob. 2CYPCh. 7.7 - Prob. 3CYPCh. 7.7 - Prob. 1CYUCh. 7.7 - Prob. 2CYUCh. 7.7 - Prob. 3CYUCh. 7.7 - Prob. 4CYUCh. 7.7 - Prob. 5PPSCh. 7.7 - Prob. 6PPSCh. 7.7 - Prob. 7PPSCh. 7.7 - Prob. 8PPSCh. 7.7 - Prob. 9PPSCh. 7.7 - Prob. 10PPSCh. 7.7 - Prob. 11PPSCh. 7.7 - Prob. 12PPSCh. 7.7 - Prob. 13PPSCh. 7.7 - Prob. 14PPSCh. 7.7 - Prob. 15PPSCh. 7.7 - Prob. 16PPSCh. 7.7 - Prob. 17PPSCh. 7.7 - Prob. 18PPSCh. 7.7 - Prob. 19PPSCh. 7.7 - Prob. 20PPSCh. 7.7 - Prob. 21HPCh. 7.7 - Prob. 22HPCh. 7.7 - Prob. 23HPCh. 7.7 - Prob. 24HPCh. 7.7 - Prob. 25HPCh. 7.7 - Prob. 26STPCh. 7.7 - Prob. 27STPCh. 7.7 - Prob. 28STPCh. 7.7 - Prob. 29STPCh. 7.7 - Prob. 30SPRCh. 7.7 - Prob. 31SPRCh. 7.7 - Prob. 32SPRCh. 7.7 - Prob. 33SPRCh. 7.7 - Prob. 34SPRCh. 7.7 - Prob. 35SPRCh. 7.7 - Prob. 36SPRCh. 7.7 - Prob. 37SPRCh. 7.7 - Prob. 38SPRCh. 7.7 - Prob. 39SPRCh. 7.7 - Prob. 40SPRCh. 7.7 - Prob. 41SPRCh. 7.7 - Prob. 42SPRCh. 7.7 - Prob. 43SPRCh. 7.7 - Prob. 44SPRCh. 7.7 - Prob. 45SRCh. 7.7 - Prob. 46SRCh. 7.7 - Prob. 47SRCh. 7.7 - Prob. 48SRCh. 7.7 - Prob. 49SRCh. 7 - Prob. 1GRFCCh. 7 - Prob. 2GRFCCh. 7 - Prob. 3GRFCCh. 7 - Prob. 4GRFCCh. 7 - Prob. 5GRFCCh. 7 - Prob. 6GRFCCh. 7 - Prob. 7GRFCCh. 7 - Prob. 8GRFCCh. 7 - Prob. 1MCQCh. 7 - Prob. 2MCQCh. 7 - Prob. 3MCQCh. 7 - Prob. 4MCQCh. 7 - Prob. 5MCQCh. 7 - Prob. 6MCQCh. 7 - Prob. 7MCQCh. 7 - Prob. 8MCQCh. 7 - Prob. 9MCQCh. 7 - Prob. 10MCQCh. 7 - Prob. 11MCQCh. 7 - Prob. 12MCQCh. 7 - Prob. 13MCQCh. 7 - Prob. 14MCQCh. 7 - Prob. 15MCQCh. 7 - Prob. 1SGRCh. 7 - Prob. 2SGRCh. 7 - Prob. 3SGRCh. 7 - Prob. 4SGRCh. 7 - Prob. 5SGRCh. 7 - Prob. 6SGRCh. 7 - Prob. 7SGRCh. 7 - Prob. 8SGRCh. 7 - Prob. 9SGRCh. 7 - Prob. 10SGRCh. 7 - Prob. 11SGRCh. 7 - Prob. 12SGRCh. 7 - Prob. 13SGRCh. 7 - Prob. 14SGRCh. 7 - Prob. 15SGRCh. 7 - Prob. 16SGRCh. 7 - Prob. 17SGRCh. 7 - Prob. 18SGRCh. 7 - Prob. 19SGRCh. 7 - Prob. 20SGRCh. 7 - Prob. 21SGRCh. 7 - Prob. 22SGRCh. 7 - Prob. 23SGRCh. 7 - Prob. 24SGRCh. 7 - Prob. 25SGRCh. 7 - Prob. 26SGRCh. 7 - Prob. 27SGRCh. 7 - Prob. 28SGRCh. 7 - Prob. 29SGRCh. 7 - Prob. 30SGRCh. 7 - Prob. 31SGRCh. 7 - Prob. 32SGRCh. 7 - Prob. 33SGRCh. 7 - Prob. 34SGRCh. 7 - Prob. 35SGRCh. 7 - Prob. 1PTCh. 7 - Prob. 2PTCh. 7 - Prob. 3PTCh. 7 - Prob. 4PTCh. 7 - Prob. 5PTCh. 7 - Prob. 6PTCh. 7 - Prob. 7PTCh. 7 - Prob. 8PTCh. 7 - Prob. 9PTCh. 7 - Prob. 10PTCh. 7 - Prob. 11PTCh. 7 - Prob. 12PTCh. 7 - Prob. 13PTCh. 7 - Prob. 14PTCh. 7 - Prob. 15PTCh. 7 - Prob. 16PTCh. 7 - Prob. 17PTCh. 7 - Prob. 1STPCh. 7 - Prob. 2STPCh. 7 - Prob. 3STPCh. 7 - Prob. 4STPCh. 7 - Prob. 5STPCh. 7 - Prob. 6STPCh. 7 - Prob. 7STPCh. 7 - Prob. 8STPCh. 7 - Prob. 9STPCh. 7 - Prob. 10STPCh. 7 - Prob. 11STPCh. 7 - Prob. 12STPCh. 7 - Prob. 13STPCh. 7 - Prob. 14STPCh. 7 - Prob. 15STP

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