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Chapter 4, Problem 1RE

(a)

Expert Solution
Check Mark
To determine

To calculate: The value of (g∘f)(−8) using the graphs of y=f(x) and y=g(x).

Answer to Problem 1RE

Solution:

The value of (g∘f)(−8) using the graphs of y=f(x) and y=g(x) is −4.

Explanation of Solution

Given Information: The figure given is

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition), Chapter 4, Problem 1RE , additional homework tip 1

Calculation:

From the graph we get, f(−8)=2 and g(−8)=−2

(g∘f)(−8)=g∘f(−8)⇒g(f(−8))we have f(−8)=2∴g(f(−8))=g(2)g(2)=−4 (from graph)

Therefore, the value of (g∘f)(−8) using the graphs of y=f(x) and y=g(x) is −4.

(b)

Expert Solution
Check Mark
To determine

To calculate: The value of (f∘g)(−8) using the graphs of y=f(x) and y=g(x).

Answer to Problem 1RE

Solution:

The value of (f∘g)(−8) using the graphs of y=f(x) and y=g(x) is 1.

Explanation of Solution

Given Information: The figure given is

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition), Chapter 4, Problem 1RE , additional homework tip 2

Calculation:

From the graph we get, f(−8)=2 and g(−8)=−2

(f∘g)(−8)=f∘g(−8)⇒f(g(−8))we have g(−8)=−2∴f(g(−8))=f(−2)f(−2)=1 (from graph)

Therefore, the value of (f∘g)(−8) using the graphs of y=f(x) and y=g(x) is 1.

(c)

Expert Solution
Check Mark
To determine

To calculate: The value of (g∘g)(7) using the graphs of y=f(x) and y=g(x).

Answer to Problem 1RE

Solution:

The value of (g∘g)(7) using the graphs of y=f(x) and y=g(x) is −6.

Explanation of Solution

Given Information: The figure given is

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition), Chapter 4, Problem 1RE , additional homework tip 3

Calculation:

From the graph we get, f(7)=6 and g(7)=0

(g∘g)(7)=g∘g(7)⇒g(g(7))we have g(7)=0∴g(g(7))=g(0)g(0)=−6 (from graph)

Therefore, the value of (g∘g)(7) using the graphs of y=f(x) and y=g(x) is −6.

(d)

Expert Solution
Check Mark
To determine

To calculate: The value of (g∘f)(−5) using the graphs of y=f(x) and y=g(x).

Answer to Problem 1RE

Solution:

The value of (g∘f)(−5) using the graphs of y=f(x) and y=g(x) is −6.

Explanation of Solution

Given Information: The figure given is

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition), Chapter 4, Problem 1RE , additional homework tip 4

Calculation:

From the graph we get, f(−5)=4 and g(−5)=−4

(g∘f)(−5)=g∘f(−5)⇒g(f(−5))we have f(−5)=4∴g(f(−5))=g(4)g(4)=−6 (from graph)

Therefore, the value of (g∘f)(−5) using the graphs of y=f(x) and y=g(x) is −6.

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Chapter 4 Solutions

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)

Chapter 4.1, Problem 11AYU Chapter 4.1, Problem 12AYU Chapter 4.1, Problem 13AYU Chapter 4.1, Problem 14AYU Chapter 4.1, Problem 15AYU Chapter 4.1, Problem 16AYU Chapter 4.1, Problem 17AYU Chapter 4.1, Problem 18AYU Chapter 4.1, Problem 19AYU Chapter 4.1, Problem 20AYU Chapter 4.1, Problem 21AYU Chapter 4.1, Problem 22AYU Chapter 4.1, Problem 23AYU Chapter 4.1, Problem 24AYU Chapter 4.1, Problem 25AYU Chapter 4.1, Problem 26AYU Chapter 4.1, Problem 27AYU Chapter 4.1, Problem 28AYU Chapter 4.1, Problem 29AYU Chapter 4.1, Problem 30AYU Chapter 4.1, Problem 31AYU Chapter 4.1, Problem 32AYU Chapter 4.1, Problem 33AYU Chapter 4.1, Problem 34AYU Chapter 4.1, Problem 35AYU Chapter 4.1, Problem 36AYU Chapter 4.1, Problem 37AYU Chapter 4.1, Problem 38AYU Chapter 4.1, Problem 39AYU Chapter 4.1, Problem 40AYU Chapter 4.1, Problem 41AYU Chapter 4.1, Problem 42AYU Chapter 4.1, Problem 43AYU Chapter 4.1, Problem 44AYU Chapter 4.1, Problem 45AYU Chapter 4.1, Problem 46AYU Chapter 4.1, Problem 47AYU Chapter 4.1, Problem 48AYU Chapter 4.1, Problem 49AYU Chapter 4.1, Problem 50AYU Chapter 4.1, Problem 51AYU Chapter 4.1, Problem 52AYU Chapter 4.1, Problem 53AYU Chapter 4.1, Problem 54AYU Chapter 4.1, Problem 55AYU Chapter 4.1, Problem 56AYU Chapter 4.1, Problem 57AYU Chapter 4.1, Problem 58AYU Chapter 4.1, Problem 59AYU Chapter 4.1, Problem 60AYU Chapter 4.1, Problem 61AYU Chapter 4.1, Problem 62AYU Chapter 4.1, Problem 63AYU Chapter 4.1, Problem 64AYU Chapter 4.1, Problem 65AYU Chapter 4.1, Problem 66AYU Chapter 4.1, Problem 67AYU Chapter 4.1, Problem 68AYU Chapter 4.1, Problem 69AYU Chapter 4.1, Problem 70AYU Chapter 4.1, Problem 71AYU Chapter 4.1, Problem 72AYU Chapter 4.1, Problem 73AYU Chapter 4.1, Problem 74AYU Chapter 4.1, Problem 75AYU Chapter 4.1, Problem 76AYU Chapter 4.1, Problem 78AYU Chapter 4.1, Problem 79AYU Chapter 4.2, Problem 1AYU Chapter 4.2, Problem 2AYU Chapter 4.2, Problem 3AYU Chapter 4.2, Problem 4AYU Chapter 4.2, Problem 5AYU Chapter 4.2, Problem 6AYU Chapter 4.2, Problem 7AYU Chapter 4.2, Problem 8AYU Chapter 4.2, Problem 9AYU Chapter 4.2, Problem 10AYU Chapter 4.2, Problem 11AYU Chapter 4.2, Problem 12AYU Chapter 4.2, Problem 13AYU Chapter 4.2, Problem 14AYU Chapter 4.2, Problem 15AYU Chapter 4.2, Problem 16AYU Chapter 4.2, Problem 17AYU Chapter 4.2, Problem 18AYU Chapter 4.2, Problem 19AYU Chapter 4.2, Problem 20AYU Chapter 4.2, Problem 21AYU Chapter 4.2, Problem 22AYU Chapter 4.2, Problem 23AYU Chapter 4.2, Problem 24AYU Chapter 4.2, Problem 25AYU Chapter 4.2, Problem 26AYU Chapter 4.2, Problem 27AYU Chapter 4.2, Problem 28AYU Chapter 4.2, Problem 29AYU Chapter 4.2, Problem 30AYU Chapter 4.2, Problem 31AYU Chapter 4.2, Problem 32AYU Chapter 4.2, Problem 33AYU Chapter 4.2, Problem 34AYU Chapter 4.2, Problem 35AYU Chapter 4.2, Problem 36AYU Chapter 4.2, Problem 37AYU Chapter 4.2, Problem 38AYU Chapter 4.2, Problem 39AYU Chapter 4.2, Problem 40AYU Chapter 4.2, Problem 41AYU Chapter 4.2, Problem 42AYU Chapter 4.2, Problem 43AYU Chapter 4.2, Problem 44AYU Chapter 4.2, Problem 45AYU Chapter 4.2, Problem 46AYU Chapter 4.2, Problem 47AYU Chapter 4.2, Problem 48AYU Chapter 4.2, Problem 49AYU Chapter 4.2, Problem 50AYU Chapter 4.2, Problem 51AYU Chapter 4.2, Problem 52AYU Chapter 4.2, Problem 53AYU Chapter 4.2, Problem 54AYU Chapter 4.2, Problem 55AYU Chapter 4.2, Problem 56AYU Chapter 4.2, Problem 57AYU Chapter 4.2, Problem 58AYU Chapter 4.2, Problem 59AYU Chapter 4.2, Problem 60AYU Chapter 4.2, Problem 61AYU Chapter 4.2, Problem 62AYU Chapter 4.2, Problem 63AYU Chapter 4.2, Problem 64AYU Chapter 4.2, Problem 65AYU Chapter 4.2, Problem 66AYU Chapter 4.2, Problem 67AYU Chapter 4.2, Problem 68AYU Chapter 4.2, Problem 69AYU Chapter 4.2, Problem 70AYU Chapter 4.2, Problem 71AYU Chapter 4.2, Problem 72AYU Chapter 4.2, Problem 73AYU Chapter 4.2, Problem 74AYU Chapter 4.2, Problem 75AYU Chapter 4.2, Problem 76AYU Chapter 4.2, Problem 77AYU Chapter 4.2, Problem 78AYU Chapter 4.2, Problem 79AYU Chapter 4.2, Problem 80AYU Chapter 4.2, Problem 81AYU Chapter 4.2, Problem 82AYU Chapter 4.2, Problem 83AYU Chapter 4.2, Problem 84AYU Chapter 4.2, Problem 85AYU Chapter 4.2, Problem 86AYU Chapter 4.2, Problem 87AYU Chapter 4.2, Problem 88AYU Chapter 4.2, Problem 89AYU Chapter 4.2, Problem 90AYU Chapter 4.2, Problem 91AYU Chapter 4.2, Problem 92AYU Chapter 4.2, Problem 93AYU Chapter 4.2, Problem 94AYU Chapter 4.2, Problem 95AYU Chapter 4.2, Problem 96AYU Chapter 4.2, Problem 97AYU Chapter 4.2, Problem 98AYU Chapter 4.2, Problem 99AYU Chapter 4.2, Problem 100AYU Chapter 4.2, Problem 101AYU Chapter 4.2, Problem 102AYU Chapter 4.2, Problem 103AYU Chapter 4.2, Problem 104AYU Chapter 4.2, Problem 105AYU Chapter 4.2, Problem 106AYU Chapter 4.2, Problem 107AYU Chapter 4.2, Problem 108AYU Chapter 4.2, Problem 109AYU Chapter 4.2, Problem 110AYU Chapter 4.2, Problem 111AYU Chapter 4.2, Problem 112AYU Chapter 4.2, Problem 113AYU Chapter 4.2, Problem 114AYU Chapter 4.2, Problem 115AYU Chapter 4.2, Problem 116AYU Chapter 4.3, Problem 1AYU Chapter 4.3, Problem 2AYU Chapter 4.3, Problem 3AYU Chapter 4.3, Problem 4AYU Chapter 4.3, Problem 5AYU Chapter 4.3, Problem 6AYU Chapter 4.3, Problem 7AYU Chapter 4.3, Problem 8AYU Chapter 4.3, Problem 9AYU Chapter 4.3, Problem 10AYU Chapter 4.3, Problem 11AYU Chapter 4.3, Problem 12AYU Chapter 4.3, Problem 13AYU Chapter 4.3, Problem 14AYU Chapter 4.3, Problem 15AYU Chapter 4.3, Problem 16AYU Chapter 4.3, Problem 17AYU Chapter 4.3, Problem 18AYU Chapter 4.3, Problem 19AYU Chapter 4.3, Problem 20AYU Chapter 4.3, Problem 21AYU Chapter 4.3, Problem 22AYU Chapter 4.3, Problem 23AYU Chapter 4.3, Problem 24AYU Chapter 4.3, Problem 25AYU Chapter 4.3, Problem 26AYU Chapter 4.3, Problem 27AYU Chapter 4.3, Problem 28AYU Chapter 4.3, Problem 29AYU Chapter 4.3, Problem 33AYU Chapter 4.3, Problem 30AYU Chapter 4.3, Problem 32AYU Chapter 4.3, Problem 31AYU Chapter 4.3, Problem 34AYU Chapter 4.3, Problem 35AYU Chapter 4.3, Problem 36AYU Chapter 4.3, Problem 37AYU Chapter 4.3, Problem 38AYU Chapter 4.3, Problem 39AYU Chapter 4.3, Problem 40AYU Chapter 4.3, Problem 41AYU Chapter 4.3, Problem 42AYU Chapter 4.3, Problem 43AYU Chapter 4.3, Problem 44AYU Chapter 4.3, Problem 45AYU Chapter 4.3, Problem 46AYU Chapter 4.3, Problem 47AYU Chapter 4.3, Problem 48AYU Chapter 4.3, Problem 49AYU Chapter 4.3, Problem 50AYU Chapter 4.3, Problem 51AYU Chapter 4.3, Problem 52AYU Chapter 4.3, Problem 53AYU Chapter 4.3, Problem 54AYU Chapter 4.3, Problem 55AYU Chapter 4.3, Problem 56AYU Chapter 4.3, Problem 57AYU Chapter 4.3, Problem 58AYU Chapter 4.3, Problem 59AYU Chapter 4.3, Problem 60AYU Chapter 4.3, Problem 61AYU Chapter 4.3, Problem 62AYU Chapter 4.3, Problem 63AYU Chapter 4.3, Problem 64AYU Chapter 4.3, Problem 65AYU Chapter 4.3, Problem 66AYU Chapter 4.3, Problem 67AYU Chapter 4.3, Problem 68AYU Chapter 4.3, Problem 69AYU Chapter 4.3, Problem 70AYU Chapter 4.3, Problem 71AYU Chapter 4.3, Problem 72AYU Chapter 4.3, Problem 73AYU Chapter 4.3, Problem 74AYU Chapter 4.3, Problem 75AYU Chapter 4.3, Problem 76AYU Chapter 4.3, Problem 77AYU Chapter 4.3, Problem 78AYU Chapter 4.3, Problem 80AYU Chapter 4.3, Problem 81AYU Chapter 4.3, Problem 82AYU Chapter 4.3, Problem 83AYU Chapter 4.3, Problem 84AYU Chapter 4.3, Problem 85AYU Chapter 4.3, Problem 86AYU Chapter 4.3, Problem 87AYU Chapter 4.3, Problem 88AYU Chapter 4.3, Problem 89AYU Chapter 4.3, Problem 90AYU Chapter 4.3, Problem 91AYU Chapter 4.3, Problem 92AYU Chapter 4.3, Problem 93AYU Chapter 4.3, Problem 94AYU Chapter 4.3, Problem 95AYU Chapter 4.3, Problem 96AYU Chapter 4.3, Problem 97AYU Chapter 4.3, Problem 98AYU Chapter 4.3, Problem 99AYU Chapter 4.3, Problem 100AYU Chapter 4.3, Problem 101AYU Chapter 4.3, Problem 102AYU Chapter 4.3, Problem 103AYU Chapter 4.3, Problem 104AYU Chapter 4.3, Problem 105AYU Chapter 4.3, Problem 106AYU Chapter 4.3, Problem 107AYU Chapter 4.3, Problem 108AYU Chapter 4.3, Problem 109AYU Chapter 4.3, Problem 110AYU Chapter 4.3, Problem 111AYU Chapter 4.3, Problem 112AYU Chapter 4.3, Problem 113AYU Chapter 4.3, Problem 114AYU Chapter 4.3, Problem 115AYU Chapter 4.3, Problem 116AYU Chapter 4.3, Problem 117AYU Chapter 4.3, Problem 118AYU Chapter 4.3, Problem 119AYU Chapter 4.3, Problem 120AYU Chapter 4.3, Problem 121AYU Chapter 4.3, Problem 122AYU Chapter 4.3, Problem 123AYU Chapter 4.3, Problem 124AYU Chapter 4.3, Problem 125AYU Chapter 4.3, Problem 126AYU Chapter 4.3, Problem 127AYU Chapter 4.3, Problem 128AYU Chapter 4.3, Problem 129AYU Chapter 4.3, Problem 130AYU Chapter 4.3, Problem 131AYU Chapter 4.3, Problem 132AYU Chapter 4.3, Problem 133AYU Chapter 4.3, Problem 134AYU Chapter 4.3, Problem 135AYU Chapter 4.3, Problem 136AYU Chapter 4.3, Problem 137AYU Chapter 4.3, Problem 138AYU Chapter 4.3, Problem 139AYU Chapter 4.4, Problem 1AYU Chapter 4.4, Problem 2AYU Chapter 4.4, Problem 3AYU Chapter 4.4, Problem 4AYU Chapter 4.4, Problem 5AYU Chapter 4.4, Problem 6AYU Chapter 4.4, Problem 7AYU Chapter 4.4, Problem 8AYU Chapter 4.4, Problem 9AYU Chapter 4.4, Problem 10AYU Chapter 4.4, Problem 11AYU Chapter 4.4, Problem 12AYU Chapter 4.4, Problem 13AYU Chapter 4.4, Problem 14AYU Chapter 4.4, Problem 15AYU Chapter 4.4, Problem 16AYU Chapter 4.4, Problem 17AYU Chapter 4.4, Problem 18AYU Chapter 4.4, Problem 19AYU Chapter 4.4, Problem 20AYU Chapter 4.4, Problem 21AYU Chapter 4.4, Problem 22AYU Chapter 4.4, Problem 23AYU Chapter 4.4, Problem 24AYU Chapter 4.4, Problem 25AYU Chapter 4.4, Problem 26AYU Chapter 4.4, Problem 27AYU Chapter 4.4, Problem 28AYU Chapter 4.4, Problem 29AYU Chapter 4.4, Problem 30AYU Chapter 4.4, Problem 31AYU Chapter 4.4, Problem 32AYU Chapter 4.4, Problem 33AYU Chapter 4.4, Problem 34AYU Chapter 4.4, Problem 35AYU Chapter 4.4, Problem 36AYU Chapter 4.4, Problem 37AYU Chapter 4.4, Problem 38AYU Chapter 4.4, Problem 39AYU Chapter 4.4, Problem 40AYU Chapter 4.4, Problem 41AYU Chapter 4.4, Problem 42AYU Chapter 4.4, Problem 43AYU Chapter 4.4, Problem 44AYU Chapter 4.4, Problem 45AYU Chapter 4.4, Problem 46AYU Chapter 4.4, Problem 47AYU Chapter 4.4, Problem 48AYU Chapter 4.4, Problem 49AYU Chapter 4.4, Problem 50AYU Chapter 4.4, Problem 51AYU Chapter 4.4, Problem 52AYU Chapter 4.4, Problem 53AYU Chapter 4.4, Problem 54AYU Chapter 4.4, Problem 55AYU Chapter 4.4, Problem 56AYU Chapter 4.4, Problem 57AYU Chapter 4.4, Problem 58AYU Chapter 4.4, Problem 59AYU Chapter 4.4, Problem 60AYU Chapter 4.4, Problem 61AYU Chapter 4.4, Problem 62AYU Chapter 4.4, Problem 63AYU Chapter 4.4, Problem 64AYU Chapter 4.4, Problem 65AYU Chapter 4.4, Problem 66AYU Chapter 4.4, Problem 67AYU Chapter 4.4, Problem 68AYU Chapter 4.4, Problem 69AYU Chapter 4.4, Problem 70AYU Chapter 4.4, Problem 71AYU Chapter 4.4, Problem 72AYU Chapter 4.4, Problem 73AYU Chapter 4.4, Problem 74AYU Chapter 4.4, Problem 75AYU Chapter 4.4, Problem 76AYU Chapter 4.4, Problem 77AYU Chapter 4.4, Problem 78AYU Chapter 4.4, Problem 79AYU Chapter 4.4, Problem 80AYU Chapter 4.4, Problem 81AYU Chapter 4.4, Problem 82AYU Chapter 4.4, Problem 83AYU Chapter 4.4, Problem 84AYU Chapter 4.4, Problem 85AYU Chapter 4.4, Problem 86AYU Chapter 4.4, Problem 87AYU Chapter 4.4, Problem 88AYU Chapter 4.4, Problem 89AYU Chapter 4.4, Problem 90AYU Chapter 4.4, Problem 91AYU Chapter 4.4, Problem 92AYU Chapter 4.4, Problem 93AYU Chapter 4.4, Problem 94AYU Chapter 4.4, Problem 95AYU Chapter 4.4, Problem 96AYU Chapter 4.4, Problem 97AYU Chapter 4.4, Problem 98AYU Chapter 4.4, Problem 99AYU Chapter 4.4, Problem 100AYU Chapter 4.4, Problem 101AYU Chapter 4.4, Problem 102AYU Chapter 4.4, Problem 103AYU Chapter 4.4, Problem 104AYU Chapter 4.4, Problem 105AYU Chapter 4.4, Problem 106AYU Chapter 4.4, Problem 107AYU Chapter 4.4, Problem 108AYU Chapter 4.4, Problem 109AYU Chapter 4.4, Problem 110AYU Chapter 4.4, Problem 111AYU Chapter 4.4, Problem 112AYU Chapter 4.4, Problem 113AYU Chapter 4.4, Problem 114AYU Chapter 4.4, Problem 115AYU Chapter 4.4, Problem 116AYU Chapter 4.4, Problem 117AYU Chapter 4.4, Problem 118AYU Chapter 4.4, Problem 119AYU Chapter 4.4, Problem 120AYU Chapter 4.4, Problem 121AYU Chapter 4.4, Problem 122AYU Chapter 4.4, Problem 123AYU Chapter 4.4, Problem 124AYU Chapter 4.4, Problem 125AYU Chapter 4.4, Problem 126AYU Chapter 4.4, Problem 127AYU Chapter 4.4, Problem 128AYU Chapter 4.4, Problem 129AYU Chapter 4.4, Problem 130AYU Chapter 4.4, Problem 131AYU Chapter 4.4, Problem 132AYU Chapter 4.4, Problem 133AYU Chapter 4.4, Problem 134AYU Chapter 4.4, Problem 135AYU Chapter 4.4, Problem 136AYU Chapter 4.4, Problem 137AYU Chapter 4.4, Problem 138AYU Chapter 4.4, Problem 139AYU Chapter 4.4, Problem 140AYU Chapter 4.4, Problem 142AYU Chapter 4.4, Problem 141AYU Chapter 4.4, Problem 143AYU Chapter 4.5, Problem 1AYU Chapter 4.5, Problem 2AYU Chapter 4.5, Problem 3AYU Chapter 4.5, Problem 4AYU Chapter 4.5, Problem 5AYU Chapter 4.5, Problem 6AYU Chapter 4.5, Problem 7AYU Chapter 4.5, Problem 8AYU Chapter 4.5, Problem 9AYU Chapter 4.5, Problem 10AYU Chapter 4.5, Problem 11AYU Chapter 4.5, Problem 12AYU Chapter 4.5, Problem 13AYU Chapter 4.5, Problem 14AYU Chapter 4.5, Problem 15AYU Chapter 4.5, Problem 16AYU Chapter 4.5, Problem 17AYU Chapter 4.5, Problem 18AYU Chapter 4.5, Problem 19AYU Chapter 4.5, Problem 20AYU Chapter 4.5, Problem 21AYU Chapter 4.5, Problem 22AYU Chapter 4.5, Problem 23AYU Chapter 4.5, Problem 24AYU Chapter 4.5, Problem 25AYU Chapter 4.5, Problem 26AYU Chapter 4.5, Problem 27AYU Chapter 4.5, Problem 28AYU Chapter 4.5, Problem 29AYU Chapter 4.5, Problem 30AYU Chapter 4.5, Problem 31AYU Chapter 4.5, Problem 32AYU Chapter 4.5, Problem 33AYU Chapter 4.5, Problem 34AYU Chapter 4.5, Problem 35AYU Chapter 4.5, Problem 36AYU Chapter 4.5, Problem 37AYU Chapter 4.5, Problem 38AYU Chapter 4.5, Problem 39AYU Chapter 4.5, Problem 40AYU Chapter 4.5, Problem 41AYU Chapter 4.5, Problem 42AYU Chapter 4.5, Problem 43AYU Chapter 4.5, Problem 44AYU Chapter 4.5, Problem 45AYU Chapter 4.5, Problem 46AYU Chapter 4.5, Problem 47AYU Chapter 4.5, Problem 48AYU Chapter 4.5, Problem 49AYU Chapter 4.5, Problem 50AYU Chapter 4.5, Problem 51AYU Chapter 4.5, Problem 52AYU Chapter 4.5, Problem 53AYU Chapter 4.5, Problem 54AYU Chapter 4.5, Problem 55AYU Chapter 4.5, Problem 56AYU Chapter 4.5, Problem 57AYU Chapter 4.5, Problem 58AYU Chapter 4.5, Problem 59AYU Chapter 4.5, Problem 60AYU Chapter 4.5, Problem 61AYU Chapter 4.5, Problem 62AYU Chapter 4.5, Problem 63AYU Chapter 4.5, Problem 64AYU Chapter 4.5, Problem 65AYU Chapter 4.5, Problem 66AYU Chapter 4.5, Problem 67AYU Chapter 4.5, Problem 68AYU Chapter 4.5, Problem 69AYU Chapter 4.5, Problem 70AYU Chapter 4.5, Problem 71AYU Chapter 4.5, Problem 72AYU Chapter 4.5, Problem 73AYU Chapter 4.5, Problem 74AYU Chapter 4.5, Problem 75AYU Chapter 4.5, Problem 76AYU Chapter 4.5, Problem 77AYU Chapter 4.5, Problem 78AYU Chapter 4.5, Problem 79AYU Chapter 4.5, Problem 80AYU Chapter 4.5, Problem 81AYU Chapter 4.5, Problem 82AYU Chapter 4.5, Problem 83AYU Chapter 4.5, Problem 84AYU Chapter 4.5, Problem 85AYU Chapter 4.5, Problem 86AYU Chapter 4.5, Problem 87AYU Chapter 4.5, Problem 88AYU Chapter 4.5, Problem 89AYU Chapter 4.5, Problem 90AYU Chapter 4.5, Problem 91AYU Chapter 4.5, Problem 92AYU Chapter 4.5, Problem 93AYU Chapter 4.5, Problem 94AYU Chapter 4.5, Problem 95AYU Chapter 4.5, Problem 96AYU Chapter 4.5, Problem 97AYU Chapter 4.5, Problem 98AYU Chapter 4.5, Problem 99AYU Chapter 4.5, Problem 100AYU Chapter 4.5, Problem 101AYU Chapter 4.5, Problem 102AYU Chapter 4.5, Problem 103AYU Chapter 4.5, Problem 104AYU Chapter 4.5, Problem 105AYU Chapter 4.5, Problem 106AYU Chapter 4.5, Problem 107AYU Chapter 4.5, Problem 108AYU Chapter 4.5, Problem 109AYU Chapter 4.5, Problem 110AYU Chapter 4.5, Problem 111AYU Chapter 4.5, Problem 112AYU Chapter 4.5, Problem 113AYU Chapter 4.5, Problem 114AYU Chapter 4.5, Problem 115AYU Chapter 4.5, Problem 116AYU Chapter 4.5, Problem 117AYU Chapter 4.5, Problem 118AYU Chapter 4.6, Problem 1AYU Chapter 4.6, Problem 2AYU Chapter 4.6, Problem 3AYU Chapter 4.6, Problem 4AYU Chapter 4.6, Problem 5AYU Chapter 4.6, Problem 6AYU Chapter 4.6, Problem 7AYU Chapter 4.6, Problem 8AYU Chapter 4.6, Problem 9AYU Chapter 4.6, Problem 10AYU Chapter 4.6, Problem 11AYU Chapter 4.6, Problem 12AYU Chapter 4.6, Problem 13AYU Chapter 4.6, Problem 14AYU Chapter 4.6, Problem 15AYU Chapter 4.6, Problem 16AYU Chapter 4.6, Problem 17AYU Chapter 4.6, Problem 18AYU Chapter 4.6, Problem 19AYU Chapter 4.6, Problem 20AYU Chapter 4.6, Problem 21AYU Chapter 4.6, Problem 22AYU Chapter 4.6, Problem 23AYU Chapter 4.6, Problem 24AYU Chapter 4.6, Problem 25AYU Chapter 4.6, Problem 26AYU Chapter 4.6, Problem 27AYU Chapter 4.6, Problem 28AYU Chapter 4.6, Problem 29AYU Chapter 4.6, Problem 30AYU Chapter 4.6, Problem 31AYU Chapter 4.6, Problem 32AYU Chapter 4.6, Problem 33AYU Chapter 4.6, Problem 34AYU Chapter 4.6, Problem 35AYU Chapter 4.6, Problem 36AYU Chapter 4.6, Problem 37AYU Chapter 4.6, Problem 38AYU Chapter 4.6, Problem 39AYU Chapter 4.6, Problem 40AYU Chapter 4.6, Problem 41AYU Chapter 4.6, Problem 42AYU Chapter 4.6, Problem 43AYU Chapter 4.6, Problem 44AYU Chapter 4.6, Problem 45AYU Chapter 4.6, Problem 46AYU Chapter 4.6, Problem 47AYU Chapter 4.6, Problem 48AYU Chapter 4.6, Problem 49AYU Chapter 4.6, Problem 50AYU Chapter 4.6, Problem 51AYU Chapter 4.6, Problem 52AYU Chapter 4.6, Problem 53AYU Chapter 4.6, Problem 54AYU Chapter 4.6, Problem 55AYU Chapter 4.6, Problem 56AYU Chapter 4.6, Problem 57AYU Chapter 4.6, Problem 58AYU Chapter 4.6, Problem 59AYU Chapter 4.6, Problem 60AYU Chapter 4.6, Problem 61AYU Chapter 4.6, Problem 62AYU Chapter 4.6, Problem 63AYU Chapter 4.6, Problem 64AYU Chapter 4.6, Problem 65AYU Chapter 4.6, Problem 66AYU Chapter 4.6, Problem 67AYU Chapter 4.6, Problem 68AYU Chapter 4.6, Problem 69AYU Chapter 4.6, Problem 70AYU Chapter 4.6, Problem 71AYU Chapter 4.6, Problem 72AYU Chapter 4.6, Problem 73AYU Chapter 4.6, Problem 74AYU Chapter 4.6, Problem 75AYU Chapter 4.6, Problem 76AYU Chapter 4.6, Problem 77AYU Chapter 4.6, Problem 78AYU Chapter 4.6, Problem 79AYU Chapter 4.6, Problem 80AYU Chapter 4.6, Problem 81AYU Chapter 4.6, Problem 82AYU Chapter 4.6, Problem 83AYU Chapter 4.6, Problem 84AYU Chapter 4.6, Problem 85AYU Chapter 4.6, Problem 86AYU Chapter 4.6, Problem 87AYU Chapter 4.6, Problem 88AYU Chapter 4.6, Problem 89AYU Chapter 4.6, Problem 90AYU Chapter 4.6, Problem 91AYU Chapter 4.6, Problem 92AYU Chapter 4.6, Problem 93AYU Chapter 4.6, Problem 94AYU Chapter 4.6, Problem 95AYU Chapter 4.6, Problem 96AYU Chapter 4.6, Problem 97AYU Chapter 4.6, Problem 98AYU Chapter 4.6, Problem 99AYU Chapter 4.6, Problem 100AYU Chapter 4.6, Problem 101AYU Chapter 4.6, Problem 102AYU Chapter 4.6, Problem 103AYU Chapter 4.6, Problem 104AYU Chapter 4.6, Problem 105AYU Chapter 4.6, Problem 106AYU Chapter 4.6, Problem 111AYU Chapter 4.6, Problem 112AYU Chapter 4.6, Problem 113AYU Chapter 4.6, Problem 114AYU Chapter 4.6, Problem 115AYU Chapter 4.7, Problem 1AYU Chapter 4.7, Problem 2AYU Chapter 4.7, Problem 3AYU Chapter 4.7, Problem 4AYU Chapter 4.7, Problem 6AYU Chapter 4.7, Problem 5AYU Chapter 4.7, Problem 7AYU Chapter 4.7, Problem 8AYU Chapter 4.7, Problem 9AYU Chapter 4.7, Problem 11AYU Chapter 4.7, Problem 12AYU Chapter 4.7, Problem 13AYU Chapter 4.7, Problem 14AYU Chapter 4.7, Problem 15AYU Chapter 4.7, Problem 16AYU Chapter 4.7, Problem 17AYU Chapter 4.7, Problem 18AYU Chapter 4.7, Problem 19AYU Chapter 4.7, Problem 20AYU Chapter 4.7, Problem 21AYU Chapter 4.7, Problem 22AYU Chapter 4.7, Problem 23AYU Chapter 4.7, Problem 25AYU Chapter 4.7, Problem 26AYU Chapter 4.7, Problem 27AYU Chapter 4.7, Problem 28AYU Chapter 4.7, Problem 29AYU Chapter 4.7, Problem 30AYU Chapter 4.7, Problem 31AYU Chapter 4.7, Problem 32AYU Chapter 4.7, Problem 33AYU Chapter 4.7, Problem 34AYU Chapter 4.7, Problem 35AYU Chapter 4.7, Problem 36AYU Chapter 4.7, Problem 37AYU Chapter 4.7, Problem 38AYU Chapter 4.7, Problem 39AYU Chapter 4.7, Problem 40AYU Chapter 4.7, Problem 41AYU Chapter 4.7, Problem 42AYU Chapter 4.7, Problem 43AYU Chapter 4.7, Problem 44AYU Chapter 4.7, Problem 45AYU Chapter 4.7, Problem 46AYU Chapter 4.7, Problem 47AYU Chapter 4.7, Problem 48AYU Chapter 4.7, Problem 49AYU Chapter 4.7, Problem 50AYU Chapter 4.7, Problem 51AYU Chapter 4.7, Problem 52AYU Chapter 4.7, Problem 53AYU Chapter 4.7, Problem 54AYU Chapter 4.7, Problem 55AYU Chapter 4.7, Problem 56AYU Chapter 4.7, Problem 57AYU Chapter 4.7, Problem 58AYU Chapter 4.7, Problem 59AYU Chapter 4.7, Problem 60AYU Chapter 4.7, Problem 61AYU Chapter 4.7, Problem 62AYU Chapter 4.7, Problem 63AYU Chapter 4.7, Problem 64AYU Chapter 4.7, Problem 65AYU Chapter 4.7, Problem 66AYU Chapter 4.7, Problem 67AYU Chapter 4.7, Problem 68AYU Chapter 4.7, Problem 69AYU Chapter 4.7, Problem 70AYU Chapter 4.7, Problem 71AYU Chapter 4.7, Problem 72AYU Chapter 4.7, Problem 73AYU Chapter 4.7, Problem 74AYU Chapter 4.7, Problem 75AYU Chapter 4.7, Problem 76AYU Chapter 4.7, Problem 77AYU Chapter 4.7, Problem 78AYU Chapter 4.7, Problem 79AYU Chapter 4.8, Problem 1AYU Chapter 4.8, Problem 2AYU Chapter 4.8, Problem 3AYU Chapter 4.8, Problem 4AYU Chapter 4.8, Problem 5AYU Chapter 4.8, Problem 6AYU Chapter 4.8, Problem 7AYU Chapter 4.8, Problem 8AYU Chapter 4.8, Problem 9AYU Chapter 4.8, Problem 10AYU Chapter 4.8, Problem 11AYU Chapter 4.8, Problem 12AYU Chapter 4.8, Problem 13AYU Chapter 4.8, Problem 14AYU Chapter 4.8, Problem 15AYU Chapter 4.8, Problem 16AYU Chapter 4.8, Problem 17AYU Chapter 4.8, Problem 18AYU Chapter 4.8, Problem 19AYU Chapter 4.8, Problem 20AYU Chapter 4.8, Problem 21AYU Chapter 4.8, Problem 22AYU Chapter 4.8, Problem 23AYU Chapter 4.8, Problem 24AYU Chapter 4.8, Problem 25AYU Chapter 4.8, Problem 26AYU Chapter 4.8, Problem 27AYU Chapter 4.8, Problem 28AYU Chapter 4.8, Problem 29AYU Chapter 4.8, Problem 30AYU Chapter 4.8, Problem 31AYU Chapter 4.8, Problem 32AYU Chapter 4.8, Problem 33AYU Chapter 4.8, Problem 34AYU Chapter 4.8, Problem 35AYU Chapter 4.8, Problem 36AYU Chapter 4.9, Problem 1AYU Chapter 4.9, Problem 2AYU Chapter 4.9, Problem 3AYU Chapter 4.9, Problem 4AYU Chapter 4.9, Problem 5AYU Chapter 4.9, Problem 6AYU Chapter 4.9, Problem 8AYU Chapter 4.9, Problem 9AYU Chapter 4.9, Problem 10AYU Chapter 4.9, Problem 11AYU Chapter 4.9, Problem 12AYU Chapter 4.9, Problem 13AYU Chapter 4.9, Problem 14AYU Chapter 4.9, Problem 16AYU Chapter 4.9, Problem 17AYU Chapter 4.9, Problem 15AYU Chapter 4, Problem 1RE Chapter 4, Problem 2RE Chapter 4, Problem 3RE Chapter 4, Problem 4RE Chapter 4, Problem 5RE Chapter 4, Problem 6RE Chapter 4, Problem 7RE Chapter 4, Problem 8RE Chapter 4, Problem 9RE Chapter 4, Problem 10RE Chapter 4, Problem 11RE Chapter 4, Problem 12RE Chapter 4, Problem 13RE Chapter 4, Problem 14RE Chapter 4, Problem 15RE Chapter 4, Problem 16RE Chapter 4, Problem 17RE Chapter 4, Problem 18RE Chapter 4, Problem 19RE Chapter 4, Problem 20RE Chapter 4, Problem 21RE Chapter 4, Problem 22RE Chapter 4, Problem 23RE Chapter 4, Problem 24RE Chapter 4, Problem 25RE Chapter 4, Problem 26RE Chapter 4, Problem 27RE Chapter 4, Problem 28RE Chapter 4, Problem 29RE Chapter 4, Problem 30RE Chapter 4, Problem 31RE Chapter 4, Problem 32RE Chapter 4, Problem 33RE Chapter 4, Problem 34RE Chapter 4, Problem 35RE Chapter 4, Problem 36RE Chapter 4, Problem 37RE Chapter 4, Problem 38RE Chapter 4, Problem 39RE Chapter 4, Problem 40RE Chapter 4, Problem 41RE Chapter 4, Problem 42RE Chapter 4, Problem 43RE Chapter 4, Problem 44RE Chapter 4, Problem 45RE Chapter 4, Problem 46RE Chapter 4, Problem 47RE Chapter 4, Problem 48RE Chapter 4, Problem 49RE Chapter 4, Problem 50RE Chapter 4, Problem 51RE Chapter 4, Problem 52RE Chapter 4, Problem 53RE Chapter 4, Problem 54RE Chapter 4, Problem 55RE Chapter 4, Problem 56RE Chapter 4, Problem 57RE Chapter 4, Problem 58RE Chapter 4, Problem 59RE Chapter 4, Problem 1CT Chapter 4, Problem 2CT Chapter 4, Problem 3CT Chapter 4, Problem 4CT Chapter 4, Problem 5CT Chapter 4, Problem 6CT Chapter 4, Problem 7CT Chapter 4, Problem 8CT Chapter 4, Problem 9CT Chapter 4, Problem 10CT Chapter 4, Problem 11CT Chapter 4, Problem 12CT Chapter 4, Problem 13CT Chapter 4, Problem 14CT Chapter 4, Problem 15CT Chapter 4, Problem 16CT Chapter 4, Problem 17CT Chapter 4, Problem 18CT Chapter 4, Problem 19CT Chapter 4, Problem 20CT Chapter 4, Problem 21CT Chapter 4, Problem 22CT Chapter 4, Problem 23CT Chapter 4, Problem 1CR Chapter 4, Problem 2CR Chapter 4, Problem 3CR Chapter 4, Problem 4CR Chapter 4, Problem 5CR Chapter 4, Problem 6CR Chapter 4, Problem 7CR Chapter 4, Problem 8CR Chapter 4, Problem 9CR Chapter 4, Problem 10CR Chapter 4, Problem 11CR Chapter 4, Problem 12CR Chapter 4, Problem 13CR Chapter 4, Problem 14CR Chapter 4, Problem 15CR Chapter 4, Problem 16CR
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