Solution Manual for Precalculus: Graphs and Models, A Right Triangle Approach, 6th Edition

Name: Solution Manual for Precalculus: Graphs and Models, A Right Triangle Approach, 6th Edition
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Solution Manual for Precalculus: Graphs and Models, A Right Triangle Approach, 6th Edition is your study companion, providing answers to textbook exercises and reinforcing key concepts.

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SOLUTIONS MANUAL
JUDITH A. PENNA
A LGEBRA & T RIGONOMETRY
G RAPHS AND M ODELS
S IXTH E DITION
P RECALCULUS
G RAPHS AND M ODELS ,
A R IGHT T RIANGLE A PPROACH
S IXTH E DITION
Marvin L. Bittinger
Indiana University Purdue University Indianapolis
Judith A. Beecher
David J. Ellenbogen
Community College of Vermont
Judith A. Penna

Contents
Just-in-Time Review . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . 387
Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . 429
Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . 483
Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . 583
Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Chapter R . . . . . . . . . . . . . . . . . . . . . . . . . . 709

Just-in-Time Review
1. Real Numbers
1. Rational numbers: 2
3 , 6, −2.45, 18.4, −11, 3
√27, 5 1
6 , − 8
7 ,
0, √16
2. Rational numbers but not integers: 2
3 , −2.45, 18.4, 5 1
6 ,
− 8
7
3. Irrational numbers: √3, 6
√26, 7.151551555 . . . , −√35, 5
√3
(Although there is a pattern in 7.151551555 . . . , there is
no repeating block of digits.)
4. Integers: 6, −11, 3
√27, 0, √16
5. Whole numbers: 6, 3
√27, 0, √16
6. Real numbers: All of them
2. Properties of Real Numbers
1. −24 + 24 = 0 illustrates the additive inverse property.
2. 7(xy) = (7x)y illustrates the associative property of mul-
tiplication.
3. 9(r − s) = 9r − 9s illustrates a distributive property.
4. 11 + z = z + 11 illustrates the commutative property of
addition.
5. −20 · 1 = −20 illustrates the multiplicative identity prop-
erty.
6. 5(x + y) = (x + y)5 illustrates the commutative property
of multiplication.
7. q + 0 = q illustrates the additive identity property.
8. 75 · 1
75 = 1 illustrates the multiplicative inverse property.
9. (x+y)+w = x+(y+w) illustrates the associative property
of addition.
10. 8(a + b) = 8a + 8b illustrates a distributive property.
3. Order on the Number Line
1. 9 is to the right of −9 on the number line, so it is false
that 9 < −9.
2. −10 is to the left of −1 on the number line, so it is true
that −10 ≤ −1.
3. −5 = −√25, and −√26 is to the left of −√25, or −5, on
the number line. Thus it is true that −√26 < −5.
4. √6 = √6, so it is true that √6 ≤ √6.
5. −30 is to the left of −25 on the number line, so it is false
that −30 > −25.
6. − 4
5 = − 16
20 and − 5
4 = − 25
20 ; − 16
20 is to the right of − 25
20 ,
so it is true that − 4
5 > − 5
4 .
4. Absolute Value
1. | − 98| = 98 (|a| = −a, if a < 0.)
2. |0| = 0 (|a| = a, if a ≥ 0.)
3. |4.7| = 4.7 (|a| = a, if a ≥ 0.)
4.
∣
∣
∣
∣ − 2
3
∣
∣
∣
∣ = 2
3 (|a| = −a, if a < 0.

2 Just-in-Time Review
10. −13 − (−33) = −13 + 33 = 20
11. −60 + 45 = −15
12. 1
2 − 2
3 = 1
2 +
(
− 2
3
)
= 3
6 +
(
− 4
6
)
= − 1
6
13. −24 ÷ 3 = −8
14. −6 + (−16) = −22
15. − 1
2 ÷
(
− 5
8
)
= − 1
2 ·
(
− 8
5
)
= 1 · 8
2 · 5 = 1 · 2/ · 4
2/ · 5 = 4
5
6. Interval Notation
1. This is a closed interval, so we use brackets. Interval no-
tation is [−5, 5].
2. This is a half-open interval. We use a parenthesis on
the left and a bracket on the right. Interval notation is
(−3, −1].
3. This interval is of unlimited extent in the negative direc-
tion, and the endpoint −2 is included. Interval notation is
(−∞, −2].
4. This interval is of unlimited extent in the positive direc-
tion, and the endpoint 3.8 is not included. Interval nota-
tion is (3.8, ∞).
5. {x|7 < x}, or {x|x > 7}.
This interval is of unlimited extent in the positive direction
and the endpoint 7 is not included. Interval notation is
(7, ∞).
6. The endpoints −2 and 2 are not included in the interval,
so we use parentheses. Interval notation is (−2, 2).
7. The endpoints −4 and 5 are not included in the interval,
so we use parentheses. Interval notation is (−4, 5).
8. The interval is of unlimited extent in the positive direc-
tion, and the endpoint 1.7 is included. Internal notation
is [1.7, ∞).
9. The endpoint −5 is not included in the interval, so we use a
parenthesis before −5. The endpoint −2 is included in the
interval, so we use a bracket after −2. Interval notation is
(−5, −2].
10. This interval is of unlimited extent in the negative direc-
tion, and the endpoint √5 is not included. Interval nota-
tion is (−∞, √5).
7. Integers as Exponents
1. 3−6 = 1
36 Using a−m = 1
am
2. 1
(0.2)−5 = (0.2)5 Using a−m = 1
am
3. w−4
z−9 = z9
w4 Using a−m
b−n = bn
am
4.
( z
y
)2
= z2
y2 Raising a quotient to a power
5. 1000 = 1 Using a0 = 1, a = 0
6. a5
a−3 = a5−(−3) = a5+3 = a8 Using the quotient rule
7. (2xy3)(−3x−5y) = 2(−3)x · x−5 · y3 · y
= −6x1+(−5)y3+1
= −6x−4y4, or − 6y4
x4
8. x−4 · x−7 = x−4+(−7) = x−11, or 1
x11
9. (mn)−6 = m−6n−6, or 1
m6n6
10. (t−5)4 = t−5·4 = t−20, or 1
t20
8. Scientific Notation
1. Convert 18,500,000 to scientific notation.
We want the decimal point to be positioned between the
1 and the 8, so we move it 7 places to the left. Since
18,500,000 is greater than 10, the exponent must be posi-
tive.
18, 500, 000 = 1.85 × 107
2. Convert 0.000786 to scientific notation.
We want the decimal point to be positioned between the
7 and the 8, so we move it 4 places to the right. Since
0.000786 is between 0 and 1, the exponent must be nega-
tive.
0.000786 = 7.86 × 10−4
3. Convert 0.0000000023 to scientific notation.
We want the decimal point to be positioned between the
2 and the 3, so we move it 9 places to the right. Since
0.0000000023 is between 0 and 1, the exponent must be
negative.
0.0000000023 = 2.3 × 10−9
4. Convert 8,927,000,000 to scientific notation.
We want the decimal point to be positioned between the
8 and the 9, so we move it 9 places to the left. Since
8,927,000,000 is greater than 10, the exponent must be
positive.
8, 927, 000, 000 = 8.927 × 109
5. Convert 4

Just-in-Time Review 3
6. Convert 5.17 × 106 to decimal notation.
The exponent is positive, so the number is greater than
10. We move the decimal point 6 places to the right.
5.17 × 106 = 5, 170, 000
7. Convert 6.203 × 1011 to decimal notation.
The exponent is positive, so the number is greater than
10. We move the decimal point 11 places to the right.
6.203 × 1011 = 620, 300, 000, 000
8. Convert 2.94 × 10−5 to scientific notation.
The exponent is negative, so the number is between 0 and
1. We move the decimal point 5 places to the left.
2.94 × 10−5 = 0.0000294
9. Order of Operations
1. 3 + 18 ÷ 6 − 3 = 3 + 3 − 3 Dividing
= 6 − 3 = 3 Adding and subtracting
2. = 5 · 3 + 8 · 32 + 4(6 − 2)
= 5 · 3 + 8 · 32 + 4 · 4 Working inside parentheses
= 5 · 3 + 8 · 9 + 4 · 4 Evaluating 32
= 15 + 72 + 16 Multiplying
= 87 + 16 Adding in order
= 103 from left to right
3. 5[3 − 8 · 32 + 4 · 6

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4
2
2
4
4224 x
y
(1, 4)
(3, 5)
(0, 2)(4, 0)
(2, 2)
22 42
2
4
22
24
24
y
x
(25, 0)
(2, 24)
(1, 4)
(0, 3)
(24, 22)
4
2
2
4
424 x
y
(5, 1)
(2, 3)
(0, 1) (5, 1)
(2, 1)
22 42
2
4
22
24
24
y
x
(25, 2)
(4, 23)
(0, 21)
(2, 0)
(21, 25)
Chapter 1
Graphs, Functions, and Models
Exercise Set 1.1
1. Point A is located 5 units to the left of the y-axis and
4 units up from the x-axis, so its coordinates are (−5, 4).
Point B is located 2 units to the right of the y-axis and
2 units down from the x-axis, so its coordinates are (2, −2).
Point Cis located 0 units to the right or left of the y-axis
and 5 units down from the x-axis, so its coordinates are
(0, −5).
Point D is located 3 units to the right of the y-axis and
5 units up from the x-axis, so its coordinates are (3, 5).
Point E is located 5 units to the left of the y-axis and
4 units down from the

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