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Solutions Manual Algebra and Trigonometry 5th Edition James Stewart, Lothar Redlin, Saleem Watson,9780357753644 (Chapters 1-13).
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Solutions Manual Algebra and Trigonometry 5th Edition James Stewart, Lothar Redlin, Saleem Watson,9780357753644 (Chapters 1-13). ALGEBRA AND TRIGONOMETRY, 5th Edition Solutions / James Stewart 5e Solutions Manual. SOLUTIONS FOR Algebra and Trigonometry 5th Edition.

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SOLUTIONS MANUAL

Algebra and Trigonometry 5th Edition James Stewart




CHAPTER P PREREQUISITES 1
P.1 Modeling the Real World with Algebra 1
P.2 Real Numbers 2
P.3 Integer Exponents and Scientific Notation 7
P.4 Rational Exponents and Radicals 12
P.5 Algebraic Expressions 16
P.6 Factoring 19
P.7 Rational Expressions 24
P.8 Solving Basic Equations 31
P.9 Modeling with Equations 36
Chapter P Review 42
Chapter P Test 48
¥ FOCUS ON MODELING: Making Optimal Decisions 51

,P PREREQUISITES

P.1 MODELING THE REAL WORLD WITH ALGEBRA
1. Using this model, we find that 15 cars have W  4 15  60 wheels. To find the number of cars that have a total of
W
W wheels, we write W  4X  X  .If the cars in a parking lot have a total of 124 wheels, we find that there are
4
X  124
4  31 cars in the lot.
2. If each gallon of gas costs $350, then x gallons of gas costs $35x. Thus, C  35x. We find that 12 gallons of gas would
cost C  35 12  $42.
3. If x  $120 and T  006x, then T  006 120  72. The sales tax is $720.
4. If x  62,000 and T  0005x, then T  0005 62,000  310. The wage tax is $310.
5. If   70, t  35, and d  t, then d  70  35  245. The car has traveled 245 miles.
 
6. V  r 2 h   32 5  45  1414 in3
N 240
7. (a) M    30 miles/gallon 8. (a) T  70  0003h  70  0003 1500  655 F
G 8
175 175 (b) 64  70  0003h  0003h  6  h  2000 ft
(b) 25  G  7 gallons
G  25   
9. (a) V  95S  95 4 km3  38 km3 10. (a) P  006s 3  006 123  1037 hp

(b) 19 km3  95S  S  2 km3 (b) 75  006s 3  s 3  125 so s  5 knots

11. (a) (b) We know that P  30 and we want to find d, so we solve the
Depth (ft) Pressure (lb/in2 ) equation 30  147  045d  153  045d 
0 045 0  147  147 153
d  340. Thus, if the pressure is 30 lb/in2 , the depth
10 045 10  147  192 045
20 045 20  147  237 is 34 ft.

30 045 30  147  282
40 045 40  147  327
50 045 50  147  372
60 045 60  147  417

12. (a) (b) We solve the equation 40x  120,000 
Population Water use (gal) 120,000
x  3000. Thus, the population is about 3000.
0 0 40
1000 40 1000  40,000
2000 40 2000  80,000
3000 40 3000  120,000
4000 40 4000  160,000
5000 40 5000  200,000
13. The number N of cents in q quarters is N  25q.
ab
14. The average A of two numbers, a and b, is A  .
2
1

,2 CHAPTER P Prerequisites

15. The cost C of purchasing x gallons of gas at $350 a gallon is C  35x.
16. The amount T of a 15% tip on a restaurant bill of x dollars is T  015x.
17. The distance d in miles that a car travels in t hours at 60 mi/h is d  60t.
d
18. The speed r of a boat that travels d miles in 3 hours is r  .
3
19. (a) $12  3 $1  $12  $3  $15
(b) The cost C, in dollars, of a pizza with n toppings is C  12  n.
(c) Using the model C  12  n with C  16, we get 16  12  n  n  4. So the pizza has four toppings.
20. (a) 3 30  280 010  90  28  $118
       
daily days cost miles
(b) The cost is    , so C  30n  01m.
rental rented per mile driven
(c) We have C  140 and n  3. Substituting, we get 140  30 3  01m  140  90  01m  50  01m 
m  500. So the rental was driven 500 miles.
21. (a) (i) For an all­electric car, the energy cost of driving x miles is Ce  004x.
(ii) For an average gasoline powered car, the energy cost of driving x miles is C g  012x.
(b) (i) The cost of driving 10,000 miles with an all­electric car is Ce  004 10,000  $400.
(ii) The cost of driving 10,000 miles with a gasoline powered car is C g  012 10,000  $1200.
22. (a) If the width is 20, then the length is 40, so the volume is 20  20  40  16,000 in3 .
(b) In terms of width, V  x  x  2x  2x 3 .
4a  3b  2c  1d  0 f 4a  3b  2c  d
23. (a) The GPA is  .
abcd  f abcd  f
(b) Using a  2  3  6, b  4, c  3  3  9, and d  f  0 in the formula from part (a), we find the GPA to be
463429 54
  284.
649 19


P.2 THE REAL NUMBERS
1. (a) The natural numbers are 1 2 3   .
(b) The numbers     3 2 1 0 are integers but not natural numbers.
p
(c) Any irreducible fraction with q  1 is rational but is not an integer. Examples: 32 ,  12
5 , 1729 .
23
q
p  
(d) Any number which cannot be expressed as a ratio of two integers is irrational. Examples are 2, 3, , and e.
q
2. (a) ab  ba; Commutative Property of Multiplication
(b) a  b  c  a  b  c; Associative Property of Addition
(c) a b  c  ab  ac; Distributive Property
3. (a) In set­builder notation: x  3  x  5 (c) As a graph:
_3 5
(b) In interval notation: 3 5
4. The symbol x stands for the absolute value of the number x. If x is not 0, then the sign of x is always positive.
5. The distance between a and b on the real line is d a b  b  a. So the distance between 5 and 2 is 2  5  7.
6. (a) If a  b, then any interval between a and b (whether or not it contains either endpoint) contains infinitely many
ba
numbers—including, for example a  n for every positive n. (If an interval extends to infinity in either or both
2
directions, then it obviously contains infinitely many numbers.)

, SECTION P.2 The Real Numbers 3

(b) No, because 5 6 does not include 5.
7. (a) No: a  b   b  a  b  a in general.
(b) No; by the Distributive Property, 2 a  5  2a  2 5  2a  10  2a  10.
8. (a) Yes, absolute values (such as the distance between two different numbers) are always positive.
(b) Yes, b  a  a  b.

9. (a) Natural number: 100 10. (a) Natural numbers: 2, 9  3, 10

(b) Integers: 0, 100, 8 (b) Integers: 2,  100
2  50, 9  3, 10
   
(c) Rational numbers: 15, 0, 25 , 271, 314, 100, 8 (c) Rational numbers: 45  29 , 31 , 16666     53 ,
 
(d) Irrational numbers: 7,  2,  100
2 , 9  3, 10
 
(d) Irrational numbers: 2, 314

11. Commutative Property of addition 12. Commutative Property of multiplication

13. Associative Property of addition 14. Distributive Property

15. Distributive Property 16. Distributive Property

17. Commutative Property of multiplication 18. Distributive Property

19. x  3  3  x 20. 7 3x  7  3 x

21. 4 A  B  4A  4B 22. 5x  5y  5 x  y

23. 2 x  y  2x  2y 24. a  b 5  5a  5b
 
25. 5 2x y  5  2 x y  10x y 26. 34 6y  34 6 y  8y

27.  52 2x  4y   25 2x  52 4y  5x  10y 28. 3a b  c  2d  3ab  3ac  6ad

29. (a) 32  57  14 15 29
21  21  21 30. (a) 52  38  16 15 1
40  40  40
5  3  10  9  1
(b) 12 (b) 23  58  16  24
36  15  4  25
8 24 24 24 24 24 24
  2
2
31. (a) 23 6  32  23  6  23  32  4  1  3 32. (a) 2  3  2  32  23  12  3  31  93  13  83
      2
3
(b) 3  14 1  45  12 4  4
1 5  4  13  1  13
5 5 4 5 20 2  1 2  1 2  1
(b) 15 23  51 21  51 21  10 45 9
10  12  3  3
10  15 10  5 10  5

33. (a) 2  3  6 and 2  72  7, so 3  72 34. (a) 3  32  2 and 3  067  201, so 23  067

(b) 6  7 (b) 23  067

(c) 35  27 (c) 06  06

35. (a) False 36. (a) False: 3  173205  17325.

(b) True (b) False

37. (a) True (b) False 38. (a) True (b) True

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