Solutions for Algebra and Trigonometry 5th Edition 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 $350, then x gallons of gas costs $35x. Thus, C 35x. We find that 12 gallons of gas would
cost C 35 12 $42.
3. If x $120 and T 006x, then T 006 120 72. The sales tax is $720.
4. If x 62,000 and T 0005x, then T 0005 62,000 310. The wage tax is $310.
5. If 70, t 35, and d t, then d 70 35 245. The car has traveled 245 miles.
6. V r 2 h 32 5 45 1414 in3
N 240
7. (a) M 30 miles/gallon 8. (a) T 70 0003h 70 0003 1500 655 F
G 8
175 175 (b) 64 70 0003h 0003h 6 h 2000 ft
(b) 25 G 7 gallons
G 25
9. (a) V 95S 95 4 km3 38 km3 10. (a) P 006s 3 006 123 1037 hp
(b) 19 km3 95S S 2 km3 (b) 75 006s 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 30 147 045d 153 045d
0 045 0 147 147 153
d 340. Thus, if the pressure is 30 lb/in2 , the depth
10 045 10 147 192 045
20 045 20 147 237 is 34 ft.
30 045 30 147 282
40 045 40 147 327
50 045 50 147 372
60 045 60 147 417
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.
ab
14. The average A of two numbers, a and b, is A .
2
1
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 $350, then x gallons of gas costs $35x. Thus, C 35x. We find that 12 gallons of gas would
cost C 35 12 $42.
3. If x $120 and T 006x, then T 006 120 72. The sales tax is $720.
4. If x 62,000 and T 0005x, then T 0005 62,000 310. The wage tax is $310.
5. If 70, t 35, and d t, then d 70 35 245. The car has traveled 245 miles.
6. V r 2 h 32 5 45 1414 in3
N 240
7. (a) M 30 miles/gallon 8. (a) T 70 0003h 70 0003 1500 655 F
G 8
175 175 (b) 64 70 0003h 0003h 6 h 2000 ft
(b) 25 G 7 gallons
G 25
9. (a) V 95S 95 4 km3 38 km3 10. (a) P 006s 3 006 123 1037 hp
(b) 19 km3 95S S 2 km3 (b) 75 006s 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 30 147 045d 153 045d
0 045 0 147 147 153
d 340. Thus, if the pressure is 30 lb/in2 , the depth
10 045 10 147 192 045
20 045 20 147 237 is 34 ft.
30 045 30 147 282
40 045 40 147 327
50 045 50 147 372
60 045 60 147 417
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.
ab
14. The average A of two numbers, a and b, is A .
2
1
