Intermediate Algebra (11th edition)

49. 12 51. 10 53. 2 55. 57. 59. 61. 63.x


50. 
    
    
    
    67. 69.C 71.97.381 73.16.863
    
    
    
    


51. 77.7.507 79.3.162 81.1.885 83.A
    85.1,183,000 cycles per sec 87.10 mi 89.392,000


52. (a)1.732 amps (b)2.236 amps 93. orx 95.

Section 8.2 (pages 441– 443)

1.C 3.A 5.H 7.B 9.D 11. 13 13. 9 15. 2 17.

19. 21.It is not a real number. 23. 1000 25. 27 27.


20. 16 31. 33. 35. 37. 39. 41.


21. 
    
    
    
    45. 
        
        
        
        47. 
            
        
        
        
        
    
    
    
    


22. 
    
    
    
    51. 64 53. 64 55. 57.
    
    
    
    


23. 
    
    
    
    61. 9 63. 4 65. 67. 69.
    
    
    
    


24. 
    
    
    
    73. 
        
        
        
        75. 
            
            
            
            77. 
                
                
                
                79. 
                    
                    
                    
                    81. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


25. 
    
    
    
    85. 
        
        
        
        87. 
            
            
            
            89. 
                
            
            
            
            
        
        
        
        
    
    
    
    


26. 
    
    
    
    93. 
        
        
        
        95. 
            
            
            
            97. 
                
                
                
                99. 
                    
                    
                    
                    101. 
                         
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


27. ;;

105.4.5 hr 107.19.0°; The table gives 19°. 109.4.2°; The table
gives 4°. 111.30; 30; They are the same.

Section 8.3 (pages 450–453)

1. or 3 3. or 6 5. 7. 9.


2. 
   
   
   
   13. 
       
       
       
       15. 
           
           
           
           17. 19.This expression
           
           
           
           
       
       
       
       
   
   
   
   

cannot be simplified by the product rule. 21. 23. 25.

27. 
    
    
    
    29. 
        
        
        
        31. 
            
            
            
            33. 
                
                
                
                35. 
                    
                    
                    
                    37. 
                        
                        
                        
                        39. 
                            
                        
                        
                        
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


28. 
    
    
    
    43. 45.This radical cannot be simplified further.
    
    
    
    


29. 
    
    
    
    49. 
        
        
        
        51. 
            
            
            
            53. 
                
                
                
                55. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


30. 
    
    
    
    59. 61.His reasoning was incorrect. Here, 8 is a
    
    
    
    

term, not a factor. 63. 65. 67. 69.

71. 
    
    
    
    73. 
        
        
        
        75. 
            
            
            
            77. 
                
                
                
                79. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


72. 
    
    
    
    83. 
        
        
        
        85. 
            
            
            
            87. 
                
            
            
            
            
        
        
        
        
    
    
    
    


73. 
    
    
    
    91. 
        
        
        
        93. 
            
            
            
            95. 
                
            
            
            
            
        
        
        
        
    
    
    
    


74. 
    
    
    
    99. 
        
        
        
        101. 
             
             
             
             103. 
                  
                  
                  
                  105. 
                       
                  
                  
                  
                  
             
             
             
             
        
        
        
        
    
    
    
    


75. 5 109. 111. 113. 13 115.


76. 217 119. 5 121. 622 123. 25 y^2 - 2 xy+x^2

822 2214 922

25 x^22 x 26432 2126912 26 x^5

423

x^523 x

3

y^52 y

6

• 3 r^3 s^2242 r^3 s^2

x^3 y^4213 x 2 z^2 w^3 - 2 zt^2232 z^2 t 3 x^3 y^4

• 10 m^4 z^25 a^2 b^3 c^412 r^2 t^55 x 22 x - 10 r^525 r

6 k 22 12 xy^42 xy 11 x^3 - 3 t^4

• 3252 2262

4232 - 2232 2235 - 4242 2252

• 422 - 227

223 1222

1

x^3

• 3
  x

23 r^2

2

-^34

p^3

9

2 x

5

23

5

8

11

2310 2314 xy 2433 246 x^3

29 , 236 , 230 214 x 242 pqr

2 a^2 +b^2 = 232 + 42 = 5 a+b= 3 + 4 = 75 Z 7

y5/6z1/3 m1/12 x1/8 x1/24

1

x3/2

x17/20

p+ 2 p^2 k7/4-k3/4 6 + 18 a - 5 x^2 + 5 x

q5/3

9 p7/2

c11/3

b11/4

p^2

1

m1/4n3/4

1

x10/3

x^3 y^8

215 t^8 y x5/12 k2/3

x^1026 x^5

1

A^233 m^4 +^2 k^2 B^2

A 232 y+xB^2

1

A 22 mB^3

A 289 qB^5 - A 232 xB^2

81 5121 259 278 ^10 A^248 B^3

• 3 - 1024

8

9

33

23

, or

27

8

x^1 ,

mi^2

• 9.055

x^5 |x|^51 or|x^5 | 2

• 9 - 5 |x| |z|
  125. 127.15.3 mi 129.27.0 in. 131. 581
  133. and ; , so the statement
  is false. 135.MSX-77: 18.4 in.; MSX-83: 17.0 in.; MSX-60: 14.1 in.
  137. 139.

Section 8.4 (pages 456 – 457)

1. 
   
   
   
   3. 
      
      
      
      5. 
         
         
         
         7. 
            
            
            
            9. 11.The expression
               cannot be simplified further. 13. 15.
            
            
            
            
         
         
         
         
      
      
      
      
   
   
   
   


2. 
   
   
   
   19. 7 21. 23. 25.
   
   
   
   


3. 
   
   
   
   29. 
       
       
       
       31. 
           
           
           
           33. 
               
           
           
           
           
       
       
       
       
   
   
   
   


4. 
   
   
   
   37. 
       
       
       
       39. 
           
       
       
       
       
   
   
   
   


5. 
   
   
   
   43. 
       
       
       
       45. 
           
           
           
           47. 
               
               
               
               49. 
                   
               
               
               
               
           
           
           
           
       
       
       
       
   
   
   
   


6. 
   
   
   
   53. 55.B
   
   
   
   

57.15; Each radical expression simplifies to a whole number.

59.A; 42 m 61. 63.

65. 
    
    
    
    67. 
        
        
        
        69. 
            
        
        
        
        
    
    
    
    

71.

Connections ( page 463) 1. 2.

3. 
   
   
   
   4. ;
   
   
   
   

Instead of multiplying by the conjugate of the numerator, we use the con-

jugate of the denominator.

Section 8.5 (pages 464 – 466)

1.E 3.A 5.D 7. 9. 11.

13. 
    
    
    
    15. 6 17.
    
    
    
    


14. 
    
    
    
    21. 
        
        
        
        23. 
            
        
        
        
        
    
    
    
    


15. 
    
    
    
    27. 
        
        
        
        29. 
            
        
        
        
        
    
    
    
    


16. 
    
    
    
    33. 
        
    
    
    
    


17. 
    
    
    
    37. 
        
        
        
        39. 
            
            
            
            41. 
                
            
            
            
            
        
        
        
        
    
    
    
    


18. 
    
    
    
    45. 
        
        
        
        47. 
            
            
            
            49. 
                
                
                
                51. 
                    
                    
                    
                    53. 
                        
                    
                    
                    
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


19. 
    
    
    
    57. 
        
        
        
        59. 
            
            
            
            61. 
                
            
            
            
            
        
        
        
        
    
    
    
    


20. 
    
    
    
    65. 
        
        
        
        67. 
            
            
            
            69. 
                
                
                
                71. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


21. 
    
    
    
    75. 
        
        
        
        77. 
            
            
            
            79. 
                
                
                
                81. 
                    
                
                
                
                
            
            
            
            
        
        
        
        
    
    
    
    


22. 
    
    
    
    85. 
        
        
        
        87. 
            
        
        
        
        
    
    
    
    


23. 
    
    
    
    91. 
        
    
    
    
    


24. 
    
    
    
    95. 
        
        
        
        97. 
            
        
        
        
        
    
    
    
    

52 kA 22 k- 2 qB

4 k-q

x- 22 xy+y

x-y

4 A 2 x+ 22 yB

x- 4 y

223 + 210 - 322 - 215 2 m- 2

2 A 325 - 223 B

33

622 + 4

7

3 A 4 - 25 B

11

242 yz^3

z

224 x^3

x

x^223 y^2

y

• 
  

232 pr

r

2318

4

2312

3

2318

3

-^4 k^23 z
z

522 my

y^2

12 x^322 xy

y^5

• 5 m^226 mn
  n^2


• 823 k
  k

226 x

x

• 214
  10

214

2

• 723
  12

9215

5

26

2

27 523

4234 y^2 - 19232 y- 5 3 x- 4 4 x-y 226 - 1

6 x+ 32 x- 225 x- 25 9 r-s

26 - 22105 4 - 2336 10

222 + 255 - 214 - 235 8 - 215 9 + 425

• 1 26 - 22 + 23 - 1

326 + 223 2022 - 2

A^32 a+^2 bBA^2 b+^2 aB

b-a

9 a-b

A 2 b- 2 aBA 32 a- 2 bB

9 a-b

bA 32 a- 2 bB

319

(^6) A 825 + (^1) B
4 x- 5
3 x
10 x^3 y^4 - 20 x^2 y a^4 - b^264 x^9 + 144 x^6 + 108 x^3 + 27
A 1225 + 523 B in. A 2422 + 1223 B in.
3 x 232 - 4235
x^3
m 23 m^2
2
5 + 3 x
x^4
522 + 4
522
3
722
6
525
6
4 t 233 st- 3 s 23 st 4 x 23 x+ 6 x 24 x 222 - 2
19242 x 24 xy 9242 a^314 + 3 xy 223 xy^2

• 11 m 22 232 223 x - 723 x^2 y -x 23 xy^2

2025 422 x

• 4 723 14232 5242 2422

22 x^4 - 10 x^38 q^2 - 3 q

29 + 29 = 3 + 3 =6, 24 = 26 Z 2

22106 + 422

A-18 Answers to Selected Exercises

45. 
    
    
    
    47. 
        
    
    
    
    

x

y

0

3

11

–5

f(x) =^3 √x – 3

1 - q,q 2 ; 1 - q,q 2

x

y

0

–3

–8 8

f(x) =^3 √x – 3

1 - q,q 2 ; 1 - q,q 2