Basic Engineering Mathematics, Fifth Edition

346 Basic Engineering Mathematics

5.x= 2 ,y= 4 ,z= 5 6. x= 1 ,y= 6 ,z= 7

7.x= 5 ,y= 4 ,z= 2 8. x=− 4 ,y= 3 ,z= 2

9.x= 1. 5 ,y= 2. 5 ,z= 4. 5

10.i 1 =− 5 ,i 2 =− 4 ,i 3 = 2

11. F 1 = 2 ,F 2 =− 3 F 3 = 4

Chapter 14

Exercise 54 (page 104)

1.4or− 4 2.4or− 8 3.2or− 6

4.− 1 .5or1. 5 5.0or−

4

3

6.2or− 2

7. 4 8.− 5 9. 1
   10.−2or− 3 11.−3or− 7 12.2or− 1
   13.4or− 3 14.2or7 15.− 4


8. 2 17.− 3 18.3or− 3

19.−2or−

2

3

20.− 1. 5 21.

1

8

or−

1

8

22.4or− 7 23.−1or1. 5 24.

1

2

or

1

3

25.

1

2

or−

4

5

26. 1

1

3

or−

1

7

27.

3

8

or− 2

28.

2

5

or− 3 29.

4

3

or−

1

2

30.

5

4

or−

3

2

31.x^2 − 4 x+ 3 = 0 32. x^2 + 3 x− 10 = 0

33.x^2 + 5 x+ 4 = 0 34. 4 x^2 − 8 x− 5 = 0

35.x^2 − 36 = 0 36. x^2 − 1. 7 x− 1. 68 = 0

Exercise 55 (page 106)

1.− 3 .732 or− 0. 268 2. − 3 .137 or 0. 637

3. 1 .468 or− 1. 135 4. 1 .290 or 0. 310


4. 2 .443 or 0. 307 6. − 2 .851 or 0. 351

Exercise 56 (page 107)

1. 0 .637 or− 3. 137 2. 0 .296 or− 0. 792


2. 2 .781 or 0. 719 4. 0 .443 or− 1. 693


3. 3 .608 or− 1. 108 6. 1 .434 or 0. 232


4. 0 .851 or− 2. 351 8. 2 .086 or− 0. 086


5. 1 .481 or− 1. 081 10. 4 .176 or− 1. 676
   11.4or2. 167 12. 7 .141 or− 3. 641


6. 4 .562 or 0. 438

Exercise 57 (page 109)

1. 1 .191s 2. 0 .345A or 0.905A 3. 7 .84cm


2. 0 .619m or 19.38m 5. 0. 0133


3. 1 .066m 7. 86 .78cm


4. 1 .835m or 18.165m 9. 7m


5. 12ohms,28ohms

Exercise 58 (page 110)

1.x= 1 ,y=3andx=− 3 ,y= 7

2.x=

2

5

,y=−

1

5

and− 1

2

3

,y=− 4

1

3

3.x= 0 ,y=4andx= 3 ,y= 1

Chapter 15

Exercise 59 (page 112)

1. 4 2. 4 3. 3 4.− 3 5.

1

3

6. 3 7. 2 8. − 2 9. 1

1

2

10.

1

3

11. 2 12. 10000 13. 100000 14. 9 15.

1

32

16. 
    
    
    
    0. 01 17.
    
    
    
    

1

16

18. e^3

Exercise 60 (page 115)

1. log6 2.log15 3. log2 4. log3


2. log12 6.log500 7. log100 8. log6


3. log10 10.log1= 0 11. log2


4. log243 or log3^5 or 5log3


5. log16 or log2^4 or 4log2


6. log64 or log2^6 or 6log2


7. 
   
   
   
   0. 5 16. 1. 5 17. x= 2. 5 18. t= 8
   
   
   
   


8. b= 2 20.x= 2 21. a= 6 22. x= 5

Exercise 61 (page 116)

1. 
   
   
   
   1. 690 2. 3. 170 3. 0. 2696 4. 6. 058 5. 2. 251
   
   
   
   


2. 
   
   
   
   3. 959 7. 2. 542 8.− 0. 3272 9. 316. 2