344 Basic Engineering Mathematics
Chapter 10
Exercise 39 (page 69)
1.x^2 + 5 x+ 6 2. 2 x^2 + 9 x+ 4- 4 x^2 + 12 x+ 9 4. 2 j^2 + 2 j− 12
- 4 x^2 + 22 x+ 30 6. 2 pqr+p^2 q^2 +r^2
7.a^2 + 2 ab+b^2 8. x^2 + 12 x+ 36
9.a^2 − 2 ac+c^2 10. 25 x^2 + 30 x+ 9 - 4 x^2 − 24 x+ 36 12. 4 x^2 − 9
- 64 x^2 + 64 x+ 16 14.r^2 s^2 + 2 rst+t^2
- 3 ab− 6 a^2 16. 2 x^2 − 2 xy
- 2 a^2 − 3 ab− 5 b^2 18. 13 p− 7 q
- 7 x−y− 4 z 20. 4 a^2 − 25 b^2
21.x^2 − 4 xy+ 4 y^2 22. 9 a^2 − 6 ab+b^2 - 0 24. 4 −a
- 4 ab− 8 a^2 26. 3 xy+ 9 x^2 y− 15 x^2
- 2 + 5 b^2 28. 11 q− 2 p
Exercise 40 (page 71)- 2 (x+ 2 ) 2. 2 x(y− 4 z)
- p(b+ 2 c) 4. 2 x( 1 + 2 y)
- 4 d(d− 3 f^5 ) 6. 4 x( 1 + 2 x)
- 2 q(q+ 4 n) 8.x( 1 + 3 x+ 5 x^2 )
9.bc(a+b^2 ) 10.r(s+p+t) - 3 xy(xy^3 − 5 y+ 6 ) 12. 2 pq^2
(
2 p^2 − 5 q)- 7 ab( 3 ab− 4 ) 14. 2 xy(y+ 3 x+ 4 x^2 )
- 2 xy
(
x− 2 y^2 + 4 x^2 y^3)- 7 y( 4 +y+ 2 x)
17.3 x
y- 0 19.
2 r
t
20.(a+b)(y+ 1 ) 21.(p+q)(x+y)
22.(x−y)(a+b) 23.(a− 2 b)( 2 x+ 3 y)Exercise 41 (page 72)- 2 x+ 8 x^2 2. 12 y^2 − 3 y
- 4 b− 15 b^2 4. 4 + 3 a
5.3
2− 4 x 6. 1- 10 y^2 − 3 y+
1
4- 9 x^2 +
1
3− 4 x- 6 a^2 + 5 a−
1
7- − 15 t
11.1
5−x−x^2 12. 10 a^2 − 3 a+ 2Chapter 11
Exercise 42 (page 75)- 1 2. 2 3. 6 4. − 4 5. 2
- 1 7. 2 8.
1
2- 0 10. 3
- 2 12.− 10 13. 6 14. − 2 15. 2. 5
- 2 17. 6 18. − 3
Exercise 43 (page 76)- 5 2.− 2 3. − 4
1
2- 2 5. 12
- 15 7.− 4 8. 5
1
3- 2 10. 13
- − 10 12. 2 13. 3 14.− 11 15.− 6
- 9 17. 6
1
4 - 3 19. 4 20. 10
- ± 12 22.− 3
1
3- ± 3 24.± 4
Exercise 44 (page 79)- 10 −^7 2.8m/s^2 3. 3. 472
- (a) 1. 8 (b) 30
- digital camera battery £9, camcorder battery £14
- 800 7.30m/s^2
Exercise 45 (page 80)- 12cm,240cm^2 2. 0. 004 3. 30
- 45 ◦C 5. 50 6.£312,£240
- 30kg 8.12m,8m 9. 3 .5N
Chapter 12
Exercise 46 (page 84)- d=c−e−a−b 2. x=
y
7 - v=
c
p4.a=v−u
t- R=
V
I- y=
1
3(t−x)- r=
c
2 π- x=
y−c
m