354 Basic Engineering Mathematics
3.Mean 4.7225, median 4.72, mode 4.72
4.Mean 115.2, median 126.4, no modeExercise 126 (page 301)- 23 .85kg 2. 171 .7cm
3.Mean 89.5, median 89, mode 89.2
4.Mean 2.02158cm, median 2.02152cm, mode
2 .02167cm
Exercise 127 (page 303)
1.4.60 2. 2. 83 μF
3.Mean 34.53MPa, standard deviation 0.07474MPa- 0 .296kg 5. 9 .394cm 6. 0 .00544cm
Exercise 128 (page 304)
1.30, 25.5, 33.5 days 2.27, 26, 33 faults- Q 1 = 164 .5cm,Q 2 = 172 .5cm,Q 3 =179cm,
7 .25cm
4.37 and 38; 40 and 41 5.40, 40, 41; 50, 51, 51
Chapter 33
Exercise 129 (page 308)1.(a)2
9or 0.2222 (b)7
9or 0.77782.(a)23
139or 0.1655 (b)47
139or 0.3381(c)
69
139or 0.49643.(a)1
6(b)1
6(c)1
364.5
36
5.(a)2
5(b)1
5(c)4
15(d)13
15
6.(a)1
250(b)1
200(c)9
1000(d)1
50000Exercise 130 (page 311)
1.(a) 0.6 (b) 0.2 (c) 0.15 2.(a) 0.64 (b) 0.32
3.0.0768 4.(a) 0.4912 (b) 0.4211
5.(a) 89.38% (b) 10.25%
6.(a) 0.0227 (b) 0.0234 (c) 0.0169Chapter 34
Exercise 131 (page 313)
1.1, 5, 21, 9, 61 2.0, 11,−10, 21 3.proofExercise 132 (page 314)
1.16, 8Exercise 133 (page 317)- 28 x^3 2. 2 3. 2 x− 1
- 6 x^2 − 5 5.−
1
x^2
- 1 +
2
x^3- 15 x^4 − 8 x^3 + 15 x^2 + 2 x
- −
6
x^4- 4 − 8 x 11.
1
2√
x12.3
2√
t 13.−3
x^4- 1 +
3
2√
x- 2 x− 2
- −
10
x^3+7
2√
x^9- 6 t− 12 20. 1 −
4
x^2- (a) 6 (b)
1
6(c) 3 (d)−1
16(e)−1
4(f )− 7- 12 x−3(a)−15 (b) 21
- 6 x^2 + 6 x− 4 , 32 24.− 6 x^2 + 4 ,− 9. 5
Exercise 134 (page 320)- (a) 12cos3x(b)−12sin6x
- 6cos3θ+10sin2θ 3. − 0. 707 4. − 3
- 270 .2A/s 6. 1393 .4V/s
- 12cos( 4 t+ 0. 12 )+6sin( 3 t− 0. 72 )
Exercise 135 (page 321)- (a) 15e^3 x(b)−
4
7 e^2 x2.5
θ−4
θ=1
θ- 16
- 2.80 5. 664
Exercise 136 (page 322)
1.(a)−1 (b) 16
2.−4
x^3+2
x+10sin5x−12cos2x+6
e^3 xExercise 137 (page 322)- (a) 36x^2 + 12 x(b) 72x+ 12 2. 8 +
2
x^3- (a)
4
5−12
t^5+6
t^3+1
4√
t^3(b)− 4. 95- −12sin2t−cost 5. −
2
θ^2