Engineering Mathematics 4 Episode 9 pptx

... Table 40 .1. PRESENTATION OF STATISTICAL DATA 317 39. 5 40 .0 39. 8 39. 5 39. 9 40 .1 40 .0 39. 7 40 .4 39. 3 40 .7 39. 9 40 .2 39. 9 40 .0 40 .1 39. 7 40 .5 40 .5 39. 9 40 .8 40 .0 40 .2 40 .0 39. 9 39. 8 39. 7 39. 5 40 .1 40 .2 40 .6 ... B 74 200 ð 73 199 ð 86 198 D 0.0 590 AB A 74 200 ð 86 199 ð 73 198 D 0.0 590 BA A 86 200 ð 74 199 ð 73 198 D 0.0 59...

Ngày tải lên: 13/08/2014, 08:21

... (a) 1 7 e 3 .46 29 (b) 8.52e 1.2651 (c) 5e 2. 692 1 3e 1.1171  (a) 4. 55 848 (b) 2 .40 444 (c) 8.051 24  6. (a) 5.6823 e 2.1 347 (b) e 2.1127  e 2.1127 2 (c) 4 e 1.7 295  1 e 3.6817  (a) 48 . 041 06 (b) 4. 0 748 2 (c) ... 24. 07 e 0.1762 (a) 1 4 ln 4. 7 291 D 1 4 1.5537 3 49 D 0 .38 843 , correct to 5 significant figures. (b) ln 7.8 693 7.8 693 D 2.06 296 911 7.8 6...

Ngày tải lên: 13/08/2014, 08:21

... theorem: 41 2 D 9 2 CYZ 2 from which YZ D p 41 2  9 2 D 40 units. Thus, sin X = 40 41 ,tanX = 40 9 = 4 4 9 , cosec X = 41 40 = 1 1 40 ,secX = 41 9 = 4 5 9 and cot X = 9 40 Problem 4. If sin ... tangent is 1.76 29 are 60 .44 ° and 180 ° C 60 .44 ° ,i.e. 240 .44 ° 1.76 29 60 .44 240 .44 90 ° 270° 360° x 180° y = tan x 0 y Figure 22.8 90 ° 180° 270...

Ngày tải lên: 13/08/2014, 08:21

... 1toC4 R.m.s. deviation D  1 4 1  4 1 y 2 dx D  1 5  4 1 2x 2  1 2 dx D  1 5  4 1 4x 4  4x 2 C 1dx D  1 5  4x 5 5  4x 3 3 C x  4 1 D        1 5  4 5 4 5  4 3 4 3 C ... e x 2 3 0.20 0 .98 676 0.60 0.88 692 1.00 0.71653 1 .40 0.52031 1.80 0.3 396 0 2.20 0. 199 22 From equation (2):  2 .4 0 e x 2 3 dx ³ 0 .40 [0 .98 676 C0.88 692 C 0.71...

Ngày tải lên: 13/08/2014, 09:20

... switching circuits 48 3 59. 2 Simplifying Boolean expressions 48 8 59. 3 Laws and rules of Boolean algebra 48 8 59 .4 De Morgan’s laws 49 0 59. 5 Karnaugh maps 49 1 59. 6 Logic circuits 49 5 59. 7 Universal logic ... integration by parts 43 6 53 Numerical integration 43 9 53.1 Introduction 43 9 53.2 The trapezoidal rule 43 9 53.3 The mid-ordinate rule 44 1 53 .4 Simp...

Ngày tải lên: 13/08/2014, 08:21

... sides by 5x gives: 5x  3 x  D 5x  4 5  Cancelling gives: 15 D 4x1 15 4 D 4x 4 i.e. x D 15 4 or 3 3 4 Check: LHS D 3 3 3 4 D 3 15 4 D 3  4 15  D 12 15 D 4 5 D RHS (Note that when there is ... ð10 3 (b) 0.375 m 2 (c) 240 ð10 3 Pa  60 ENGINEERING MATHEMATICS Check: LHS D 3 4  2 D 3 6 D 1 2 RHS D 4 3 4 C 4 D 4 12 C4 D 4 8 D 1 2 Hence the solution t...

Ngày tải lên: 13/08/2014, 08:21

... 1 or n P r = n! .n − r /! Thus, 4 P 2 D 4 3 D 12 or 4 P 2 D 4! 4 2! D 4! 2! D 4 ð3 ð2 2 D 12 Problem 19. Evaluate: (a) 7 C 4 (b) 10 C 6 (a) 7 C 4 D 7! 4! 7 4 ! D 7! 4! 3! D 7 ð6 ð5 4 ð3 ð2 4 ð3 ð23 ð2 D ... 5cos x 3  9 f0 D 0 C4 3  e 0 C 5cos0 9 D 59 f1 D 5 3  e 1 .92 C 5cos 1 3  9 ³ 1 14 f2 D 6 3  e 3. 84 C 5cos 2 3  9 ³ 1 64 f3 D 7...

Ngày tải lên: 13/08/2014, 08:21

... x D 6.3680 3.7588 D 1.6 94 2 i.e. tan x D 1.6 94 2 , and x D tan 1 1.6 94 2 D 59 .44 9 ° or 59 ° 27  [Check: LHS D 4sin 59. 44 9 °  20 °  D 4sin 39 .44 9 ° D 2. 542 RHS D 5cosx D 5 cos 59 .44 9 ° D 2. 542 ] Now try the ... is: (a) 2 74. 7 m (b) 36 .4 m (c) 34. 3 m (d) 94 . 0 m 32. (7, 141 ° ) in Cartesian co-ordinates is: (a) (5 .44 , 4. 41) (b) (5 .44 , 4. 41) (c) (5 ....

Ngày tải lên: 13/08/2014, 08:21

... below. t 10 20 30 40 50 60 80 100 s 4. 9 7.6 11.1 15 .4 20 .4 26 .4 40.6 58.0 s 3 t 0. 19 0.23 0.27 0.31 0.35 0. 39 0 .47 0.55 240 ENGINEERING MATHEMATICS Stress s N/cm 2 8 .46 8. 04 7.78 Temperature ... them Let y D 4x 3  8x 2  15x C 9. A table of values is drawn up as shown below: x 2 10 1 2 3 4x 3 32 40 43 2108 8x 2 32 808 32 72 15x 30 15 0 15 30 45 C9 99...

Ngày tải lên: 13/08/2014, 08:21

... [ p 74 6 144 .46 ° ] 4 D p 74 4 6 4 ð 144 .46 ° D 547 6 6 577. 84 ° D 547 6 66 217. 84 ° or 547 6 66 217 ° 15  in polar form. Since r 6  D r cos  C jr sin Â, 547 6 6 217. 84 ° D 547 6 cos 217. 84 ° C j 547 6 ... form. [ p 10 6  18 .43 ° , 3162 6  1 29. 03 ° ] In Problems 4 to 7, express in both polar and rectangular forms: 4. 6 C j5 3 [47 6 .4 6 1 19 .42 ° , 2...

Ngày tải lên: 13/08/2014, 08:21