Engineering Mathematics 4 Episode 11 pps

... figures (a)  2 1 4 e 2x dx D  4 2 e 2x  2 1 D 2[ e 2x ] 2 1 D 2[ e 4  e 2 ] D 2[ 54. 5982 7.3891] D 94 .42 (b)  4 1 3 4u du D  3 4 ln u  4 1 D 3 4 [ln 4 ln 1] D 3 4 [1.3863 0] D 1 . 040 Now try ... Evaluate:   4 0 4cos 4  dÂ, correct to 4 significant figures   4 0 4cos 4  d D 4   4 0 cos 2 Â 2 d D 4   4 0  1 2 1 Ccos 2Â  2 d D ...

Ngày tải lên: 13/08/2014, 09:20

... 24 14 21 10101 25 15 22 1 0110 26 16 23 1 0111 27 17 24 110 00 30 18 25 110 01 31 19 26 110 10 32 1A 27 110 11 33 1B 28 111 00 34 1C 29 111 01 35 1D 30 111 10 36 1E 31 111 11 37 1F 32 100000 40 20 1A4E 16 D ... 4 4 5 0101 5 5 6 0110 6 6 7 0111 7 7 8 1000 10 8 9 1001 11 9 10 1010 12 A 11 1 011 13 B 12 110 0 14 C 13 110 1 15 D 14 111 0 16 E 15 111 1 17 F 16 10000 20...

Ngày tải lên: 13/08/2014, 08:21

... 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 .44 , 4. 41) (d) (5 .44 , 4. 41) 33. If tanA D 1 .42 76, sec ... x D 6.3680 3.7588 D 1.6 942 i.e. tan x D 1.6 942 , and x D tan 1 1.6 942 D 59 .44 9 ° or 59 ° 27  [Check: LHS D 4sin59. 44 9 °  20 °  D 4sin39 .44 9 ° D 2. 542 RHS D 5co...

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 ... as shown below: I 2.2 3.6 4. 1 5.6 6.8 lg I 0. 342 0.556 0.613 0. 748 0.833 P 116 311 40 3 753 111 0 lg P 2.0 64 2 .49 3 2.605 2.877 3. 045 A graph of lg P against lg I is...

Ngày tải lên: 13/08/2014, 08:21

... 171.1 xy x 2 y 2 45 9.2 43 .2 48 86  744 .8 25.7 21580 8.9 9 .4 8 4. 3 0 3733 46 .5 3.7 581  242 .1 24. 3 241 1 6 74. 8 62.9 7 242  xy D2172  x 2 D 169.2  y 2 D 40 441 Thus r D 2172 p 169.2 40 441 D −0.830 This ... 20 144 11 25 121 9 30 81 7 35 49 5 40 25  X D 145  Y D 180  X 2 D 46 01 XY Y 2 275 25 300 100 240 225 240 40 0 275 625 270 900 245 1225 200 1600 ...

Ngày tải lên: 13/08/2014, 09:20

... second moment of area about axis QQ, I QQ D 3 84 C 48 10 2 D 51 84 cm 4 Radius of gyration, k QQ D  I QQ area D  51 84 48 D 10 .4cm 49 8 ENGINEERING MATHEMATICS the techniques introduced in Sections ... matrices (a)  2 1  74  and  30 7 4  and (b)  31 4 43 1 14 3  and  275 21 0 63 4  . (a) Adding the corresponding elements gives:  2 1  74  C  30 7 4 ...

Ngày tải lên: 13/08/2014, 09:20

... 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

... (a) 1 7 e 3 .46 29 (b) 8.52e 1.2651 (c) 5e 2.6921 3e 1 .117 1  (a) 4. 55 848 (b) 2 .40 444 (c) 8.051 24  6. (a) 5.6823 e 2.1 347 (b) e 2 .112 7  e 2 .112 7 2 (c) 4 e 1.7295  1 e 3.6817  (a) 48 . 041 06 (b) 4. 0 748 2 (c) ... equal 11x, the only combination to give this is C1and 4, i.e. 3x 2  11x  4 D 3x C 1x  4 1 04 ENGINEERING MATHEMATICS i.e. t D 40 0 10 3...

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 ... decimal places. [2. 742 , 4. 742 ] 2. 3x 3  10x D 14, correct to 4 significant figures. [2.313] 3. x 4  3x 3 C 7x D 12, correct to 3 decimal places. [1...

Ngày tải lên: 13/08/2014, 08:21

... 1.0724x 0. 344 3x C 0. 344 3120 D 1.0724x 0. 344 3120 D 1.07 24 0. 344 3x 41 .316 D 0.7281x x D 41 .316 0.7281 D 56. 74 m From equation (2), height of building, h D 1.0724x D 1.07 24 56. 74 D 60 .85 ... 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...

Ngày tải lên: 13/08/2014, 08:21