Engineering Mathematics 4 Episode 12 pptx

... 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 ... is given by 3 ð150 D 45 0 kPa m 3 or 45 0 kJ. Hence p v D 45 0, or p D 45 0 v Work done D  6 2 45 0 v dv D [45 0 ln v] 6 2 D 45 0[ln 6 ln 2] D 45 0 ln 6 2 D 45 0 l...

Ngày tải lên: 13/08/2014, 09:20

... (a) 1 7 e 3 .46 29 (b) 8.52e 1.2651 (c) 5e 2.6921 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 1.7295  1 e 3.6817  (a) 48 . 041 06 (b) 4. 0 748 2 (c) ... D 2u C 2a1 Substituting s D 144 , t D 4intos D ut C 1 2 at 2 gives: 144 D 4u C 1 2 a 4 2 i.e. 144 D 4u C 8a2 Multiplying equation (1) by 2 gives: 84...

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...

Ngày tải lên: 13/08/2014, 08:21

... samples of tin were determined and found to be: 34. 61, 34. 57, 34. 40, 34. 63, 34. 63, 34. 51, 34. 49, 34. 61, 34. 52, 34. 55, 34. 58, 34. 53, 34. 44, 34. 48 and 34. 40 Calculate the mean and standard deviation from ... 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...

Ngày tải lên: 13/08/2014, 08:21

... between curves 44 8 54. 1 Area under a curve 44 8 54. 2 Worked problems on the area under a curve 44 9 54. 3 Further worked problems on the area under a curve 45 2 54. 4 The area between curves 45 4 55 Mean ... 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 Simpson’s rule 44 3...

Ngày tải lên: 13/08/2014, 08:21

... 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 D 4 is correct. Problem 12. Solve: p x ... 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...

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...

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

... 2 1 012 34 (b) y D x C 2 x 4 3 2 1 012 34 y 2 1 0 12 345 6 (c) y D x C 5 x 4 3 2 1 012 34 y 12 345 6789 (d) y D x  3 x 4 3 2 1 012 34 y 7 6  5 4 3 2 101 The co-ordinates are plotted ... 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...

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 ... Cj1.000 5 6 45 ° D 5cos 45 °  Cj sin 45 °  D 5cos 45 °  Cj5sin 45 °  D 3.536 j3.536 4 6 120 ° D 4 cos 120 ° C j sin 120 °  D 4 cos 12...

Ngày tải lên: 13/08/2014, 08:21