Engineering Mathematics 4 Episode 2 docx

... x 2y 2 (ii) 3a b 2  (i) x 2  4xy C4y 2 (ii) 9a 2  6ab C b 2  7. 3a C2[a  3a  2 ] [4 a] 8. 2 5[aa  2b  a  b 2 ] [2 C5b 2 ] 9. 24 p  [2 35p q 2 p C2q C3q] [11q  2p] In ... following: 1. 2x ł4x C 6x  1 2 C 6x  2. 2x ł4x C6x  1 5  3. 3a 2a ð4a C a [4a1 2a] 4. 3a 2a4a C a [a3 10a] 5. 2y C 4 ł6y C 3 4 5y  2 3y  3y C 12 ...

Ngày tải lên: 13/08/2014, 08:21

... ð 123 .69 ° , by De Moivre’s theorem D 21 97 6 7 42 . 14 ° D 21 97 6 3 82. 14 ° since 7 42 . 14 Á 7 42 . 14 °  360 ° D 3 82. 14 °  D 21 97 66 22 . 14 ° since 3 82. 14 ° Á 3 82. 14 °  360 ° D 22 . 14 °  Problem 2. ... Cj5 4 D [ 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 21 7. 84 ° or 547 6 66 21 7 ° 15  in polar form....

Ngày tải lên: 13/08/2014, 08:21

... of (a) 2 3 ð 2 4 2 7 ð 2 5 and (b) 3 2  3 3 ð 3 9 From the laws of indices: (a) 2 3 ð 2 4 2 7 ð 2 5 D 2 3C4 2 7C5 D 2 7 2 12 D 2 7 12 D 2 5 D 1 2 5 D 1 32 (b) 3 2  3 3 ð 3 9 D 3 2 3 3 1C9 D 3 6 3 10 D ... š3(c)š 1 2 (d) š 2 3  In Problems 4 to 8, evaluate the expressions given. 4. 9 2 ð 7 4 3 4 ð 7 4 C 3 3 ð 7 2  147...

Ngày tải lên: 13/08/2014, 08:21

... MATHEMATICS (b) 5  e 0 .25  e 0 .25 e 0 .25 C e 0 .25  D 5  1 .2 840 2 541  0.77880078 1 .2 840 2 541 C 0.77880078  D 5  0.50 52 24 6 2. 0 628 261  D 1 .2 24 6 , correct to 4 decimal places Problem 4. The instantaneous ... x 2 C 4x  32 D 0 [4, 8] 2. x 2  16 D 0 [4, 4] 3. x C 2 2 D 16 [2, 6] 4. 2x 2  x  3 D 0  1, 1 1 2  5. 6x 2  5x C 1...

Ngày tải lên: 13/08/2014, 08:21

... Cx n , 2  1 C x 4  1 2 D 2  1 C  1 2   x 4  C  1 /2  1 /2  2!  x 4  2 C  1 /2  1 /2  3 /2  3!  x 4  3 CÐÐÐ  D 2  1 C x 8  x 2 128 C x 3 10 24 ÐÐÐ  = 2 Y x 4 − x 2 64 Y x 3 5 12 −··· This ... frequency, f 1 D 1 2  k 1 I 1 D 1 2 k 1 2 1 I  1 2 1 D 1 2 [1 C0. 04 k] 1 2 [1 0. 02 I]  1 2 D 1 2 1 C0. 04 1...

Ngày tải lên: 13/08/2014, 08:21

... equations (1) and (2) gives: 0. 344 3x C 120  D 1.0 724 x 0. 344 3x C 0. 344 3 120  D 1.0 724 x 0. 344 3 120  D 1.07 24 0. 344 3x 41 .316 D 0. 728 1x x D 41 .316 0. 728 1 D 56. 74 m From equation (2) , height of ... 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 ,s...

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 9 42 i.e. tan x D 1.6 9 42 , and x D tan 1 1.6 9 42 D 59 .44 9 ° or 59 ° 27  [Check: LHS D 4sin59. 44 9 °  20 °  D 4sin39 .44 9 ° D 2. 5...

Ngày tải lên: 13/08/2014, 08:21

... 9 C7 .2 7 .2 7 .2 7 .2 7 .2 y D5x 2 C 9x C 7 .2 6.8 1 .45 7 .2 11 .2 x 22 .53 5x 2 20 31 .25 45 C9x 18 22 .5 27 C7 .2 7 .2 7 .2 7 .2 y D5x 2 C 9x C 7 .2 5 .2 1.55 10.8 Problem 5. Plot a graph of: y D 2x 2 and hence ... y D 2x 2  3x  4and y D 2 4x y D 2x 2 3x 4 is a parabola and a table of values is drawn up as shown below: x 2 10 12 3 2x 2 820...

Ngày tải lên: 13/08/2014, 08:21

... 22 .4 22 .8 21 .5 22 .6 21 .1 21 .6 22 .3 22 .9 20 .5 21 .8 22 .2 21.0 21 .7 22 .5 20 .7 23 .2 22. 9 21 .7 21 .4 22 .1 22 .2 22. 3 21 .3 22 .1 21 .8 22 .0 22 .7 21 .7 21 .9 21 .1 22 .6 21 .4 22 .4 22 .3 20 .9 22 .8 21 .2 22. 7 21 .6 22 .2 ... 48 places and the results are as shown. 2. 10 2. 29 2. 32 2 .21 2. 14 2. 22 2 .28 2. 18 2. 17 2...

Ngày tải lên: 13/08/2014, 08:21

... Y Y 2 12 7 .25 6 .25 5 9 4. 25 9 .25 3 13 6 .25 5 .25 12 21 2. 75 2. 75 14 17 4. 75 1 .25 7 22 2. 25 3.75 3 31 6 .25 12. 75 28 47 18.75 28 .75 14 17 4. 75 1 .25 7 10 2. 25 8 .25 3 9 6 .25 9 .25 13 ... 35 49 5 40 25  X D 145  Y D 180  X 2 D 46 01 XY Y 2 275 25 300 100 24 0 22 5 24 0 40 0 27 5 625 27 0 900 24 5 122 5 20 0 1600  XY...

Ngày tải lên: 13/08/2014, 09:20