482 PRACTICAL MATHEMATICS 



(17) 11-226-4-790 sin + 9-956 cos + 0-013 sin 20 + 1-431 cos 20 



+ 0-175 sin 30 + 0-013 cos 30 



(18) 11-724-2-816 sin + 9-949 cos 0-0-001 sin 20 + 1-122 cos 20 



+ 0-037 sin 30 + 0-015 cos 30 



(19) 10-810 + 0-664 'sin + 10-408 cos + 0-794 sin 20 + 0-890 cos 20 



+ 0-022 sin 30 - 0-065 cos 30 



(20) 10-731 + 2-417 sin + 10-236 cos + 1-108 sin 20 + 0-528 cos 20 



- 0-032 sin 30 - 0-073 cos 30 



(21) 13-627 + 3-157 sin + 11-055 cos + 1-657 sin 20 0-065 cos 20 



- 0-188 sin 30 - 0-145 cos 30 



(22) 11-100 + 9-848 sin + 1-736 cos + 0-643 sin 20 + 0-766 cos 20 



(23) 10 + 3-265 sin + 5-030 cos + cos 20 + 0-2 sin 40 



XXIII (pages 423, 424, 425) 



(1) (n + 4)(n + 5), 132 (2) (n - 2)(n - 5), 28 



(3) n s - lOn + 18, 450 (4) i fen* + 9n 2 + 25n + 18 j, 154 



(5) n 4 - lOn 2 + 36, 9036 (6) n 3 - 3n 2 +8n+ 32, 122 

 (7) 10-96, 10-96 (8) 31-68, 31-68 



(9) 257-259456 (10) 1-8527598, 1-8527597 



(11) 1-83409, 2-22510 (12) 0-5827 



(18) 0-8013 (14) 3-813 

 (15) 5-456 (16) 3-340755 



(17) 15-75, 17-0 (18) 0-5252, 0-01560 



(19) 1-0402, 0-02678 



XXIV (pages 444, 445) 



(1) A + B = 12-07 49 , 3 ,, A - B = 5-694 353 o 3r 



(2) A + B = 9-181 222 o 29 ,, A - B = 34-96 53 o u , 



(3) 5-148, 9-982 (4) 6-233 79 <, 66 . (5) 8-933 56 . w 



(6) 10-09 76 . 4r (7) 13-21 100 o 22 , (8) 16-44 321 . 2 , 

 (0) 5-416, 72 47', 35 32', 59 58' 



(10) 29-68, 54 48', 55 4', 54 20' 



(11) 16-90, 78 54', 40 21', 51 41' 



(12) 9-69, 54 23', 55 10', 54 32' 



(13) 1874 137 48 , (14) 130-7 80 o 10 , 



(15) Magnitude = b 2 + a 2 (3 2 + 2ab$*t + 



direction = + tan- 1 (3 ft + 



(16) See paragraph 212. 



