(2) 1.8 mi. 4 fur. 10 po. 4 yds. 1 ft. 1 in. ; 2. 363 lbs. 11 oz. 8 dwts. 6 grs. (3) 2 qrs. 1 lb. (5) £188 10s. 513 (8) 5 dwts. 39 grs. (4) 11 lbs. 7 oz. 16 dwts. (6) £524 13s. 9d. 931 (9) 1. 13; 2. 221; 3. 2. (7) 18 days. (10) 1. 02016; 2. 286·5; 3. 100·032. (11) 52 sq. ft. (12) 11a. II. (a.) 119 160' (2) 1878704 (4) 1. 207 c. yds. 17 c. ft. 409 c. in.; 2. £449 6s. 7 d. (5) 84 ft. 71 1568 (9) 1. ; 2. 3; 3. (10) 1. 16; 2. 5136; 3. 88. 9d. (3) 12151 (6) £129 15s. 10d. (7) 357 days. (11) 26. (12) £55. (13) £41 118. 5 d. (10) 1. 00002; 628000; 2. 1.7395; 3. 821875. (8) 7 days. (1) 1 ton 18 cwt. 1 qr. 11 lbs. ; 335 tons 10 cwt. 3 qrs. 21 lbs. (2) 53. (8) 4; £304 6s. 8d. (9) 1. 128; 2. 2s. 7d.; (4) £224, £240, £350. (7) £18 13s. 6d. 365 (5) 28. (3) 1846. ·5740. (10) £1507 10s. (11) 12. (12) 1.8; 186 (13) £1 15s. 3·008d. VII. (a.) 400 2475; 2. 1200. (1) 1. £41344 7s. 10d.; 19845309; 2. £110 12s. 7 d. (2) 7040. (3) 15. (4) 1.7; 2. 3; 3. 33·384; 4. ·390625. (6) 530-8416; 12·0191. (7) 2; x3-6x2+11x-6. (10) 1. x=10; 2. x=4; 3. x=168, y=56. (11) 4000. (12) 2. 4, 7, 10. (5) 33. ; 2. x3 + y3 + z3 — 3xyz; 3. 2x3 — (3x+1). (9) x-b. (13) 1. 4641587; 2, 000002211518. VIII. (a.) (14) 487-2983 c. f.; 623 6095 c. f. (1) 1. 4 tons 14 cwt. 1 qr. 22 lbs. 103 oz.; 2. £87 10s. (9) 1. x-20; 2. (x+a) (x − a) (x2 + ax + (10) 1. x=2 ; 2. x=20; 3. x=8, y=5. (11) 30 days. (8) 1. x3-10x2 + 33x-36; 2. 2x2 −3x+4; 3. X- 2 x+2 (9) 1. x=8; 2. x=3; 3. x=- ∙1·2; 4. x=463, y=55. (10) 1.5 h. cr. 17 sixp. ; 2. 18 and 24. (12) 10. (11) 6 and 8 yards. (13) 1. 507-61; 2. £1515 12s. * 5a (8) 2. 36. (9) 1. ́; 2. ao — 8a5b + 15a1b2 — 25a3b3 + 21a2ba—14ab3 + 8b6 ; 3. (a1 — x1)2=a3 — 2a1x1+x3 ;_4. x3 + 3x2y + 9xy2+27y3. (10) 1. x-2y. (11) 1. x=5; 2.x=21; 3. x= (12) 260. (13) 12. = 2013, y=18. (14) 1. 4·643453, 5·643453; 2. 1·041393; 3. 3·918071; 4. 02160564. 23a 11a2 (9) 1.1 + + (6) £2 18. 5d. (8) 1. x+x2+x3 or x+ 12 12 (5) 1. 143; 2. 51; 3. ·035=20. X X + ·; 2. (a—x)o; 3. 2x2 — (3ax +a2); 4. 8xỗ + 27y3. (14) 1. √10 3.162277; 2. 00000000033373; 3. 000547. (15) 408-75 sq. ft. XII. (a.) (1) 1. 50688000; 2. 7s. 10d. ; 3. £87 0s. 9d. (2) 1. 2718, 12; 2. 4s. 6d. (4) £2536 108. (3) 1. £9 1s. 8d.; 2. 37; 3. 269700. (5) 7070. (6) 1. x3 — y3 — 23 — 2xyz + xy2 + 3x2y — x2z — xz2 — y2z —yz2; a- -b a + b 2. −(3+x+4x2); 3. ; 4. -96. (7) 1. x=8; 2. x=3; 3. x=25; 4. x=97, y=−4. (8) A, 22s.; B, 26s. (9) 2§ miles, 34 miles. (11) 1. √x=1, −14; 2. x=3, y=}, z=2. (13) 1. 5409683; 2. 6.29. (15) 1. 7·6942 yds.; 2. 31 ac. 3 ro. 15-2728 po. (10) (2a3—¿ ̄3)2. XIII. (a.) (1) 1. 60048000; 2. £37 5s. 10d.; 3. 2 oz. 3 dwts. 7 grs. x-3 x2-3' (2) 200. (5) 567. (10) 1. (a−b)5; 2. x2 + 2xy — 3y2; 3. (x+y) (x2 + xy + y2). (11) 1. x=2; 2. x=4; 3. x=5, y=10. 2a x-2 a2—bzi 3. x-3 (12) 1470. (1) 1. 7200000; 2. 38. 11d.; 3. £37 28. (2) 2 lbs. 10 oz. 11 dwts. 12 grs. (3) 22 cwt. 2 qrs. (4) 1. 000999; 2. £1 9s.; 3. 00298828125; 4. 3007. (5) £33 14s. 4 d. (6) 1. a1-x12; 2. x1+y1; 3. a2 + 2a-3 = (a+3) (a−1); (a2 + 5a + 6) =(a+3) (a + 2). (7) 1. x=1; 2. x=3; 3. x= =10, y=12, z=15; 4. x=1. (8) 1. 158. 6d., £2 6s. 6d., £4 13s.; 2. 78 yards. (9) 1. x=3, 5; 2. x=3, y=0. (10) 1904 yards. (11) 0. (12) 1. 21.5878; 2. 000045498. (13) 1. 2377-292 ft.; 2. 12 ac. 2 ro. 7·6832 po. (14) 1507-352 ft. 293 122 (15) T c. ft. 30, (13) 2√3. b 3 26 191 (10) 850. b 3 a+ ; 2. 414; 3. 5, 10, 20, 40; or -15, 3 a+ 60, 120. (12) 1.3.162277; 2. 6·402364; 3. 1536-582. (7) 1. 2x; 2. q2—2ab-b2; 3. 3x2+1; a−3a2x3+3a3x3 —x. (8) 1. x=1; 2. x=4; 3. x= =4, y=2; 4. x=3, 110; 5. x=1, -1; y = −1, 3; 5. 22. (9) 1. 49485; 2. 8286-97; 3. 11 years. (12) 86° 30′ 57′′. (10) 20-10624 ft. (13) Fulcrum distant 6 in. from wt. 10 lbs.; pressure=2√91 lbs. (15) 5.449". XIX. (a.) (1) 1. £1432 14s. 9d.; 2. £21 3s. 5d. (2) 6. (3) 144 fr.=1178. (4) 1. x=1; 2. x=1, y=2, z=3; 3. Put the equation in the form X= x2 + 2x2 + 1 = x2 - 2√2x+2; x = ·}{ ±1 ± 4. x=3, -3, ± √ −3. (6) 1. 3220239; 2. 15238860000000. |