A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone

EXTRACTION OF ROOTS.

141. 625, 2401, and 6561. 143. 8.6802, 6576,and 29.606. 145. 2.3094, 13, 249, and 42.291.

147. 98, and 512. 149. 192, and 0386.

151. 9.05538, and 1.0583005. 153. 5'1961524.

155. 53, and 16,7.

157. 24253, 31943, and 3'952847.

159. 12966, and 181. 160. 8.2207, and 9859. 162. 3.968118, and 288982. 164. 1207106, and 6·162277. 166. 1.837117, and 1.551. 168. 033124, and 7·231.

170. 614298, and 003851.

DUODECIMALS.

175. 28 ft. 5' 6" 8"

177. 3252 ft. 7' 2" 1""'.

179. 1375 ft. 2' 11"

3"".

172. 436 ft. II.

174. 1627 ft. 4' 6". 176. 107 ft. 4' 6" 9" 81v. 178. 80 ft. 11' 8".

302. £800 stock.

304. £821 58. purchase. 306. 8963.

303. £1444 10s. 27 d. pur

chase.

305. £67 158. 11d. income. 307. £408 6s. old. purchase.

SINGLE FELLOWSHIP.

308. A's share £10 58. 1019d.
B's share £11 158. 31,d.
C's share £13 48. 8,87d.
D's share £14 148. 177d.

309. £136 118. 1142d.
£163 18s. 439d.
£229 98. 82%d.

310. A £666 13s. 4d.
B £333 68. 8d.
C £166 138. 4d.
D £83 68. 8d.

311. 41, 3114, and 267.
312. 32, 33, 34, 35, 36, and
37 men.

11. x5 — (a + t)x2 + (b+at+s) x3 — (c+bt+as)x2 + (ct+bs)x−cs.

14.

15.

xy(−x2+y2+z2—yz)+xz(x2 — z2) +2yz(y2 — ≈2).
-3a3cd+a2b3d+4a2bc2-3a2bcd-3a2c2d-3a2cd2-2abcd
+ab3d+ab3cd+4ab2c2+4abc3 + ab2d2+4abc2d—2b2cd2

-2bc2d2-2bcd3.

16. 2a2m+2ambr—4amcTM — 3amb—3b+1—6bc".

34. (b-c)an-2+ (b2 — c2) an−3+ (b3 — c3) an−4 + ... + (br—2— cm−2) a +(bn−1 — cn−1).

47. 21x4-26x3-55x2+78x-24.

48. 2x4+(2a-3b+2c) x3-(3ab-2ac+2b+3bc)x2

Bøger