71. Extract the cube root of 17 to nine places of decimals. 72. Extract the cube root of 28 to ten places of decimals. 73. Find the cube root of 7 to ten places of decimals. 74. The population of Great Britain in 1851 was 21,121,967, and the increase during the previous half century had been 93·47 per cent. What was the population in 1801 ? 75. The Income Tax upon a certain income at 18. 4d. in the pound amounts to £20; find the sum invested in the 3 per cents. from which the income is derived. 5 76. The simple interest on a certain sum for 9 months, at per cent. per annum, is £150 less than the simple interest on the same sum for 15 months, at 4 per cent. per annum. Find the principal. 77. An estate purchased at £84. 78. 6d. per acre was sold at £90. 148. 03d. per acre; find the gain per cent. 78. The investment of a certain sum at 3 per cent. produces an income of £501. 15s. A portion of this, sufficient, when re-invested at 5 per cent., to produce the same income as the whole formerly did, is called in. Find the amount of income derived from the whole when this re-investment has been effected. 79. Multiply together 11 ft. 4 in. and 4 ft. 7 in., by duodecimals, stating clearly the value of the superficial unit in each denomination. 80. Multiply 3 feet 2 inches 8 lines by 1 foot 8 inches 10 lines, using the duodecimal method; a line being a twelfth part of an inch; and state what each term of the result expresses. 81. Multiply 6 feet 5 inches by 4 feet 9 inches, according to the duodecimal notation, and exhibit the result in the decimal scale, the unit of measure being a square foot. 82. Multiply 17 feet 9 inches 5 lines by 3 feet 2 inches 7 lines by duodecimals, and state the value of the superficial unit in each denomination. Find the result also by decimals, and shew that the two agree. 83. Multiply 5237684 by 4539, in the duodecimal scale, using a to express ten, and ẞ to express eleven. 84. Multiply 1432312 by 31422 in the quinary scale; and transform the former to the denary scale. 85. Express the undenary number 57a4685 in the octenary scale: where a expresses 10. 86. Convert the senary number 5321425 to the quinary scale. 87. Transform the quinary number 3241342 to the octenary scale. II. ALGEBRA. INTRODUCTORY OPERATIONS. 88. Find the numerical value of 3a2 — 2b {aa — 3c (b3 — 2a) + c3} — 4c (a —b)3, to five places of decimals; when a=10, b=2, c=7, d=5, e=−3. and ƒ= 6. 91. Give the numerical values of the following expressions, when a 5, b=25, c=1, d=7, e=0 and f= }}: = when a 16, b=2, and c=9; having previously reduced it to = and give this result in terms of b when b=a-1, |