Calendar: 1881-1882 Page 677

678 SCIENCE FREAKE SAMBR00KE months and Β £240 for months they gain £115 find their respective gains Explain the method of pointing in the extraction of the square and cube roots of whole numbers and decimals Extract the square root of 042849 and the cube root of to places of decimals Simplify ah χ χ2 x2 cib x2 b2 Λ λ ע-6 Λ 0- י -& Solve the equations xy xz ys χ 641 10 Show that the difference of two numbers consisting of the same digits is divisible by 11 The sum of numbers in Arithmetical Progression is 16 and if to the second third and fourth respectively be added 11 57 while the first remains unaltered the numbers so formed are in Geometrical Progression Find the numbers 12 Show that the number of combinations of η things taken together is the same as the number taken η together 13 If in the 7th and 8th terms are in the same ratio as the 6th and 7th in find 14 Every convergent to continued fraction is nearer to the value of the fraction than any preceding convergent Express JVI as continued fraction 15 Give geometrical proofs for the expansions of sin cos Deduce the values of sin 2A cos sin 3A cos in terms of sin and cos