Calendar: 1848-1849 Page 299

THE SCHOOL 207 Eliminate χ from the equations- Αχ2 Bx A'x2 Ii'x Insert harmonic means between and Find the number of combinations of η things taken together Ρ rove the Binomial Theorem when the index is an integer 10 Show by actual multiplication that the product of ο זרד &c and י ττο &c ו ט j1v &c 181 172 T72T3 11 Hence prove tbe ExponentialTheorem 12 Express the number 12479 in the septenary scale 13 Find the logarithm of 25 the logarithm of being 30103 Find also the logarithms of and 1250 14 The mantissa of the logarithms of 7302 and 7303 are 86341 and 86350 find the logarithms of 73028 and 30264 15 Find in what time sum of money will double itself at compound interest of per cent per annum due half-yearly ΊΜ Β log 025 01072 log 30103 II -Cvtgonomctn Prove that sin sin cos Β -f cos sin and deduce from this the formula for cos In triangle show that cos Β -j- cos and sin Β sin Hence show that a2 b2 -f c2 2bc cos Reduce this formula to one adapted to logarithmic calculation Find in terms of and and explain geometrically the meaning of the double sign