# Calendar: 1858-1859 Page 432

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434 APPLIED SCIENCES person travels part of journey by rail and the rest by coach and observes that if the rate of the train is 20 miles an hour and that of the coach he takes 3£ hours to complete it but if the rates are 30 and miles respectively he takes hours 50 minutes How long would he take to travel the whole by rail at the rate of 25 miles an hour The sum of an infinite Geometric series is and the sum of the squares of the terms is s2 find the sum of terms Determine the greatest term in the expansion of χ Ex When 17 If 6x cx2 &c b'χ c'χ2 &c for all values of show that sat a' b' c' &c x2 Resolve into its'partial fractions-- x2 gives Β bill for £p payable at the end of years in dis- charge of bill for &q payable at the end of η years For what amount should Β return to bill payable at the end of years to balance the account compound interest being reckoned The sum of two angles is 25 degrees and their difference 25 grades Find the angles in degrees and grades 10 Prove that- sin cos cosec cos sin cos sin ύ 11 Solve the equation sin θ cos θ cos β sin Θ 12 Prove the formula sin λ א an del be duce thatif is right angle sin sin sin Β sin χ sin sin 13 Determine sin χ and cos χ in terms of sin χ and cos and deduce the expansion of sin and cos in terms of lt Show that the sum of the infinite series whose nlh termis7- j-7-A 4rc π4 is equal to that whose term is ---- י η

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