London graduation mathematics, questions in arithmetic and algebra set from 1839 to 1879. [With] Solutions

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Page xxi - Explain how you would proceed to find the distance from a given point to any object on the other side of a river, supposing that you cannot cross the river, and that you have no instrument for measuring angles. 7. Find the equation to the straight line drawn from the given point (h, k) perpendicular to the given straight line Find also the equation to the system of circles passing through this given point, and touching this straight line. Prove, in any way, that the centres of these circles lie on...
Page xxxviii - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page xli - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Page xi - ... yards of the wall. It is required to determine how many men must be added to the former, that the whole number of them may just finish the wall in the time proposed, at the same rate of working.
Page xviii - У. 7. (1) Explain what are meant by discount and present value ; and (2) find expressions for the discount and present value of a sum due at the end of a given time, reckoning compound interest. (3) A given sum is to be invested in an annuity such that each annual payment is one-third of the preceding, to continue for n years ; reckoning compound interest at a given rate, find the payment for the first year. 8. Solve the equation : 6 x* — 17 ax + 4 bx + 12 a" — 7 ab — 10 i
Page xxxvii - I - -J&. 81. What number is that which is the same multiple of 7, that its excess above 20 is of its defect from 30 ? 82. How many different arrangements can be made of the letters of the word Novogorodf How many with two o's at the beginning and two at the end?
Page xii - If 180 men, in 6 days of 10 hours each, can dig a trench 200 yards long, 3 wide, and 2 deep ; in how many days, of 8 hoars long, will 100 men dig a trench of 360 yards long, 4 wide, and 3 deep ? Ans.
Page xxvii - Find the equation to a straight line which passes through a given point, and cuts off a given area from the co-ordinate axes, determining the condition that this may be possible. HH 14. Interpret the equations (1) ír^+T (2) я? + y' + a
Page vii - Two detachments of foot being ordered to a station at the distance of 39 miles from their present quarters, begin their march at the same time ; but one party, by travelling...

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