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Solutions of Weekly Problem Papers

Solutions of Weekly Problem Papers


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1885 Excerpt: ... the extremity of the straight line which represents their resultant is a circle. Paper XVII. 7. Along the sides of a regular hexagon taken in order act 6 forces represented by 1, 2, 3, 4, 5, 6 respectively. Prove that their resultant will be represented by 6, and that its direction will be parallel to one of the sides, and at a distance from the centre of the hexagon equal to times the radius of the inscribed circle. Paper XVIII. 1. A road runs from A to meet another at right angles. Shew that there are two points on the second road which may be reached in the same time from A whether we travel by road or across country, the rates of travelling by road and across country being as 7: 5. Also shew that for places between these the quickest route is across country, nnd the quickest for all other places is by road. 2. If 16 be added to the product of four consecutive odd or even numbers, the result is always a square number. For odd numbers its lust digit in four cases out of five is 1, in the remaining case 5. For even numbers the last digit in four cases out of five is 6, in the remaining case 0. 3. If /, m, n be the distances of any point in the plane of a triangle ABC from its angular points, and d its distance from the circum-centre, shew that P sin 2A + nfi sin IB + -z sin 2C = 4(222 + P) sin A sin B sin C, R being the radius of the ciicum-circle. 7. A conic passes through the centres of the four circles which touch the sides of a triangle. Prove that the locus of its centre is the circumscribing circle. Paper XIX. jj Solve the equations i.. (1) - + - = 4ax(x + cF). 1 k' (2) + +-=-+f+-=-+-+-= )/ a y z x b z x y c (/ 4. If R be the radius of the circum-circle, shew that the area of the triangle = 5 R? (sin3 A cos (B-C) + sin' B cos (...


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Product Details
  • ISBN-13: 9781154977486
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 115497748X
  • Publisher Date: 14 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 86 gr


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