• ISBN13: 9781130467383
• Binding: Paperback
• Subject: Career CounsellingMathematics and Statistics
• Publisher: RareBooks
• Publisher Imprint: RareBooks
• Publication Date: January 1, 2012
• Pages: 38
• Original Price: USD 13.19
• Language: English
• Edition: N/A
• Item Weight: 87 grams
• BISAC Subject(s): N/A

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. 1904 Excerpt: ... in pairs, lie in a straight line. 3. If (l+a; + a;2+...+x2m)n=a0 + a1x + a2x2+ prove that o r. mn(2m+l)n " a2 + 6a2 + 6a4 + 10a5+... =--(3mn + m-2). 4. If all the letters denote positive integers, prove that (ar+2+1 + br+2+1 + cr+s+1) (ar+s+2 +... +...) (ar+, +M-1+... +...) (an+a +... +...)n+r(a3+... +...y. 5. A square is circumscribed to a convex quadrilateral. Prove that its area is x2 + y"--4A' where A is the area of the quadrilateral and x, y its diagonals. 6. If n be an odd integer, shew that, (2r-l)x---5 8. Prove that the locus of the intersection of normals to the 8J2 If. ellipse 2 + 1) which are equidistant from the centre consists of points at infinity, the axes and the two curves r2 (a cos20 + b sin 6) = (a + bf (a b) cos2 20. 9. If 6 be the angle between the asymptotes of a conic represented by the general trilinear equation of the second degree, prove that-(a + b + c-2/cos A-2g cos B-2h cos C) tan20 = 0. 10. If the greatest possible cube be cut out of a solid hemisphere of uniform density, prove that the remainder can rest with its curved surface on a perfectly rough inclined plane of angle a, with its base inclined to the horizon at an angle.. (8(3tt-V6). ) sin t 9.-8 smr 11. In a truck of mass M is fixed a vertical tube of small radius, inside which is fixed a particle of mass m. The truck is made to slide on a smooth horizontal table by a horizontal string which, passing over a pulley, is attached to a mass M' which hangs freely. Motion ensues for time t, after which the particle is allowed to fall down the tube. Prove that the particle will describe in space a parabola whose latus-rectum is (M+M' + mf + M). 12. A fountain is formed by a jet of water issuing horizontally with velocity u from, and at right angles to, a horizon...