Weekly Problem Papers, with Notes. [With] Solutions (Paperback)

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: ...2. If (1 + x + x) = P0 + P1x + P +... + PrxT +... prove (1) Pn = itf-IV + P./-... (MP-1 f(2--l)l (2--4)l -(-- ) (2 -7) ) w (--l)l -I "(--3)I 21 "(-6) " 5., 5, C, i) are four points not in one plane. If AB is perpendicular to CD, and AC is perpendicular to BD, then will JI) be perpendicular to BC. 6. TP, are tangents to a parabola whose focus is S. LM, a third tangent cuts them in L and M. Prove that the triangles SPL, STM are similar. Hence shew that TL: LP:: QM: MT. Papeb XXXII. 1. Of three events it is 2 to 1 against the first and second happening, 3 to 2 against the second and third, and 9 to 1 against the first and third. Shew that the odds against all three happening are 5 V3-1 to 1. 2. 0 is the centre of gravity of a triangle. AO, BO, CO are produced to points D, E, F such that AD = /. AO, BE = m. BO, CF = n. CO. Find the values of I, m, n so that the sides of the triangle DEF may pass through the points A, B, C. 5. A, B, C, D are four points in space. AB, AC are divided in E, F so that AE: EB:: AF: EC. BB, BC are divided in &, H so that DG: GB:: BR: HC. Shew that the lines GF and HE will intersect. Paper XXXIII. 1. A river flows from P to Q, a distance of 12 miles, at a uniform rate. B starts at 12 o'clock from Q to row to P, and A starts at 5 minutes past 12 to row from Q to P and back again. A overtakes B a mile from Q; he rows on to P, and at once turning back meets B two miles below A. A reaches Q 35 minutes after B reaches P. Find the times at which A passed B, and the rate of the stream. 5. Any point P is taken on a given segment of a circle described on a line AB, aud perpendiculars AG-and BH are let fall on BP and AP respectively. Prove that Gil touches a fixed circle. Paper XXXIV....