# Intermediate Mathematics; A Guide to the Mathematics of the Intermediate Examinations in Arts and Science of the University of London. (5th Thousand)

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## Description

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. 1890 edition. Excerpt: ... point of intersection of the straight lines whose equations are 2a-3?/+7=0;r+4y+3=0, a straight line is drawn at right angles to the axis of x. Find its equation. '77. 34. If Jc=x JT+p+y Jl+x--prove that /l+k=xy+ VI+a2 Sl+y2 '77. 35. Solve the equations 3x+9y-6z=8 x-7y+12z=z\$ 12x-3y-bz=U. '77. 36. Out of a cask containing 360 quarts of pure alcohol a quantity is drawn off and replaced by water. Of the mixture a second quantity, 84 quarts more than the first, is drawn off and replaced by water. The cask now contains as much water as alcohol. Find how many quarts were taken out the first time. Show that the problem has only one solution. '77 37. Find the L.C.M. of 3x+x2-8x+4, 3a? + 7a;2-4, %+2x2-x--2, and 3x3--2a?-3x+2; and also the factors of their sum. Find the sum of their reciprocals. '77. 38. Convert the circulating decimal fraction 1-4631 into a vulgar fraction. '77. 39. An equilateral triangle being supposed to revolve round the line through its vertex perpendicular to its base; show that the area of the cone generated by either of its sides is double that of the circle generated by either half of its base. '77. 40. Three cylinders of equal altitudes being supposed to have for bases the three circles described on the three sides of a right-angled triangle as diameters; show that the volumes of the greatest of them is equal to the sum of those of the remaining two. '77. 41. A cone and hemisphere being supposed to have a common base, and to lie at opposite sides of it, required the ratio of the altitude of the cone to the radius of the hemisphere, in order that the volumes of both solids should be equal. '77. 42. If, r, ?/, a;2 2/2, x.t y3, be the Cartesian co-ordinates of three points Plt P2, Ps, in a plane with respect to any pair of...show more

## Product details

• Paperback | 34 pages
• 189 x 246 x 2mm | 82g
• Miami Fl, United States
• English
• black & white illustrations
• 1236544056
• 9781236544056