Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times Volume . 33

Mathematical Questions and Solutions in Continuation of the Mathematical Columns of the Educational Times Volume . 33

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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. 1880 edition. Excerpt: ...working days of the week, but when the time comes for their going to church together on Sunday it is found to be absolutely impossible to continue it any further. Investigate whether the rule can have been correctly carried out during the six previous days; and if so, show how. Solution by the Proposer. The question is possible, and may be answered in various ways. One solution will leave out-the duads 1. 2, 1. 3, 2. 3, 4. 6, 4. 6, 5. 6, '7.8, 7. 9, 8. 9, 10. 11, 11.12, 12.13, 13. 14, 14. 15, 15. 10, which 15 duads evidently cannot be contained in 5 triads, on account of the cycle 10, 11, 12, 13, 14, 16. 5403. (By Dr. Hopxinson, F.R.S.)--An iron hoop, 10 feet in diameter, revolves about an axis through its centre, perpendicular to its plane, with a velocity a; find the greatest value u can have without breaking the hoop. Solution by J. J. Walker, M.A. Let T be the tensile strength, io the weight in lbs. weight per cubic inch, R the radius, a the breadth, and b the (small) thickness, of die hoop; then the critical value of a is determined by 2irrm- o2r-g 2irT ab, or a2- T-i-R2u, where g and R are expressed in inches. Taking the tensile strength to be 10 tons weight to the square inch, this would give, for R = 60, a = 90 about; say 14 revolutions per second. Multiplying the equation above by ZR, integrating and reducing, we have the more general result o2 = 0, t-s-r'r"m for a fly-wheel of exterior and interior radii R', R" respectively. 5992. (By Elizabeth Blaciwood.)--If P, Q, R, S be four random points on the surface of a given sphere; find the chance that the point S will be within the spherical triangle PQR. Solution by Professor Settz, M.A. The required chance is evidently equal to the average area of the triangle Pyit, ...show more

Product details

  • Paperback | 34 pages
  • 189 x 246 x 2mm | 82g
  • Rarebooksclub.com
  • United States
  • English
  • black & white illustrations
  • 1236513975
  • 9781236513977