A Collection of Examples in Pure and Mixed Mathematics, with Hints and Answers, by A. Wrigley and W. H. Johnstone. by A. Wrigley

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General Books LLC, 2013 - 54 pàgines
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1852 edition. Excerpt: ...of 2 to 3; find the angle between them, when their resultant is a mean proportional between them. 5. Two forces, which are to each other as 2 to 3, when compounded, produced a force equivalent to half the greater. Find the angle at which they are inclined to one another. 6. The resultant of two forces is 10 lbs.; one of them is 8 lbs., and the other is inclined to the resultant at an angle of 360: find the other force, and the angle between the two. 7. Three forces acting on a point, and in the same plane, are in equilibrium when their directions are inclined to each other at angles of 6o, 135, and 165 respectively. Find the ratio of the forces. 8. Three forces acting on a point, keep it at rest; and they are in the ratios of Vl + 1: /6: 2. Find the angles at which they are respectively inclined to each other. 9. Three equal forces, each equivalent to 6 lbs., act on a point; the first two are inclined to each other at an angle of 75, and the third is inclined at an angle of 150 to the first. Find the magnitude and direction of the resultant. 10. Four forces, represented by 1, 2, 3 and 4, act on a point. The directions of the first and third are at right angles to each other; and so are the directions of the second and fourth; and the second is inclined at an angle of 6o to the first. Find the magnitude and direction of the resultant. 11. Three forces act perpendicularly to the sides of a triangle at the middle points, and each is proportional to the side on which it acts. Show that they will keep each other at rest. 12. If forces, proportional to the sides of any polygon, act perpendicularly to these sides respectively at their middle points, they will keep each other at rest. 13. If three forces A, B, C act upon a given point, and keep...

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