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By Karakhanyan M.I., Khor'kova T.A.

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Topics in Computational Algebra

The most function of those lectures is first to in brief survey the elemental con­ nection among the illustration thought of the symmetric staff Sn and the speculation of symmetric features and moment to teach how combinatorial tools that come up evidently within the idea of symmetric services bring about effective algorithms to specific a variety of prod­ ucts of representations of Sn when it comes to sums of irreducible representations.

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Find the 3. A CHAP. IV] CONCURRENT CO-PLANAR FORCES 45 Q and the magnitude of the force P, using logarithms. Construct the force triangle to the scale of 1 inch = 20 pounds and compare with the calculated results. 4. The resultant of two forces of 16 pounds and 24 pounds in a horizontal plane is a force of 34 pounds north 10 degrees east. Find the direction of the forces by means of the formula for the tangent of the half angle. direction of the force When it is method the To of desired to find the resultant of of calculation by means solve such problems each force is more than two of triangles is forces, laborious.

Problems Find the magnitude and direction of the resultant of the following pounds north 75 degrees east, 15 pounds north 20 degrees east, and 8 poun,ds north 25 degrees west. Solve graphi1. forces in a horizontal plane: 20 = 5 pounds. cally to the scale of 1 inch 2. Two ropes in a vertical plane are attached to a fixed point. One rope, which supports a mass of 40 pounds on the free end, runs over a smooth pulley located 16 feet higher than the fixed point, and 7 feet to the left of the vertical line through it.

In Fig. 34, the upward pull knot A by the combined of the vertical cord is replaced at the The upward pull of the cords which lead to the spring balances. pull in the vertical cord is equal to the resultant of the forces in the other two cords. The downward pull of the vertical cord at the knot, which balances the combined upward pull of the other two cords, is called the equilibrant. The resultant of a combination of forces is the single force whose effect on the equilib- rium of a body is equivalent to that of the combination of forces.

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