Mathematical Exercises ...

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Page 12 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Page 109 - From the top of a hill the angles of depression of two successive milestones, on a straight level road leading to the hill, are observed to be 5° and 15°.
Page 279 - Find the distance of the centre of gravity of the remainder from the intersection of the diagonals.
Page 374 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 221 - A body is projected with a velocity v in a direction making an angle a with the horizon...
Page 225 - Hence the conditions of equilibrium of any system of forces, acting in one plane upon a rigid body, may be obtained as follows ; I.
Page 198 - A manufacturer having a capital of £5000 on which he can realise by hand labour 10 per cent. profit, buys a machine for £1000, by which his profit on the remainder of his capital is raised to 20 per cent. This machine lasts 5 years. Of how...
Page 84 - A number is divisible by 9 if the sum of its digits is divisible by 9.
Page 291 - Assuming the parallelogram of forces, prove that the algebraic sum of the moments of two forces about a point in the space between their directions is the same as the moment of their resultant.
Page 165 - One company guarantees to pay 5 per cent. on shares of £100 each; another guarantees at the rate of 4f per cent.

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