London graduation mathematics, questions in arithmetic and algebra set from 1839 to 1879. [With] Solutions - Softcover
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Synopsis
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 Excerpt: ...having given the first and last terms, and the number of terms. The sum of 40 terms of an arithmetical series is a, and the sum of 50 terms is b. Find the common difference. 6. Find the number of combinations of n things taken r together. How many different arrangements can be made of the letters of the alphabet, taking them three at a time, two consonants and one vowel being in each arrangement? 7. Investigate the rule to find the discount on any sum ŁA due years hence at r per cent, per annum. 8. If log. 4 =-6020600, log. 27 = 1-4313638, and log. 7 =-8450980, find log.-0027 and log. 3528. Explain what is meant by the modulus of a system of logarithms. 9. Solve the equations:--x-6 x + 3 _ X_J_. W To + 5 To' 10. A certain number consists of two digits, and another number is formed from it by reading it backwards. If the sum of the two numbers is 99, and the difference 45, find the digits. (Afternoon.--Trigonometry and Conies.) 11. Determine the values of the trigonometrical ratios for an angle of 60. Find A, B, and C, from the equations cos. (A + B--C) = i; cos. (A--B + C) =; cos. (A + B) = sin. C. 12. Show how to find the height and the distance of an inaccessible object on a horizontal plane. A person standing on the bank of a river observes the angular elevation of the top of a tree on the opposite bank to be 60; and when he retires 100 feet from the edge of the river, he observes the angle to be 30. Find the height of the tree and the breadth of the river. 13. In any triangle ABC the tangent of half the difference of the angles B and C is to the tangent of half their sum as the difference of the two sides A B and A C is to their sum. If b = 17, c = 7, a = 60, find B and C, having given log. 2 =-3010300; L tan. 35 49' = 9-8583357; log. 3 =-4771213; ...
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