Miscellaneous Examples in Algebra: With Equation Papers Originally Proposed at St. John's College, CambridgeLongman, Brown, Green, and Longmans, 1851 - 94 من الصفحات |
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2ax² a²x² a³x Algebra Ambleside Arithmetic Atlas ax² ax³ balls cent coin cube roots Dictionary difference Divide Elementary English Grammar English Notes Expand Extract the square find the chance Find the G. C. M. Find the number Find the sum find the value five terms fractions French French Grammar gallons Geography Gleig's Greek guineas half History increased infinitum integers irreducible fraction Latin Grammar Lexicon London LONGMAN M'Leod's miles an hour MISCELLANEOUS EXAMPLES Multiply nth term Obtain the square partial fractions Paternoster Row persons post 8vo Question and Answer ratio Reading-Book Reduce royal 8vo Schools septenary shew shillings Simplify Solve the equation square number square root Sum the G. P. Tate's vols
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الصفحة 18 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards ; but if the circumference of each wheel be increased...
الصفحة 55 - ... 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the stock of provisions unconsumed at the end of the sixth day to support 6 men for 61 days ; it is required to find how long it would support the garrison, and the number of men alive when the provisions were exhausted.
الصفحة 32 - A certain number of sovereigns, shillings, and sixpences together amount to 8/. 6s. 6d., and the amount of the shillings is a guinea less than that of the sovereigns, and a guinea and a half more than that of the sixpences : Find the numbers of each coin.
الصفحة 57 - ... pounds per chain, as there were chains in the street leading to A. The sewer, however, being insufficient to carry off the water, an additional drain was made from a point in this street distant 4 chains from the bridge A., which entered the river at the same point with the sewer, and was equally inclined to the river and sewer. Now it was found that a drain down the middle of each street, at the rate of £9 per chain, would have cost only £54 more than the expense of the sewer.
الصفحة 63 - The gas contractors engage to light a shop with 5 large and 3 small burners ; but having by them only one large burner, supply the deficiency with 5 small ones. The shopkeeper, not finding this light sufficient, procures two more small burners, and at the same time agrees for the lights to burn double the usual time on Saturday nights, for which additional gas he was to pay 11.
الصفحة 36 - In every geometrical progression consisting of an odd number of terms ; the sum of the squares of the terms is equal to the sum of all the terms multiplied by the excess of the odd terms above the even.
الصفحة 33 - A train, an hour after starting, meets with an accident which detains it an hour, after which it proceeds at...
الصفحة 46 - Prove that 1, 3, 5, 7, &c. is the only arithmetic progression beginning from 1, in which the sum of the first half of any even number of terms bears to the sum of the second half the same constant ratio, and find that ratio.
الصفحة 45 - Find the chance that a person with two dice will throw aces at least four times in six trials. 19. Find the chance of throwing an ace with a single die once at least in six trials. 20. If on an average 9 ships out of 10 return safe to port, find the chance that out of 5 ships expected at least 3 will arrive.
الصفحة 56 - At the review of an army, the troops were drawn up in a solid mass, 40 deep, when there were just one-fourth as many men in front as there were spectators. Had the depth however been increased by 5, and the spectators drawn up in the mass with the army, the number of men in front would have been 100 fewer than before.