"Wentworth & Hill's Exercise Manuals: Algebra, Issue 2Ginn & Company, 1889 |
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Common terms and phrases
a+b)² a²+ab+b² a²b² a²x² ab² ab³ ALGEBRA arithmetical progression arithmetical series ax² binomial bx² cent coefficient compound interest cube difference digits distance Divide dollars equal Expand Extract the square feet Find the H.C.F. Find the numbers Find the square Find the sum Find the value geometrical progression given logarithms Lower base lowest terms miles an hour miles per hour minutes Multiply number of terms partial fractions proportion Prove quadratic equation quantities quotient ratio Resolve Simplify Solve the equations square root Subtract travels UNIVERSITY OF OXFORD upper base walk white ball x² y² x²+xy x²y xy² xy³ yards α α ах
Popular passages
Page 54 - У x 3. Two vessels, one of which sails faster than the other by 2 miles an hour, start at the same time on voyages of 1152 and 720 miles, respectively. The slower vessel reaches its destination one day before the other. What is the rate per hour of the faster vessel ? 4. There are five numbers in arithmetical progression. Their sum is to the sum of their squares as 9 : 89. The sum of the first four numbers is 32. Find the numbers. 5. Find the limit of the sum of 4 + 3 + f + 6. Find the value of...
Page 82 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare ? Let x be the number of leaps taken by the hound.
Page 12 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Page 80 - Now, if the first horse be harnessed in the carriage, he and the carriage together will be worth three times as much as the second horse ; but if the second horse be harnessed, he and the carriage will together be worth 7 times as much as the first.
Page 52 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Page 116 - Prove that a ratio of greater inequality is diminished, and a ratio of less inequality is increased, by adding the same number to each of its terms.
Page 69 - Щ miles down a river and back again in 1 hour and 40 minutes : supposing the river to have a current of 2 miles per hour, find the rate at which the crew would row in still water.
Page 117 - Prove that the number of combinations of n things taken r together is equal to that of n things taken n — r together, and greater than that of n— I things taken r— l together.
Page 136 - ... slowly than himself. Find the distance of the town from the starting point, and the rate at which each man walks. 8. Three lamps of equal brilliancy are placed in three different corners of a square room. Compare the intensities of light at the fourth corner and at the centre of the room, assuming that the illumination from a source of light varies inversely as the square of its distance. 9. Show how to insert any number of harmonic means between two given quantities. If 2p and...
Page 34 - The plate of a looking-glass is 18 inches by 12 inches, and it is to be framed with a frame of uniform width, whose area is to be equal to that of the glass. Find the width of the frame.