A first book of algebra, including the binomial theorem1867 |
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Página 22
... leaving 3a . Also 4a - 7a would be written —3a ; that is , there are 7a to be taken from 4a , but this cannot be done ; therefore the 4a are taken , as it were , on account , leaving 3a still to be taken from some other quantity ; and ...
... leaving 3a . Also 4a - 7a would be written —3a ; that is , there are 7a to be taken from 4a , but this cannot be done ; therefore the 4a are taken , as it were , on account , leaving 3a still to be taken from some other quantity ; and ...
Página 26
... leaving 3by ; this is sub- traction . Many such instances of subtraction occur in the examples given for addition . In subtraction , as in addition , unlike terms cannot be operated upon further than by connecting them by the sign -Thus ...
... leaving 3by ; this is sub- traction . Many such instances of subtraction occur in the examples given for addition . In subtraction , as in addition , unlike terms cannot be operated upon further than by connecting them by the sign -Thus ...
Página 27
... leaving 76. The complete answer is 3a2 + 76 . ( 6. ) From 6x2 + 8y + 3 take 2x2 + 9y + 2 . 6x2 + 8y + 3 2x2 + 9y + 2 4x2 y + 1 In this example the 2x2 taken from 6a2 leave 4x2 , and the 2 taken from the 3 leave 1. But the middle term ...
... leaving 76. The complete answer is 3a2 + 76 . ( 6. ) From 6x2 + 8y + 3 take 2x2 + 9y + 2 . 6x2 + 8y + 3 2x2 + 9y + 2 4x2 y + 1 In this example the 2x2 taken from 6a2 leave 4x2 , and the 2 taken from the 3 leave 1. But the middle term ...
Página 29
... leaving 5x2 ; -5y becomes + 5y , meaning that 5y are to be added to 2y , making 7y . There- fore the answer is 5x2 + 7y . ( 18. ) 3xy - 8- ( xy - 18 ) . Here we have to subtract - 18 from - 8 , The rule of changing the sign will easily ...
... leaving 5x2 ; -5y becomes + 5y , meaning that 5y are to be added to 2y , making 7y . There- fore the answer is 5x2 + 7y . ( 18. ) 3xy - 8- ( xy - 18 ) . Here we have to subtract - 18 from - 8 , The rule of changing the sign will easily ...
Página 32
... leaving 1 still to be subtracted . ― - It will now be very easy to write down subtraction operations without the bracket , but it will be necessary to bear in mind the fact that to subtract + x is expressed by -x ; and that to subtract ...
... leaving 1 still to be subtracted . ― - It will now be very easy to write down subtraction operations without the bracket , but it will be necessary to bear in mind the fact that to subtract + x is expressed by -x ; and that to subtract ...
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A First Book of Algebra, Including the Binomial Theorem William Rossiter Sin vista previa disponible - 2016 |
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Página 160 - A square court yard has a rectangular gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the gravel walk ; and the number of square yards in the walk exceeds the number of yards in the periphery of the court by 164. Required the area of the court ? All equations of the second degree may be reduced to one of the following forms.
Página 39 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 169 - How many hours a day must 42 boys work, to do in 45 days what 27 men can do in 28 days of 10 hours each, the work of a boy being half that of a man ? 11. If 8 guineas be expended in purchasing Brussels carpet f yd. wide, at 3».
Página 120 - Divide the first term of the remainder by twice the first term of the root, and add the quotient to the part of the root already found, and also to the trial-divisor.
Página 120 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
Página 128 - N, and divide the first term of the remainder by 3 times the square of the first term of R, the quotient will be the third term of the root.
Página 206 - Eequired the numbers. 6. The sum of three numbers in geometrical progression is 35, and the mean term is to the difference of the extremes as 2 to 3. Required the numbers. Ans. 5, 10, 20. 7. The sum of £ 14 was divided between three persons, whose shares were in geometrical progression ; the sum of the shares of the first and second was to the sum of the shares of the second and third as 1 to 2.
Página 88 - Divide the number 36 into 3 such parts, that* \ of the first, \ of the second, and \ of the third, shall be equal to each other.
Página 207 - Bought two flocks of sheep for 65/. 13s., one containing 5 more than the other. Each sheep cost as many shillings as there were sheep in the flock. Required the number in each flock. Ans. 23, and 28.
Página 93 - ... 2. A can do a piece of work in a days and B in b days.