The elements of algebraOliver & Boyd, 1857 - 95 σελίδες |
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Σελίδα 33
... substitution in the second , we get 5x 3 . - = 13 , or 3 22 2x -- 3 7x = 35 . Having eliminated one of the unknown quantities by any of the above methods , the value of the other is found from the resulting equation ; and by ...
... substitution in the second , we get 5x 3 . - = 13 , or 3 22 2x -- 3 7x = 35 . Having eliminated one of the unknown quantities by any of the above methods , the value of the other is found from the resulting equation ; and by ...
Σελίδα 51
... substitution in the general formula . If the surd be of the form a -y , and proceed as before . -- b , assume the root = √x If the surd be of the form a c√bc , or can be put under the form c ( a + b ) , its square root may be found by ...
... substitution in the general formula . If the surd be of the form a -y , and proceed as before . -- b , assume the root = √x If the surd be of the form a c√bc , or can be put under the form c ( a + b ) , its square root may be found by ...
Σελίδα 56
... substitution , - = x = 11+ √ ( 121 +240 ) 9 12 or x = 1119 12 .. x = 21 or - . There are therefore two values for x ; and that this is al- ways the case appears from the general formula , which will give one value for x when the surd ...
... substitution , - = x = 11+ √ ( 121 +240 ) 9 12 or x = 1119 12 .. x = 21 or - . There are therefore two values for x ; and that this is al- ways the case appears from the general formula , which will give one value for x when the surd ...
Σελίδα 57
... substituted for them . ( 4. ) When the sum of the dimensions of the unknown quantities is the same in every term of both equations , we may substitute for one of the unknown quantities the product of the other and a third . x 2 ( 1. ) 2 ...
... substituted for them . ( 4. ) When the sum of the dimensions of the unknown quantities is the same in every term of both equations , we may substitute for one of the unknown quantities the product of the other and a third . x 2 ( 1. ) 2 ...
Σελίδα 78
... substitution , 1 + x = 1 + 3x + 6x2 + 12x ° + · • 3.2n - 2n - 1 . 1 2x Example 2. Let it be required to find the sum of n terms of the series 1o + 2o + 3o + 4o + , & c . , to no . Since the sum is evidently less than n2 + n2 + n2 + ...
... substitution , 1 + x = 1 + 3x + 6x2 + 12x ° + · • 3.2n - 2n - 1 . 1 2x Example 2. Let it be required to find the sum of n terms of the series 1o + 2o + 3o + 4o + , & c . , to no . Since the sum is evidently less than n2 + n2 + n2 + ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c a²+2ab+b² annex arithmetical series ax² binomial binomial theorem coefficient common denominator common difference common ratio compound quantity consecutive numbers cube root deno denote the number Divide divisor double equal equation contains EXERCISES expressed Extract the square factor Find a number find the Greatest Find the number Find the sum following fractions following quantities geometric means given quantity Greatest Common Measure Hence Least Common Multiple letters miles per hour mixed quantities multiplied negative number of balls number of combinations number of permutations number of terms numbers whose sum numerator and denominator Prove QUADRATIC EQUATIONS quotient remainder shillings side sign changed simple quantity square root subtracting surd t₁ things taken third total number transposing travelled unknown quantity ах
Δημοφιλή αποσπάσματα
Σελίδα 61 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 88 - The fore-wheel of a carriage makes six revolutions more than the hind-wheel in going 120 yards ; but if the circumference of each wheel be increased one yard, it will make only four revolutions more than the hind-wheel in going the same distance.
Σελίδα 60 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Σελίδα 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.
Σελίδα 44 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Σελίδα 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.
Σελίδα 66 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 41 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.
Σελίδα 44 - Take the root of the first term, for the first term of the required root...
Σελίδα 40 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...