A Practical System of Algebra: Designed for the Use of Schools and Private StudentsBaldwin and Cradock, 1831 - 309 σελίδες |
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Σελίδα 4
... least possible quantity were to be added to either side of this sign in an equation the equality would be destroyed , and that one side would become greater than the other ; thus , 1 + 2 = 3 , where , if we were to add the millionth ...
... least possible quantity were to be added to either side of this sign in an equation the equality would be destroyed , and that one side would become greater than the other ; thus , 1 + 2 = 3 , where , if we were to add the millionth ...
Σελίδα 189
... least possible , to admit of such a multiple . EXAMPLES TO ART . II . PAGE 187 . ( 1 ) Transform the equation 3x + 2x - 56 = 0 into another , which shall have only unity for the coefficient of its first term , 3x2 + 2x - 56 = 0 3 v2v ...
... least possible , to admit of such a multiple . EXAMPLES TO ART . II . PAGE 187 . ( 1 ) Transform the equation 3x + 2x - 56 = 0 into another , which shall have only unity for the coefficient of its first term , 3x2 + 2x - 56 = 0 3 v2v ...
Σελίδα 190
... least common multiple of the denomi- nator , the second term of the progression is 242 = 576 , and the third is 243-13824 . Hence , we have , = 0 5x3 - 3x2 + x 24 576 13824 5-162432- 8640-0 ( 2 ) Clear the equation x3 - 5x + 190 ON THE ...
... least common multiple of the denomi- nator , the second term of the progression is 242 = 576 , and the third is 243-13824 . Hence , we have , = 0 5x3 - 3x2 + x 24 576 13824 5-162432- 8640-0 ( 2 ) Clear the equation x3 - 5x + 190 ON THE ...
Σελίδα 204
... least be equal to the number Ñ ; but if , while x increases , this aggregate increases also , so as to become greater than N , the values of y must have undergone a change of signs , and in this transition must have become zero ...
... least be equal to the number Ñ ; but if , while x increases , this aggregate increases also , so as to become greater than N , the values of y must have undergone a change of signs , and in this transition must have become zero ...
Σελίδα 206
... least of these two limits is the first figure of that root . * PROBLEM II . To extract a root of an equation of any degree . 1. First find the limits of the roots as directed in the pre- ceding Problem ; then to extract any particular ...
... least of these two limits is the first figure of that root . * PROBLEM II . To extract a root of an equation of any degree . 1. First find the limits of the roots as directed in the pre- ceding Problem ; then to extract any particular ...
Συχνά εμφανιζόμενοι όροι και φράσεις
1st eq 2nd eq absolute number added Algebra arithmetical progression binomial biquadratic change of signs coefficient common denominator common difference compound quantity cube root cubic equation Divide the number dividend divisor equa equal quantities EXAMPLES FOR PRACTICE expressed Extg Extracting the roots Find a number Find the sum find the value Find two numbers find x geometrical progression Given the common greatest common measure hence highest power improper fraction infinite series last term 41 less method Multg Multiply nth root number of terms operation original equation proposed equation quadratic equation ques Reduce remainder Required the cube Required the numbers RULE second term side simple equations square root substituting subtract successive sums surd terms 20 third term trans transformed equation unknown quantity Whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 154 - What two numbers are those, whose difference is to the greater as 2 to 9, and the difference of whose squares is 128 1 Prob.
Σελίδα 68 - ... the square of the two terms of the root already obtained, the remainder will be equal to twice the first two terms of the root multiplied by the third plus the square of the third. Dividing this remainder, therefore, by twice the terms of the root already found, or which is the same thing, dividing the first term of the remainder by twice the first term of the root, we shall obtain the third term sought. Subtracting from the first remainder twice the product of the first two terms of the root...
Σελίδα 302 - J of the first, \ of the second, and \ of the third, may be all equal to each other. Ans. 8, 12, and 16.
Σελίδα 120 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
Σελίδα 53 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 305 - The sum of the first and second of four numbers in geometrical progression is 15, and the sum of the third and fourth is 60. Required the numbers.
Σελίδα 33 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Σελίδα 308 - One hundred stones being placed on the ground, in a straight line, at the distance of a yard from each other, how far will a person travel who shall bring them one by one to a basket, which is placed one yard from the first Stone ? Ans.
Σελίδα 307 - Find four numbers in arithmetical progression such that the sum of the first and third shall be 22, and the sum of the second and fourth 36.