An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to GeometryEvert Duyckinck, Daniel D. Smith and George Long, 1818 - 260 σελίδες |
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Σελίδα 82
... substituted for the unknown quantity , will make both sides of the equation vanish , or become equal to each other A simple equation can have only one root ; but every compound equation has as many roots as it contains di- mensions , or ...
... substituted for the unknown quantity , will make both sides of the equation vanish , or become equal to each other A simple equation can have only one root ; but every compound equation has as many roots as it contains di- mensions , or ...
Σελίδα 92
... substitution , x - d- - 2 3. Given 1 x + y = 7 to find the values of a and y 2y Here , from the first equation , x = 14- 3 ' 3y And from the second , x = 24- Therefore , by equality , 14- 23-24- 3y , And consequently 42-2y = 72- 9y 2 ...
... substitution , x - d- - 2 3. Given 1 x + y = 7 to find the values of a and y 2y Here , from the first equation , x = 14- 3 ' 3y And from the second , x = 24- Therefore , by equality , 14- 23-24- 3y , And consequently 42-2y = 72- 9y 2 ...
Σελίδα 93
... substituted for x , in the second , gives 3 ( 17-2y ) —y = 2 , Or 51-6y - y = 2 , or 7y = 51—2—49 , 49 Whence y = = 1 , and x = 17-2y = 3 . 7 2. Given { x + y = 13 } x = 3 to find the values of x and y . From the first equation , x = 13 ...
... substituted for x , in the second , gives 3 ( 17-2y ) —y = 2 , Or 51-6y - y = 2 , or 7y = 51—2—49 , 49 Whence y = = 1 , and x = 17-2y = 3 . 7 2. Given { x + y = 13 } x = 3 to find the values of x and y . From the first equation , x = 13 ...
Σελίδα 94
... substituted for x in the second , gives ( 12 ) 2 + y2 = c , or a2 y2 + y2 = c , 62 bac Whence we have a2y2 + b2 y2 = b2c , or y2 = a2 + b2 C c And , consequently , y = b a2 + b2 and x = α√ a2 + 62 RULE III . Let one or both of the ...
... substituted for x in the second , gives ( 12 ) 2 + y2 = c , or a2 y2 + y2 = c , 62 bac Whence we have a2y2 + b2 y2 = b2c , or y2 = a2 + b2 C c And , consequently , y = b a2 + b2 and x = α√ a2 + 62 RULE III . Let one or both of the ...
Σελίδα 98
... substitution and reduction , y = 7 and x = 3 . 3. Given x + y + z = 53 , x + 2y + 32 = 105 , and x + 3y + 4z = 134 , to find the values of x , y , and z . + 1 1 3 Ans . x = 24 , y = 6 , and z = 23 4. Given x + y + 2 = 32 , 1 1 1 1 x + y ...
... substitution and reduction , y = 7 and x = 3 . 3. Given x + y + z = 53 , x + 2y + 32 = 105 , and x + 3y + 4z = 134 , to find the values of x , y , and z . + 1 1 3 Ans . x = 24 , y = 6 , and z = 23 4. Given x + y + 2 = 32 , 1 1 1 1 x + y ...
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An Introduction to Algebra; With Notes and Observations: Designed for the ... John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
Algebra arithmetical arithmetical mean arithmetical series bers coefficient common denominator compound quantity consequently cube root cubic equation decimal denoted Diophantus dividend divisor equal EXAMPLES FOR PRACTICE find the difference find the least find the product find the square find the sum find the value find two numbers fraction required geometrical geometrical progression geometrical series give given number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied negative nth root number of terms number required PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder Required the difference Required the sum required to convert required to divide required to find required to reduce result rithm rule second term side simple form square number square root square sought substituted subtracted sum required surd tion triangle unknown quantity Whence α α
Δημοφιλή αποσπάσματα
Σελίδα 10 - 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.
Σελίδα 20 - 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 27 - 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 173 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...
Σελίδα 77 - 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...
Σελίδα 93 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
Σελίδα 93 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.
Σελίδα 94 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.
Σελίδα 30 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.