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 sider |
Inni boken
Resultat 1-5 av 11
Side 76
... bers 2 , 4 , 6 , 8 , 10 , 12 , & c . Ans . 720 . 7. The first term of a decreasing arithmetical series is 10 , the common difference and the number of terms 1 3 ' 21 ; required the sum of the series . Ans . 140 . 8. One hundred stones ...
... bers 2 , 4 , 6 , 8 , 10 , 12 , & c . Ans . 720 . 7. The first term of a decreasing arithmetical series is 10 , the common difference and the number of terms 1 3 ' 21 ; required the sum of the series . Ans . 140 . 8. One hundred stones ...
Side 119
... bers , Hence tion , ( x + 3 ) = x2 + 3xy = 45 { x + y ( x + 2y ) = x2 + 3xy + 2y = 77 } by the ques- And 2y2 = 77-45-32 , by subtraction , Or y2 = 32 16 by division , and y = √16 = 4 , 2 Therefore x2 + 3xy = x2 + 12x = 45 , by the 1st ...
... bers , Hence tion , ( x + 3 ) = x2 + 3xy = 45 { x + y ( x + 2y ) = x2 + 3xy + 2y = 77 } by the ques- And 2y2 = 77-45-32 , by subtraction , Or y2 = 32 16 by division , and y = √16 = 4 , 2 Therefore x2 + 3xy = x2 + 12x = 45 , by the 1st ...
Side 138
... bers , the operation will stand thus : First Sup . Second Sup . 4.2 4.3 • 17.64 • : 18.49 . 74.088 · X3 79.507 . 95.928 Results 102.297 102.297 4.3 102.297 • • • 95.928 Therefore 4.2 6.369 : .1 :: 100 09 2.297036 So that the three roots ...
... bers , the operation will stand thus : First Sup . Second Sup . 4.2 4.3 • 17.64 • : 18.49 . 74.088 · X3 79.507 . 95.928 Results 102.297 102.297 4.3 102.297 • • • 95.928 Therefore 4.2 6.369 : .1 :: 100 09 2.297036 So that the three roots ...
Side 139
... bers ; then First Sup . 4.264 . 18.181696 • • x • x2 • 77.526752 x3 • • Second Sup . 4.265 18.190225 77.581310 · • 99.972448 Results 100.036535 Therefore 100.036535 4.265 100 99.972448 4.264 99.972448 .064087 : .001 :: .027552 .0004299 ...
... bers ; then First Sup . 4.264 . 18.181696 • • x • x2 • 77.526752 x3 • • Second Sup . 4.265 18.190225 77.581310 · • 99.972448 Results 100.036535 Therefore 100.036535 4.265 100 99.972448 4.264 99.972448 .064087 : .001 :: .027552 .0004299 ...
Side 150
... bers , which admit of no common divisor , except when it is also a divisor of c . RULE . 1. Let wh denote a whole , or integral number ; and reduce the equation to the form _by ± c c - by x = —wh , or x = . wh . α α 2. Throw all whole ...
... bers , which admit of no common divisor , except when it is also a divisor of c . RULE . 1. Let wh denote a whole , or integral number ; and reduce the equation to the form _by ± c c - by x = —wh , or x = . wh . α α 2. Throw all whole ...
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 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...
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.