Complete Secondary AlgebraFisher and Schwatt, 1901 - 288 páginas |
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Página 486
... changed , is called the minor with respect to a , and is denoted by Ag . In like manner the minor with respect to a is | b1 b2 and is C1 C2 denoted by Ag . 7. The form of the determinant of the third order given in ( III . ) , Art . 5 ...
... changed , is called the minor with respect to a , and is denoted by Ag . In like manner the minor with respect to a is | b1 b2 and is C1 C2 denoted by Ag . 7. The form of the determinant of the third order given in ( III . ) , Art . 5 ...
Página 488
... changed , the sign of the determinant is changed , but its numerical value remains the same . For , а1 ( b2Cз - b3C2 ) - ɑ¿ ( b1C3 — bg¤1 ) + а3 ( b12 — b2o1 ) - - — [ b1 ( α2¤ ̧ — ⱭçС2 ) — b2 ( α1Сç — αçС1 ) + b2 ( α ̧¤2 − α2C1 ) ...
... changed , the sign of the determinant is changed , but its numerical value remains the same . For , а1 ( b2Cз - b3C2 ) - ɑ¿ ( b1C3 — bg¤1 ) + а3 ( b12 — b2o1 ) - - — [ b1 ( α2¤ ̧ — ⱭçС2 ) — b2 ( α1Сç — αçС1 ) + b2 ( α ̧¤2 − α2C1 ) ...
Página 490
... the elements of any row , or column , be added to , or subtracted from , the corresponding elements of any other row , or column , the value of the determinant is not changed . For , | а1 + kb1 , α2 + kb2 490 [ CH . XXXIII ALGEBRA .
... the elements of any row , or column , be added to , or subtracted from , the corresponding elements of any other row , or column , the value of the determinant is not changed . For , | а1 + kb1 , α2 + kb2 490 [ CH . XXXIII ALGEBRA .
Página 506
... to the coefficient of the second- term with sign changed . The sum of the products of the roots in pairs is equal to the coefficient of the third term . The sum of the products of the roots taken three 506 [ CH . XXXIV ALGEBRA .
... to the coefficient of the second- term with sign changed . The sum of the products of the roots in pairs is equal to the coefficient of the third term . The sum of the products of the roots taken three 506 [ CH . XXXIV ALGEBRA .
Página 507
... changed ; and so on The product of the roots is equal to the last term if n be even , and to the last term with sign changed if n be odd . Ex . Given x3 – 5 x2 + 3 x + 4 = 0 . The sum of the roots is ( - 5 ) , = 5 . ― The sum of the ...
... changed ; and so on The product of the roots is equal to the last term if n be even , and to the last term with sign changed if n be odd . Ex . Given x3 – 5 x2 + 3 x + 4 = 0 . The sum of the roots is ( - 5 ) , = 5 . ― The sum of the ...
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a₁ arithmetical means arithmetical progression assume b₁ b₂ coefficient column common logarithms continued fraction convergent series corresponding d₁ d₂ decimal places denominator depressed equation determinant digits divergent series Dividing elements equal equation whose roots EXERCISES expansion factor figure Find the value finite number Form the equation geometrical means geometrical progression given equation given series graph harmonical mean Hence increases indefinitely infinite series last term less limit logarithms mantissa method multiplying nth term number of combinations obtained partial fractions partial quotient permutations preceding article principle quadratic equation r₁ r₂ ratio real roots reciprocal equation result root of f(x S₁ second member series is convergent solution Solve the equation Sturm's Theorem Substituting subtracted transformed equation u₁ U₂ unknown number variable variations of sign whence wherein x-axis
Pasajes populares
Página 415 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 354 - C„.r. That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 351 - We will now derive a formula for the number of permutations of n things, taken all at a time, when some of them are alike.
Página 313 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 317 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 310 - Two workmen can do a piece of work in 6 days. How long will it take each of them to do the work, if it takes one 5 days longer than the other ? 19.
Página 360 - V(a2 — °^)> etc-, are functions of x ; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 315 - In any proportion the terms are in proportion by. Composition ; that is, the sum of the first two terms is to the first term, as the sum of the last two terms is to the third ter.n.
Página 323 - If a body falls 256 feet in 4 seconds, how far will it fall in 10 seconds?
Página 373 - An infinite series is said to be divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great.