Complete Secondary AlgebraFisher and Schwatt, 1901 - 288 páginas |
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Página 285
... is evidently ax2 + bx + c = = 0 . The coefficient a is assumed to be positive and not 0 , but b and c may either or both be positive or negative , or 0 . Dividing by a , Transferring b x2 + x + 6-71 285 QUADRATIC EQUATIONS .
... is evidently ax2 + bx + c = = 0 . The coefficient a is assumed to be positive and not 0 , but b and c may either or both be positive or negative , or 0 . Dividing by a , Transferring b x2 + x + 6-71 285 QUADRATIC EQUATIONS .
Página 287
... last article enable us to form an equation if its roots be given . We may always assume that the coefficient of the second power of the unknown number is 1 . = - - Ex . 1. Form the equation whose 7-10 ] 287 QUADRATIC EQUATIONS .
... last article enable us to form an equation if its roots be given . We may always assume that the coefficient of the second power of the unknown number is 1 . = - - Ex . 1. Form the equation whose 7-10 ] 287 QUADRATIC EQUATIONS .
Página 327
... assumed to be that two terms , beginning with the last and counting toward the first , are to be taken . - 12. Formulæ ( I. ) and ( II . ) , or ( I. ) and ( III . ) , may be used simultaneously to determine any two of the five numbers ...
... assumed to be that two terms , beginning with the last and counting toward the first , are to be taken . - 12. Formulæ ( I. ) and ( II . ) , or ( I. ) and ( III . ) , may be used simultaneously to determine any two of the five numbers ...
Página 343
... Assuming , then , that the laws hold for ( a + b ) ” , we have + ( a + b ) " = a * + rar1b + r2 ( 1 − 1 ) ar − 2b2 + - 1.2 ... + r ( r — 1 ) ( r — 2 ) ... ( r − k + 3 ) qr - * + 278–8 ... 1.2.3 . ( k2 ) - r ( r − 1 ) ( r − 2 ) ··· ...
... Assuming , then , that the laws hold for ( a + b ) ” , we have + ( a + b ) " = a * + rar1b + r2 ( 1 − 1 ) ar − 2b2 + - 1.2 ... + r ( r — 1 ) ( r — 2 ) ... ( r − k + 3 ) qr - * + 278–8 ... 1.2.3 . ( k2 ) - r ( r − 1 ) ( r − 2 ) ··· ...
Página 363
... assumed to be a variable . It is evident that the value of this fraction can be made greater than any assigned number , however great , by taking its denominator sufficiently small . A variable which can become and remain numerically ...
... assumed to be a variable . It is evident that the value of this fraction can be made greater than any assigned number , however great , by taking its denominator sufficiently small . A variable which can become and remain numerically ...
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Términos y frases comunes
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.