Algebra for Colleges and SchoolsMacmillan, 1897 - 516 páginas |
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Página xii
... Equal Coefficients 345 • Greatest Coefficient . 345 Greatest Term . 345 Sum of the Coefficients 347 Expansion of Multinomials 347 Application when Index is Negative or Fractional 347 XXXVIII . Logarithms Properties of Logarithms ...
... Equal Coefficients 345 • Greatest Coefficient . 345 Greatest Term . 345 Sum of the Coefficients 347 Expansion of Multinomials 347 Application when Index is Negative or Fractional 347 XXXVIII . Logarithms Properties of Logarithms ...
Página 5
... equal to 0 , the product must be equal to 0 , whatever values the other factors may have . A factor 0 is usually called a zero factor . For instance , if x = 0 , then ab3xy2 contains a zero factor . Therefore ab3xy2 = 0 when x = 0 ...
... equal to 0 , the product must be equal to 0 , whatever values the other factors may have . A factor 0 is usually called a zero factor . For instance , if x = 0 , then ab3xy2 contains a zero factor . Therefore ab3xy2 = 0 when x = 0 ...
Página 8
... equal . Beginners should be particu- larly careful not to employ the sign of equality in any vague and inexact sense . 3. Unless the expressions are very short the signs of equality in the steps of the work should be placed one under ...
... equal . Beginners should be particu- larly careful not to employ the sign of equality in any vague and inexact sense . 3. Unless the expressions are very short the signs of equality in the steps of the work should be placed one under ...
Página 10
... equal in magnitude but opposite in direction to the distance represented by +30 . Thus the negative sign may here be taken as indicating a reversal of direction . Many other illustrations might be chosen ; but it will be sufficient here ...
... equal in magnitude but opposite in direction to the distance represented by +30 . Thus the negative sign may here be taken as indicating a reversal of direction . Many other illustrations might be chosen ; but it will be sufficient here ...
Página 12
... equal but with opposite signs is zero . The sum of 5 a and -5 a is 0 . Find the sum of EXAMPLES II . 1. 5a , 7 a , 11 a , a , 23 a . 9 . - - - 11b , — 5b , – 3b , - b . 10 . - 5x , x , -3x , 2x , -x . 11 . 26y , -11y , - 15y , y , -3y ...
... equal but with opposite signs is zero . The sum of 5 a and -5 a is 0 . Find the sum of EXAMPLES II . 1. 5a , 7 a , 11 a , a , 23 a . 9 . - - - 11b , — 5b , – 3b , - b . 10 . - 5x , x , -3x , 2x , -x . 11 . 26y , -11y , - 15y , y , -3y ...
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Términos y frases comunes
a²b a²b² a²x a²x² a³b ab² ab³ algebraic arithmetic means arithmetical ascending powers ax² ax³ b₁ binomial Binomial Theorem bx² cents CHAPTER coefficient column compound expressions continued fraction convergent cube denote digits dimes Divide dividend divisible divisor equal equation EXAMPLES Find the highest find the number Find the square Find the sum find the value fraction harmonic means Hence highest common factor integer letters logarithm lowest common multiple miles an hour Multiply negative number of terms numerator and denominator obtain positive quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs Simplify Solve square root Subtract surd symbols unknown quantity whence whole number x²y x²y² x³y xy² xy³ yards zero
Pasajes populares
Página 167 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Página 264 - That is, if a quadratic equation be reduced to the form x?+px = q, the algebraic sum of the roots is equal to the coefficient of x with its sign changed, and the product of the roots is equal to the second member, with its sign changed.
Página 351 - The logarithm of a product is the sum of the logarithms of its factors.
Página 352 - The Integral Part of a logarithm is called the Characteristic, and the decimal part the Mantissa.
Página 183 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Página 102 - ... remainder. The lowest common multiple of two or more algebraic expressions is the expression of lowest degree which will contain them all without a remainder.
Página 289 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Página 328 - A telegraph has 5 arms, and each arm has 4 distinct positions, including the position of rest: find the total number of signals that can be made.
Página 322 - From 7 Englishmen and 4 Americans a committee of 6 Is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Página 290 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if a...