Elements of Algebra with ExercisesMacmillan Company, 1902 - 478 páginas |
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Página viii
... 2. CONDITIONAL EQUATIONS . 80 § 3. EQUIVALENT EQUATIONS 82 Fundamental Principles for Solving Integral Equations 83 § 4. LINEAR EQUATIONS IN ONE UNKNOWN NUMBER 86 PROBLEMS . CHAPTER V. PAGE CHAPTER VI . TYPE - viii CONTENTS .
... 2. CONDITIONAL EQUATIONS . 80 § 3. EQUIVALENT EQUATIONS 82 Fundamental Principles for Solving Integral Equations 83 § 4. LINEAR EQUATIONS IN ONE UNKNOWN NUMBER 86 PROBLEMS . CHAPTER V. PAGE CHAPTER VI . TYPE - viii CONTENTS .
Página 82
... Solve an equation is to find its solution . The process of solving an equation is also frequently called the solution of the equation . An equation is said to be satisfied by its solution , or the solu- tion is said to satisfy the ...
... Solve an equation is to find its solution . The process of solving an equation is also frequently called the solution of the equation . An equation is said to be satisfied by its solution , or the solu- tion is said to satisfy the ...
Página 83
... solving integral equations depend upon principles which enable us to change a given equation into an equivalent equation whose solution is more easily obtained than that of the given one . This process is called transforming the ...
... solving integral equations depend upon principles which enable us to change a given equation into an equivalent equation whose solution is more easily obtained than that of the given one . This process is called transforming the ...
Página 85
... solving an equation . ( i . ) Any term may be transferred from one member of an equation to the other , if its sign be reversed from to , or from to + . E.g. , 2 x 4 = x + 1 and 2 x - x = 1 + 4 are equivalent equations . This step is ...
... solving an equation . ( i . ) Any term may be transferred from one member of an equation to the other , if its sign be reversed from to , or from to + . E.g. , 2 x 4 = x + 1 and 2 x - x = 1 + 4 are equivalent equations . This step is ...
Página 86
... Solve the equation 14-8x = 19-3 x . -8x + 3x = 19-14 . Transferring terms , Uniting like terms , Dividing by - 5 , - - 5x = 5 . x = - 1 . --- - Ex . 3. Solve the equation ( x + 5 ) − } x = ( 3 x − 1 ) +1 . Multiplying both members by ...
... Solve the equation 14-8x = 19-3 x . -8x + 3x = 19-14 . Transferring terms , Uniting like terms , Dividing by - 5 , - - 5x = 5 . x = - 1 . --- - Ex . 3. Solve the equation ( x + 5 ) − } x = ( 3 x − 1 ) +1 . Multiplying both members by ...
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Otras ediciones - Ver todas
Elements of Algebra with Exercises George Egbert Fisher,Isaac Joachim Schwatt Sin vista previa disponible - 2016 |
Términos y frases comunes
a₁ a²b a²b² a²x a²x² a³b ab² absolute value algebraic language ALGEBRAIC NUMBERS arithmetical arithmetical means assigned number ax² binomial coefficient Commutative Law complex number continued fraction convergent cube definition denominator digits divided divisor dollars equal number equivalent exactly divisible example illustrates EXERCISES exponent Find the values following expressions following principle given equation greater illustrates the following imaginary unit inequality integer irrational number less Let x stand logarithm miles minuend monomial multinomial multiplied negative numbers obtained parentheses positive integer positive number positive units powers quadratic equation quadratic surds r₁ radicand rational number remainder required numbers result second member Simplify solution Solve the equation square root summands symbolically unknown number whence wherein x²y xy² yards
Pasajes populares
Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - 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 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - 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 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), 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 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.