Advanced Algebra for Colleges and SchoolsAmerican Book Company, 1902 - 608 páginas |
Dentro del libro
Resultados 1-5 de 41
Página 163
... b ) are identical equations . - - An equation whose members are numerical is evidently an identical equation . 10 = 6 + 4 ; 8 × 2 = 6 + 12 - 2 are identical equations . A literal equation that is true for all values of 163 SIMPLE EQUATIONS.
... b ) are identical equations . - - An equation whose members are numerical is evidently an identical equation . 10 = 6 + 4 ; 8 × 2 = 6 + 12 - 2 are identical equations . A literal equation that is true for all values of 163 SIMPLE EQUATIONS.
Página 164
... true for all values of x and y . 192. An equation that is true for only certain values of its letters is called an Equation of Condition . An equation of condition is usually termed simply an Equation . x + 4 = 10 is an equation of ...
... true for all values of x and y . 192. An equation that is true for only certain values of its letters is called an Equation of Condition . An equation of condition is usually termed simply an Equation . x + 4 = 10 is an equation of ...
Página 192
... true . Substituting and solving , y = 1 . Substituting the value of y for y in eq . ( 3 ) , x = 4 , eq . ( 6 ) . PROOF OF THE EQUIVALENCE . - By § 196 , ( 3 ) is equivalent to ( 1 ) . In the process , ( 4 ) is obtained by substituting ...
... true . Substituting and solving , y = 1 . Substituting the value of y for y in eq . ( 3 ) , x = 4 , eq . ( 6 ) . PROOF OF THE EQUIVALENCE . - By § 196 , ( 3 ) is equivalent to ( 1 ) . In the process , ( 4 ) is obtained by substituting ...
Página 206
... true of equations ( 6 ) and ( 7 ) . Hence , ( 4 ) is only a different form of ( 3 ) , and ( 7 ) is only a different form of ( 6 ) ; that is , ( 1 ) and ( 2 ) are not inde- pendent equations . But if ab'a'b is not equal to zero , neither ...
... true of equations ( 6 ) and ( 7 ) . Hence , ( 4 ) is only a different form of ( 3 ) , and ( 7 ) is only a different form of ( 6 ) ; that is , ( 1 ) and ( 2 ) are not inde- pendent equations . But if ab'a'b is not equal to zero , neither ...
Página 239
... true for all values of m and n , the meanings of zero , negative , and fractional exponents may be readily discovered . Then , having verified the remaining laws of exponents for these exponents , all the laws will have been shown to be ...
... true for all values of m and n , the meanings of zero , negative , and fractional exponents may be readily discovered . Then , having verified the remaining laws of exponents for these exponents , all the laws will have been shown to be ...
Otras ediciones - Ver todas
Términos y frases comunes
a²b² a²x² ab² absolutely convergent algebraic sum arithmetical means arithmetical progression ax² binomial called cents coefficients column Commutative Law complex numbers continued fraction convergent convergent series cube root denominator difference digits divided dividend divisible established as follows EXAMPLES exponent expression factor Find the sum Find the value finite formula function geometrical mean geometrical progression geometrical series given equation Hence highest common divisor imaginary numbers inequality integer last term limit logarithm multiplied negative number nth root number of terms numerically less obtained polynomial positive integer positive number positive root PRINCIPLE quadratic quotient ratio real number reduced remainder represent result second term SOLUTION square root Substituting subtracted surd third Transposing twice units unknown number variable x²y x²y²
Pasajes populares
Página 212 - ... and if the number is divided by the sum of its digits, the quotient is 21 and the remainder 4.
Página 134 - Multiplying or dividing both terms of a fraction by the same number does not change the value of the fraction.
Página 343 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Página 41 - A term may be transposed from one member of an equation to the other, provided its sign is changed.
Página 435 - The number of permutations of n different things taken r at a time is denoted by „Pr.
Página 424 - The logarithm of a quotient is found by subtracting the logarithm of the divisor from that of the dividend.
Página 40 - The process of changing a term from one member of an equation to the other is called Transposition.
Página 331 - PRINCIPLE 7. — If four numbers are in proportion, the. difference between the terms of the first ratio is to either term of the first ratio as the difference between the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Division.
Página 323 - A farmer has two cubical granaries. The side of one is 3 yards longer than the side of the other, and the difference in their solid contents is 117 cubic yards.
Página 426 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.