Advanced Algebra for Colleges and SchoolsAmerican Book Company, 1902 - 608 páginas |
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Página 25
... proved similarly . Hence , for all values of a , b , and c , a + b + c = a + ( b + c ) = ( a + c ) + b = c + ( a + b ) , etc. 57. To add similar monomials . 1. Add 4a and 3 a . PROCESS 4 a 3 a 7 a - EXAMPLES EXPLANATION . Just as 4 = 1 ...
... proved similarly . Hence , for all values of a , b , and c , a + b + c = a + ( b + c ) = ( a + c ) + b = c + ( a + b ) , etc. 57. To add similar monomials . 1. Add 4a and 3 a . PROCESS 4 a 3 a 7 a - EXAMPLES EXPLANATION . Just as 4 = 1 ...
Página 33
... proved that m + s = m + ̄s . § 62 , to find the remainder when + s is subtracted from m is to find the algebraic number that added to s will give m . Since the algebraic sum of + s and -s is 0 , by the Associative Law for Addition the ...
... proved that m + s = m + ̄s . § 62 , to find the remainder when + s is subtracted from m is to find the algebraic number that added to s will give m . Since the algebraic sum of + s and -s is 0 , by the Associative Law for Addition the ...
Página 49
... prove that ( ab ) c = a ( bc ) . ( 1 ) By the Law of Order , by notation , by the Law of Order , abc = bca = ( be ) a = a ( bc ) . ( 2 ) From ( 1 ) and ( 2 ) , Similarly , it may be proved that 2. Let it be required to prove that By ...
... prove that ( ab ) c = a ( bc ) . ( 1 ) By the Law of Order , by notation , by the Law of Order , abc = bca = ( be ) a = a ( bc ) . ( 2 ) From ( 1 ) and ( 2 ) , Similarly , it may be proved that 2. Let it be required to prove that By ...
Página 51
... proved that m ( a + b ) = ma + mb . First , when m is a positive integer . m = 1 + 1 + 1 + m ( a + b ) = ( a + b ) + ( a + Since § 77 , § 56 , § 77 , ... to m terms , b ) + ( a + b ) + ... to m terms = ( a + a + a + = ma + mb . to m ...
... proved that m ( a + b ) = ma + mb . First , when m is a positive integer . m = 1 + 1 + 1 + m ( a + b ) = ( a + b ) + ( a + Since § 77 , § 56 , § 77 , ... to m terms , b ) + ( a + b ) + ... to m terms = ( a + a + a + = ma + mb . to m ...
Página 52
... proved that ( -n ) ( a + b ) = na nb . n ( a + b ) = = na + nb . By ( 1 ) and ( 2 ) , Since , if for + n in ( 3 ) , Since both ( 3 ) is positive , - ( - n ) is also positive , substituting - ( — n ) - ( - n ) ( a + b ) = − ( −n ) a ...
... proved that ( -n ) ( a + b ) = na nb . n ( a + b ) = = na + nb . By ( 1 ) and ( 2 ) , Since , if for + n in ( 3 ) , Since both ( 3 ) is positive , - ( - n ) is also positive , substituting - ( — n ) - ( - n ) ( a + b ) = − ( −n ) a ...
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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.