Elements of AlgebraMacmillan, 1918 |
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Página 65
... 3x , and its excess over 100 is 3 х 100 . - Eight times the less is 8 ( 60 - x ) , and its defect from 200 is 2008 ( 60 - x ) . and Whence the symbolical statement of the question is 3 65 Problems Leading to Simple Equations.
... 3x , and its excess over 100 is 3 х 100 . - Eight times the less is 8 ( 60 - x ) , and its defect from 200 is 2008 ( 60 - x ) . and Whence the symbolical statement of the question is 3 65 Problems Leading to Simple Equations.
Página 66
Henry Sinclair Hall. and Whence the symbolical statement of the question is 3 x 100 200 - 8 ( 60 — x ) ; - - 3x 100 200 480 + 8x , = - 480100200 8x - 3x , ... == 5 = 180 ; x = 36 , the greater part , 60x24 , the less . Ex . 3. Divide ...
Henry Sinclair Hall. and Whence the symbolical statement of the question is 3 x 100 200 - 8 ( 60 — x ) ; - - 3x 100 200 480 + 8x , = - 480100200 8x - 3x , ... == 5 = 180 ; x = 36 , the greater part , 60x24 , the less . Ex . 3. Divide ...
Página 130
... 1 + 8x2 Ex . Prove that = 2x - 6x8 +18 25 . By division 1+ 3x2 ) 2x ( 2x - 6x + 1825 2x + 6x8 - 6x8 6x3 18 25 1825 18x5 + 54x7 whence the result follows . -54x7 Here the division may be carried on to any number 130 ALGEBRA .
... 1 + 8x2 Ex . Prove that = 2x - 6x8 +18 25 . By division 1+ 3x2 ) 2x ( 2x - 6x + 1825 2x + 6x8 - 6x8 6x3 18 25 1825 18x5 + 54x7 whence the result follows . -54x7 Here the division may be carried on to any number 130 ALGEBRA .
Página 139
... ) = ( x − c ) ( x + c ) + ab . Multiplying out , we have whence x2 + ax + bx + ab — ac — c2 = x2 — c2 + ab ; - ax + bx = ac , ( a + b ) x = ac ; ac x = a + b Ex . 2. Solve a b X -a х b FRACTIONAL AND LITERAL EQUATIONS . 139.
... ) = ( x − c ) ( x + c ) + ab . Multiplying out , we have whence x2 + ax + bx + ab — ac — c2 = x2 — c2 + ab ; - ax + bx = ac , ( a + b ) x = ac ; ac x = a + b Ex . 2. Solve a b X -a х b FRACTIONAL AND LITERAL EQUATIONS . 139.
Página 149
... Whence and 7 ( 5x + 1 ) + 3y = 24 . 85y + 7 + 6y = 48 , 41 y = 41 ; ... y = 1 . ( 1 ) , ( 2 ) . This value substituted in either ( 1 ) or ( 2 ) gives x = 3 . Rule . From one of the equations , find the value of the unknown quantity to ...
... Whence and 7 ( 5x + 1 ) + 3y = 24 . 85y + 7 + 6y = 48 , 41 y = 41 ; ... y = 1 . ( 1 ) , ( 2 ) . This value substituted in either ( 1 ) or ( 2 ) gives x = 3 . Rule . From one of the equations , find the value of the unknown quantity to ...
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Elements of Algebra: Being the First Thirty-Eight Chapters of Hall and ... Henry Sinclair Hall Sin vista previa disponible - 2017 |
Términos y frases comunes
a²b a²b² a²x a²x² a³b ab² ab³ Arithmetic arithmetic means arranged ax² ax³ binomial Binomial Theorem bx² cents CHAPTER coefficient complete quotient compound expressions contains cube root denote digits dimes Divide dividend division divisor equal equation Find the highest find the number Find the square Find the sum find the value following expressions fraction harmonic means Hence highest common factor letters logarithm lowest common multiple means Multiply negative number of terms numerator and denominator obtain prefix 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 x³y² x³y³ xy² xy³ yards zero
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Página 321 - Therefore the number of permutations of n things taken r at a time is n(n -l)1n — 2)-.(n — r + 1).
Página 300 - Find the area of a circle whose radius is 12 feet, from the law that the area of a circle varies as the square of its radius.
Página 169 - 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. INVOLUTION OF MONOMIALS. 187. From definition -we have, by the rules of multiplication, (a2)* = a1 . a
Página 330 - Simoom, so that vowels and consonants occur alternately in each word ? 4. 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 353 - The logarithm of a product is the sum of the logarithms of its factors.
Página 185 - 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 354 - DEFINITION. The integral part of a logarithm is called the characteristic, and the decimal part, when it is so written that it is positive, is called the mantissa.
Página 102 - DEFINITION. The Lowest Common Multiple of two or more algebraic expressions is the expression of lowest dimensions which is divisible by each of them without remainder. The abbreviation L.
Página 324 - 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 ? (1...
Página 291 - 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.