Higher AlgebraFisher and Schwatt, 1901 - 615 páginas |
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Página 4
... Observe that in the preceding examples the reasoning is the same whether the numbers are represented by letters or by Arabic numerals . The results of these operations are numbers in all cases , whether letters or numerals , or both ...
... Observe that in the preceding examples the reasoning is the same whether the numbers are represented by letters or by Arabic numerals . The results of these operations are numbers in all cases , whether letters or numerals , or both ...
Página 8
... Observe that in the work of the last example , the expres sion a + b2a + 3b - c is to be understood on the left of the symbol ,, in the second line . - = Ex . 4. If , in the last example , a 3 , b = 1 , and c = 1 , we have a + b - 2a + ...
... Observe that in the work of the last example , the expres sion a + b2a + 3b - c is to be understood on the left of the symbol ,, in the second line . - = Ex . 4. If , in the last example , a 3 , b = 1 , and c = 1 , we have a + b - 2a + ...
Página 12
... observe that , as the minuend in equations ( i . ) de- creases by 1 , 2 , or more units ( the subtrahend remaining the same ) the remainder decreases by an equal number of units . When the minuend is equal to the subtrahend , the ...
... observe that , as the minuend in equations ( i . ) de- creases by 1 , 2 , or more units ( the subtrahend remaining the same ) the remainder decreases by an equal number of units . When the minuend is equal to the subtrahend , the ...
Página 20
... Observe that in both examples the sum is of the same quality as the number which has the greater absolute value , and that the absolute value of the sum is obtained by subtracting the less abso- lute value , 2 , from the greater , 5 ...
... Observe that in both examples the sum is of the same quality as the number which has the greater absolute value , and that the absolute value of the sum is obtained by subtracting the less abso- lute value , 2 , from the greater , 5 ...
Página 28
... Observe that in changing the order of the operations the sign of operation , + or must be transferred with each number . - The method of applying the Associative Law depends upon a proper use of parentheses , which will be taken up in ...
... Observe that in changing the order of the operations the sign of operation , + or must be transferred with each number . - The method of applying the Associative Law depends upon a proper use of parentheses , which will be taken up in ...
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Higher Algebra George Egbert Fisher,Isaac J. 1867- jt. auth Schwatt Sin vista previa disponible - 2015 |
Términos y frases comunes
a₁ a²b a²x a²x² ab² algebraic arithmetical means arithmetical progression assigned number ax² b₁ binomial coefficient Commutative Law complex number continued fraction convergent corresponding cube root definition denominator determinant difference digits divided divisor equal equivalent EXERCISES exponent Find the values finite following expressions following principle geometrical progression given equation given expression given number given series given system greater harmonical means inequality integer irrational number less logarithm mantissa method miles multinomial multiplied negative number obtained parentheses positive integer positive number powers preceding article principal root quadratic equation quotient r₁ radicand rational number remainder required numbers result S₁ second member second term Simplify solution Solve the equation square root Substituting subtracted surds unknown number whence wherein x²y 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 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 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 64 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
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.
Página 456 - 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 364 - The volume of a gas varies inversely as the pressure when the temperature is constant. When the pressure is 15, the volume is 20; what is the volume when the pressure is 20 ? Let v stand for the volume and p for the pressure. Then from pv = k we obtain k = 300. Therefore pv = 300. Consequently, when p = 20, 20 v = 300 ; whence v = 15. EXERCISES III. If zee y, what is the expression for x in terms of y, 1.
Página 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Página 204 - A system of linear equations has a definite number of solutions. (i.) When the number of equations is the same as the number of unknown numbers. (ii.) When the equations are independent and consistent.
Página 100 - The square of the sum of two numbers is equal to the square \ (¿ of the first, plus twice the product of the first and second, plus the J square of the second.