Elementary Algebra: First[-second] Year Course, Bücher 2Macmillan Company, 1916 |
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Elementary Algebra: First[-Second] Year Course, Volume 1 - Primary ..., Band 1 Florian Cajori,Letitia Rebekah Odell Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
a²b² a²x² absolute term addition and subtraction algebra arithmetical arithmetical means arithmetical series ax² binomial BINOMIAL THEOREM called coefficient commutative law complete divisor completing the square Compute cube root digits Divide both sides dividend exponent Factor Theorem Find the h. c. f. Find the square Find the sum Find the value fixed number formula fraction geometrical series given equation graph Hence imaginary numbers inches irrational linear equations logarithms mantissa negative numbers nth root number of terms obtain parenthesis Perform the indicated polynomial positive integer principal root quadratic equation quotient radical rational integral expression rectangle remainder satisfy signs Simplify solution Solve square root Substitute trial divisor Type form Univ variable weight WRITTEN EXERCISES zero
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Seite 5 - ху а every term is of the fourth degree ; the expression is homogeneous. To multiply a polynomial by a polynomial : Arrange the terms in both polynomials according to the ascending or descending powers of some letter ; multiply each term of the multiplicand by each term of the multiplier and add the partial products. Multiplication may be performed by detached coefficients. For example,
Seite 89 - In geometry it is proved that the length of a circle varies as its radius, that the area of a circle varies as the square of its radius, that the volume of a sphere varies as the cube of its radius. In symbols,
Seite 113 - TJie logarithm of a product is equal to the sum of the logarithms of the factors. We proceed to establish two other theorems that are no less fundamental. The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. The proof is similar to that of the first theorem. Let N and
Seite 6 - quotient an exponent equal to its exponent in the dividend minus its exponent in the divisor. Observe the law of signs Like signs give plus, unlike signs give minus. To divide one polynomial by another : I. Arrange the terms. II. Divide the first term of the dividend by the first term
Seite 37 - The fundamental principle of operations with fractions is — Both numerator and denominator of a fraction may be multiplied or divided by the same number, without changing the value of the fraction Thus,
Seite 96 - seconds, d = 680.2 + ft. 6. The brightness or intensity of light varies inversely as the square of the distance from the source of the light. How many times brighter is the page of a book illuminated at a distance of 3 ft. from the source than at a distance of 5 ft. ? Solution. The intensity
Seite 85 - This relation is expressed by the theorem : In a proportion, the product of the means is equal to the product of the extremes. 2.
Seite 5 - MULTIPLICATION 8. To multiply one term by another : Multiply the numerical coefficients ; annex the letters, giving to each letter in the product an exponent equal to the sum of its exponents in the two factors. Law of signs : Like signs give plus, unlike signs give minus. The degree of a term is the sum of the exponents of the literal factors. Thus
Seite 183 - The coefficient of any term after the first is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and divided by one more than the exponent
Seite 19 - that is, the product of one weight and its distance from the fulcrum is equal to the product of the other weight and its distance from the fulcrum. 19. If the lever is 8 ft. long, how far from the fulcrum will two weights, 30