Higher Algebra |
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Common terms and phrases
a₁ a²b a²b² a²x a²x² ab² algebraic arithmetical arithmetical means assigned number ax² b₁ binomial coefficient common factor Commutative Law complex number continued fraction convergent d₁ decimal definition denominator determinant difference digits divided divisor dollars equal equivalent exactly divisible EXERCISES exponent Find the values finite following expressions following principle geometrical progression given equation given expression given series given system greater harmonical means integer integral integral equation irrational number less logarithms mantissa miles monomial multinomial multiplied negative number obtained parentheses partial fractions positive integer positive number powers preceding article quadratic equation r₁ radicand ratio remainder required numbers result second term solution Solve the equation square root Substituting subtracted surd symbol unknown number whence wherein x²y
Popular passages
Page 415 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 71 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Page 354 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Page 104 - ... term by the exponent of a in that term, and dividing the product by a number greater by 1 than the exponent of b in that term.
Page 62 - 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.
Page 363 - If a body falls 256 feet in 4 seconds, how far will it fall in 10 seconds ? 18.
Page 444 - C„.r. That is, the number of combinations of n dissimilar things r at a time is equal to the number of combinations of the n things n — r at a time.
Page 351 - He thereby gained as much per cent on the first kind as he lost on the second. How much did he pay for each kind? 18. Two workmen can do a piece of work in 6 days. How long will it take each of them to do the work, if it takes one 5 days longer than the other ? 19. Two men, A and B, receive different wages. A earns $ 42, and В $40.
Page 362 - 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.
Page 361 - 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.