Higher Algebra |
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Common terms and phrases
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
Popular passages
Page 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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.
Page 379 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Page 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.
Page 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.