College Algebra |
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Common terms and phrases
10th term 2d term 7th term a₁ a³b arithmetical means arithmetical progression ax² b₁ binomial chance coefficient completing the square complex numbers constant contains coördinates determinant different things digits dividing equa equal EXERCISE exponent Extract the square extracting square roots factors Find the 7th Find the number Find the sum Find the value following equations following expressions fractions geometric means geometrical progression given equation Hence inequality irrational mantissa monomial multiplying negative nth root number of permutations number of terms obtained P₁ partial fractions points polynomial positive integer proportion quadratic equation quotient radical radicand ratio represent Simplify solution Solve the equation Solve the following square root substituting subtracting surds theorem tion total number transposing and uniting variable VERIFICATION zero
Popular passages
Page 174 - If x be the number of permutations of n different things, taken r at a time, when each of the n things can be repeated, x = n'.
Page 149 - Now all know that the intensity of illumination varies inversely as the square of the distance.
Page 167 - The number of permutations of n different things taken r at a time is denoted by „Pr.
Page 148 - The volume of a sphere varies as the cube of the radius, and the surface area of a, sphere as the square of the radius.
Page 89 - Complete the square by adding to both members the square of half the coefficient of x. Extract the square root of both members, and solve the sim259.
Page 151 - It will be observed that the coefficient of d in any term is one less than the number of the term. Hence, in the nth, or last term, the coefficient of d will be n — 1.
Page 157 - It will be observed that the exponent of r in any term is one less than the number of the term. Hence, in the nth or last term, the exponent of r will be n — 1.
Page 101 - Thus, in the equation ar — 2 x -f- 4 = 0, since a = 1, b= — 2, and с =4, the discriminant is — 12. Therefore, the roots are imaginary and unequal. The character of the roots of any given equation may therefore be found by evaluating the discriminant. The following summary will be found useful : (1) If 62 — 4 ac> 0, the roots are real and unequal. (2) If 62 = 4 ac, the roots are real and equal.
Page 139 - AB + BC, etc. : A'B' + B'C', etc. : : AB : A'B', § 266 (in a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to it That is P : P' A П : A
Page 193 - Whence x + y is the logarithm of mn. q. BD 10. Prop. 2. — Tlie logarithm of the quotient of two numbers is the logarithm, of the dividend minus the logarithm of the divisor.