## Advanced Algebra |

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algebraic arithmetic mean arithmetic progression arranged ax² b₁ Binomial Theorem coefficients cologarithm complex number constant term decimal places denominator denote Descartes determinant digits Diminish the roots divided equation whose roots equation x² Exercises expansion exponent expression factor feet Find the number Find the value following equations formula fractions function geometric progression given equation graph graphically Hence Horner's method Illustrative example Illustrative example II inches inequality loga logarithm mantissa mathematical induction maximum minimum value multiplied negative root number of permutations number of terms obtain partial fractions positive root Proof proportion Prove quadratic equation quantities quotient rational real numbers real roots rectangle remainder represent result row or column Rules of Signs Simplify Solution Solve the equation square root subtract things taken transformed equation variable Write the equation

### Popular passages

Page 98 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.

Page 282 - My lord, I have undertaken this long journey purposely to see your person, and to know by what engine of wit or ingenuity you came first to think of this most excellent help into astronomy, viz. the logarithms ; but, my lord, being by you found out, I wonder nobody else found it out before, when now known it is so easy.

Page 33 - If four quantities are in proportion, they are in proportion by inversion ; that is, the second term is to the first as the fourth is to the third.

Page 265 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.

Page 276 - ... log. 2=— 1-^3 log. 2 =2.0969100 (2.) Calculate the common logarithm of 17. Ans. 1.2304489. (3.) Given the logs, of 2 and 3 to find the logarithm of 12.5. Ans. 1+2 log. 3— 2 log. 2. (4.) Having given the logs, of 3 and .21, to find the logarithm of 83349. Ans. 6+2 log. 3+3 log. .21. ON EXPONENTIAL EQUATIONS. An exponential equation is an equation in which the unknown...

Page 34 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 267 - If the given number is greater than 1, make the characteristic of its logarithm one less than the number of figures to the left of the decimal point in the number.

Page 265 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 274 - Root of a Number, Divide the logarithm of the number by the index of the required root.

Page 86 - The square of the period of a planet is proportional to the cube of its mean distance from the Sun.