Algebra1870 |
Common terms and phrases
a+b+c a₁ annuity arithmetical arithmetical mean Arithmetical Progression ax² b₁ Binomial Theorem cent coefficient common measure contains continued fraction denote digits divergent divided divisible divisor equal example expansion Extract the square factors find the chance find the number find the value given log greater than unity Hence least common multiple less than unity letters logarithm miles Multiply negative quantity nth term number of combinations number of terms numerator and denominator obtain P₁ P₂ positive integers positive quantity preceding Article prime number proper fraction quadratic equation quadratic surd quotient radix ratio remainder result scale shew shewn shillings Similarly solution Solve square root subtraction suppose surd unknown quantities white balls whole number zero
Popular passages
Page 221 - 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 49 - Hence if the numerator and denominator of a fraction be multiplied by the same number the value of the fraction is not altered.
Page 259 - ... •will be equal to the amount. That is, (Art. 567), the Principal is the present value of the amount. 576. Discount is an allowance made for the payment of a sum of money before it is due. From the definition of present value, it follows that a debt due at some future period is equitably discharged by paying the present value at once; hence the discount will be equal to the amount due diminished by its present value. 577. To find the present value of a sum due at ilie end of a given time and...
Page 16 - 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 18 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Page 199 - Dividendo, by division ; when there are four proportionals, and it is inferred, that the excess of the first above the second, is to the second, as the excess of the third above the fourth, is to the fourth.
Page 228 - ... 26. A boat's crew consists of 8 men, 3 of whom can only row on one side and 2 only on the other. Find the number of ways in which the crew can be arranged. 27. A telegraph has m arms, and each arm is capable of n distinct positions ; find the total number of signals which can be made with the telegraph, supposing that all the arms are to be used to form a signal. 28. A pack of cards consists of 52 cards marked differently; in how many different ways can the cai-ds be arranged in four sets, each...
Page 199 - One quantity is said to vary directly as a second and inversely as a third, when it varies jointly as the second and the reciprocal of the third. Thus...
Page 109 - Another form may also be given to these results, )' = a' + 2a (b + c) + b' + 2bc + cs, The following rule may be observed to hold good in the above and similar examples : the square of any multinomial consists of the square of each term, together with twice the product of each term by the sum of all the terms which follow it.
Page 60 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.