The elements of algebraOliver & Boyd, 1857 - 95 σελίδες |
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Σελίδα 39
... whole length ? Ans . 24 feet . ( 32. ) Having paid away one - fourth of my money , and then two - fifths of what remained , I had £ 54 left ; how much had I at first ? Ans . £ 120 . ( 33. ) Having paid away half of my money , two ...
... whole length ? Ans . 24 feet . ( 32. ) Having paid away one - fourth of my money , and then two - fifths of what remained , I had £ 54 left ; how much had I at first ? Ans . £ 120 . ( 33. ) Having paid away half of my money , two ...
Σελίδα 44
... whole or fractional , it is capable of very extensive appli- cation . EXERCISES . Expand the following by means of the Binomial Theorem . ( 1. ) ( a + b ) ® . Ans . a6 + 6a5b + 15a1b2 + 20μ3b3 + 15a2b1 + 6ab5 + bo . ( 2. ) ( a2 — b2 ) 4 ...
... whole or fractional , it is capable of very extensive appli- cation . EXERCISES . Expand the following by means of the Binomial Theorem . ( 1. ) ( a + b ) ® . Ans . a6 + 6a5b + 15a1b2 + 20μ3b3 + 15a2b1 + 6ab5 + bo . ( 2. ) ( a2 — b2 ) 4 ...
Σελίδα 56
... whole expression thus found by twice the coefficient of the higher power . This is merely expressing the general formula , x = − b + √ ( b2 + 4ac ) in English ; and in all particular examples 2a " the value of the unknown quantity may ...
... whole expression thus found by twice the coefficient of the higher power . This is merely expressing the general formula , x = − b + √ ( b2 + 4ac ) in English ; and in all particular examples 2a " the value of the unknown quantity may ...
Σελίδα 57
... whole by the coefficient of the higher power . It may be observed that all quadratics may be resolved by either formula , the latter being preferable when the coef- ficient of the lower power is an even number . NOTE . In addition to ...
... whole by the coefficient of the higher power . It may be observed that all quadratics may be resolved by either formula , the latter being preferable when the coef- ficient of the lower power is an even number . NOTE . In addition to ...
Σελίδα 63
... whole and one of the parts may be equal to the square of the other . 1 . 3+ √ 5 Ans . a and a 2 " 3 No5 - 2 ( 26. ) Find a fraction which is greater than its square by Ans .. ( 27. ) A person divided £ 5 equally among some poor people ...
... whole and one of the parts may be equal to the square of the other . 1 . 3+ √ 5 Ans . a and a 2 " 3 No5 - 2 ( 26. ) Find a fraction which is greater than its square by Ans .. ( 27. ) A person divided £ 5 equally among some poor people ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c a²+2ab+b² annex arithmetical series ax² binomial binomial theorem coefficient common denominator common difference common ratio compound quantity consecutive numbers cube root deno denote the number Divide divisor double equal equation contains EXERCISES expressed Extract the square factor Find a number find the Greatest Find the number Find the sum following fractions following quantities geometric means given quantity Greatest Common Measure Hence Least Common Multiple letters miles per hour mixed quantities multiplied negative number of balls number of combinations number of permutations number of terms numbers whose sum numerator and denominator Prove QUADRATIC EQUATIONS quotient remainder shillings side sign changed simple quantity square root subtracting surd t₁ things taken third total number transposing travelled unknown quantity ах
Δημοφιλή αποσπάσματα
Σελίδα 61 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 88 - The fore-wheel of a carriage makes six revolutions more than the hind-wheel in going 120 yards ; but if the circumference of each wheel be increased one yard, it will make only four revolutions more than the hind-wheel in going the same distance.
Σελίδα 60 - Divide the number 24 into two such parts, that their product shall be to the sum of their squares, as 3 to 10.
Σελίδα 16 - If the numerator and denominator of a fraction be both multiplied or both divided by the same number, the value of the fraction is not altered.
Σελίδα 44 - Divide the first term of the remainder by three times the square of the first term of the root, and write the result as the next term of the root.
Σελίδα 9 - A power of a quantity is divided by any other power of the same quantity by subtracting the index of the divisor from that of the dividend, the quotient being that power of the quantity whose index is the remainder so obtained.
Σελίδα 66 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 41 - ... be divided by the number of terms to that place, it will give the coefficient of the term next following.
Σελίδα 44 - Take the root of the first term, for the first term of the required root...
Σελίδα 40 - A man was hired 50 days on these conditions. — that, for every day he worked, he should receive $ '75, and, for every day he was idle, he should forfeit $ '25 ; at the expiration of the time, he received $ 27'50 ; how many days did he work...