The elements of algebraOliver & Boyd, 1857 - 95 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 11.
Σελίδα 1
... negative . Thus , if a represent 7 , and b , 3 ; then a + b represents 10 , and a - b , 4 . NOTE . When no sign is prefixed , + is always understood . 4. To denote the multiplication of quantities , the letters representing them are ...
... negative . Thus , if a represent 7 , and b , 3 ; then a + b represents 10 , and a - b , 4 . NOTE . When no sign is prefixed , + is always understood . 4. To denote the multiplication of quantities , the letters representing them are ...
Σελίδα 7
... negative . NOTE . Powers of the same quantity are multiplied together by adding the indices . 19. When one factor is compound . Multiply each of its terms by the other factor . 20. When both factors are compound . Multiply each term of ...
... negative . NOTE . Powers of the same quantity are multiplied together by adding the indices . 19. When one factor is compound . Multiply each of its terms by the other factor . 20. When both factors are compound . Multiply each term of ...
Σελίδα 8
... the same sign the quotient is positive ; if they have different signs it is negative . If the divisor is an exact factor of the dividend , the quotient may be found by rejecting that factor from the 8 MULTIPLICATION . - DIVISION .
... the same sign the quotient is positive ; if they have different signs it is negative . If the divisor is an exact factor of the dividend , the quotient may be found by rejecting that factor from the 8 MULTIPLICATION . - DIVISION .
Σελίδα 43
... negative , such as b , the terms of the ex- pansion which contain the odd powers of b will be negative . Thus to raise a + b to the sixth power , the powers of a and b in the successive terms would be ao , a5b , a1b2 , a3b3 , a2b1 , ab3 ...
... negative , such as b , the terms of the ex- pansion which contain the odd powers of b will be negative . Thus to raise a + b to the sixth power , the powers of a and b in the successive terms would be ao , a5b , a1b2 , a3b3 , a2b1 , ab3 ...
Σελίδα 44
... negative , 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 ...
... negative , 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 ...
Άλλες εκδόσεις - Προβολή όλων
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...