First Lessons in Algebra: Being an Easy Introduction to that Science ; Designated for the Use of Academies and Common Schools |
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Page 10
... Exponents . 107 To divide Compound Quantities of different Powers 108 CHAP . VIII . EQUATIONS OF THE FIRST DEGREE . SECT . I. Introduction .. II . To remove Coefficients . III . To remove Denominators IV . Transposition V. Questions for ...
... Exponents . 107 To divide Compound Quantities of different Powers 108 CHAP . VIII . EQUATIONS OF THE FIRST DEGREE . SECT . I. Introduction .. II . To remove Coefficients . III . To remove Denominators IV . Transposition V. Questions for ...
Page 90
... Exponent . It shows the Power of the letter ; that is , how many times it is used as a factor in the multipli- cation . When a letter has no number annexed , the exponent is always a unit , or 1 , and the letter is said to be the first ...
... Exponent . It shows the Power of the letter ; that is , how many times it is used as a factor in the multipli- cation . When a letter has no number annexed , the exponent is always a unit , or 1 , and the letter is said to be the first ...
Page 91
... exponent of a quantity , be- ing very different things , must not be confounded to- gether . Thus , the values of 5 x and 5 are far from being equal . Let the value of x be 6 ; then 5 x = 5 × 6 = 30 ; but x5 = 6 × 6 × 6 × 6 × 6 = 7776 ...
... exponent of a quantity , be- ing very different things , must not be confounded to- gether . Thus , the values of 5 x and 5 are far from being equal . Let the value of x be 6 ; then 5 x = 5 × 6 = 30 ; but x5 = 6 × 6 × 6 × 6 × 6 = 7776 ...
Page 92
... exponent is multiplied by the exponent of the power proposed ; thus , a3x2 = a ; for a aaa , and a a a × αάα = α . H 14. What is the third power of a b3 ? Ans . a . 15. What is the second power of a3 bx2 ? 16. Raise a b3 x to the ...
... exponent is multiplied by the exponent of the power proposed ; thus , a3x2 = a ; for a aaa , and a a a × αάα = α . H 14. What is the third power of a b3 ? Ans . a . 15. What is the second power of a3 bx2 ? 16. Raise a b3 x to the ...
Page 93
... obtained by actual multiplication . These powers , however , are often expressed by means of an exponent . Thus , ( a + b + c ) 3 indicates the third power of a + b + 2. It is required to find the fifth power of POWERS . 93.
... obtained by actual multiplication . These powers , however , are often expressed by means of an exponent . Thus , ( a + b + c ) 3 indicates the third power of a + b + 2. It is required to find the fifth power of POWERS . 93.
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Common terms and phrases
A's share acres added Algebra amount answer apples asked the age binomial bought bushels cents chaise coefficient common denominator completing the square compound quantities contain cost cube root debt difference Divide dividend divisor dollars equal exponent expressed Extract the square farmer fourth power fourth root frac gain gallons gentleman give given quantity greater horse improper fraction less letter merator miles an hour mixed multiply equation negative quantity obtain oranges peaches pears pounds quan question quotient receive Reduce remainder Required the number rods second power second term SECTION shillings Simple Quantities sold square root subtracted third power tion tity transposition twice unknown quantity worth x y z x²y yards α² α³ ху
Popular passages
Page 246 - Several gentlemen made an excursion, each taking the same sum of money. Each had as many servants attending him as there were gentlemen ; the number of dollars which each had was double the number of all the servants, and the whole sum of money taken out was 3456 dollars.
Page 122 - A man driving his geese to market, was met by another, who said, good morrow, master, with your hundred geese ; says he, I have not a hundred ; but if I had half as many more as I now have, and two geese and a half, I should have a hundred ; how many had he ? /C s"~
Page 141 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days : how many days would the man alone be in drinking it ? Ans.
Page 251 - The fore-wheel of a carriage makes 6 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 4 revolutions more than the hind-wheel in the same distance.
Page 68 - Divide the first term of the dividend by the first term of the divisor, giving the first term of the quotient. Multiply the whole divisor by this term, and subtract the product from the dividend, arranging the remainder in the same order of powers as the dividend and divisor.
Page 237 - A square court yard has a rectangular gravel walk round it. The side of the court wants 2 yards of being 6 times the breadth of the gravel walk ; and the number of square yards in the walk exceeds the number of yards in the periphery of the court by 164. Required the area of the court ? All equations of the second degree may be reduced to one of the following forms.
Page 138 - A gentleman invested -J of his property in a canal. When he sold out, he lost f of the sum invested, receiving only $1,446. What was the value of his property when he began ? Ans., $11,568. 29. A gentleman leaves $315 to be divided among four servants in the following manner : B is to receive as much as A, and |- as much more; C is to receive as much as A and B, and ^ as much more ; D is to receive as much as the other three, and £ as much more. What is the share of each ? price of the chaise, the...
Page 131 - There is a fish whose head weighs 9 lb. his tail weighs as much as his head and half his body, and his body weighs as much as his head and tail both.
Page 166 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Page 125 - The distance from A to D is 34 miles. The distance from A to B is to the distance .from C to D as 2 to 3. And ± of the distance from A to B, added to half the distance from C to D, is three times the distance from B to C. What are the respective distances ? Ans.