Elementary AlgebraMacmillan and Company, 1895 - 478 páginas |
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Página 1
... greater generality ; for while the quantities used in arithmetical processes are denoted by figures which have one single definite value , algebraical quantities are denoted by symbols which may have any value we choose to assign to ...
... greater generality ; for while the quantities used in arithmetical processes are denoted by figures which have one single definite value , algebraical quantities are denoted by symbols which may have any value we choose to assign to ...
Página 3
... greater than unity are usually kept in the form of improper fractions . Example 4. If a = 4 , x = 1 find the value of 5xa . 5xα = 5xxα = 5 × 14 = 5x1 = 5 . NOTE . In the last example 14 = 1x1x1x1 = 1 . Similarly every power of 1 is 1 ...
... greater than unity are usually kept in the form of improper fractions . Example 4. If a = 4 , x = 1 find the value of 5xa . 5xα = 5xxα = 5 × 14 = 5x1 = 5 . NOTE . In the last example 14 = 1x1x1x1 = 1 . Similarly every power of 1 is 1 ...
Página 9
... greater than the sum of the subtractive terms ; and if the reverse were the case the result would have no arithmetical meaning . In Algebra , however , not only may the sum of the subtractive terms exceed that of the additive , but a ...
... greater than the sum of the subtractive terms ; and if the reverse were the case the result would have no arithmetical meaning . In Algebra , however , not only may the sum of the subtractive terms exceed that of the additive , but a ...
Página 11
... greater , will give the coefficient of the sum required . Example 1. The sum of 17x and -8x is 9x , for the difference of 17 and 8 is 9 , and the greater is positive . Example 2. To find the sum of 8a , -9a , -a , 3a , 4a , -11a , a ...
... greater , will give the coefficient of the sum required . Example 1. The sum of 17x and -8x is 9x , for the difference of 17 and 8 is 9 , and the greater is positive . Example 2. To find the sum of 8a , -9a , -a , 3a , 4a , -11a , a ...
Página 53
... greater than x by a " may not be self- evident to the beginner , who would of course readily answer an analogous arithmetical question , " find a number greater than 50 by 6. " The process of addition which gives the answer in the ...
... greater than x by a " may not be self- evident to the beginner , who would of course readily answer an analogous arithmetical question , " find a number greater than 50 by 6. " The process of addition which gives the answer in the ...
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Términos y frases comunes
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Pasajes populares
Página 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Página 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Página 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Página 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Página 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Página 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....