Elementary Algebra |
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Page 1
... symbols which may have any value we choose to assign to them . The symbols employed are letters , usually those of our own alphabet ; and , though there is no restriction as to the numerical values a symbol may represent , it is ...
... symbols which may have any value we choose to assign to them . The symbols employed are letters , usually those of our own alphabet ; and , though there is no restriction as to the numerical values a symbol may represent , it is ...
Page 5
... symbols ,,, Examples . 27 = 3 ; because 33 = 27 . / 32 = 2 ; because 25 = 32 . & c . The symbol is sometimes called the radical sign . Example 1. Find the value of 5√ ( 6a3b1c ) , when a = 3 , b = 1 , c = 8 . 5 √ ( 6a3b * c ) = 5 ...
... symbols ,,, Examples . 27 = 3 ; because 33 = 27 . / 32 = 2 ; because 25 = 32 . & c . The symbol is sometimes called the radical sign . Example 1. Find the value of 5√ ( 6a3b1c ) , when a = 3 , b = 1 , c = 8 . 5 √ ( 6a3b * c ) = 5 ...
Page 9
... symbols 7a and 36 to be additive , while 4c and 2d are subtractive . - 18. But in Arithmetic the sum of the additive terms is always greater than the sum of the subtractive terms ; and if the reverse were the case the result would have ...
... symbols 7a and 36 to be additive , while 4c and 2d are subtractive . - 18. But in Arithmetic the sum of the additive terms is always greater than the sum of the subtractive terms ; and if the reverse were the case the result would have ...
Page 23
... symbols or expressions , it is understood that the symbols or expressions are to be multi- plied together . Thus ab = axb . 3ab = 3x axb . a ( x - y ) = ax ( x - y ) . ( x + y ) ( a + b ) is the product of x + y and a + b . In Algebra ...
... symbols or expressions , it is understood that the symbols or expressions are to be multi- plied together . Thus ab = axb . 3ab = 3x axb . a ( x - y ) = ax ( x - y ) . ( x + y ) ( a + b ) is the product of x + y and a + b . In Algebra ...
Page 24
... symbol 4m means four times m , that is , m + m + m + m . .. 10m = m + m + m + ...... taking ten terms . Similarly am means that m is to be taken a times ; that is So am = m + m + m + ...... the number of terms being a . Again , ( a + b ) ...
... symbol 4m means four times m , that is , m + m + m + m . .. 10m = m + m + m + ...... taking ten terms . Similarly am means that m is to be taken a times ; that is So am = m + m + m + ...... the number of terms being a . Again , ( a + b ) ...
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Common terms and phrases
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
Popular passages
Page 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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....