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added algebraic approaches arithmetical arrangements assume called cent changed CHAPTER coefficient column common factor complete consists contain continued convergent corresponding cube denominator denote determinant digits divided divisible divisor equal equation example Exercise exponent expression Extract factors feet figures Find Find the number five four fourth fraction function given gives greater groups Hence imaginary increased indicated infinite integral interest less letters limit logarithm means method miles Multiply negative NOTE obtained positive quadratic quotient ratio Reduce relation remainder represent respectively result rule selected side Simplify Solve square root stands Subtract Suppose surd taken term things third true units unknown variable whole write written yards
Page 299 - If the number is less than 1, make the characteristic of the logarithm negative, and one unit more than the number of zeros between the decimal point and the first significant figure of the given number.
Page 137 - A cask contains 12 gallons of wine and 18 gallons of water ; another cask contains 9 gallons of wine and 3 gallons of water. How many gallons must be drawn from each cask to produce a mixture containing 7 gallons of wine and 7 gallons of water?
Page 249 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means. For, if ad = bc, then, dividing by bd, or / (л- с'- v / 316.
Page 157 - The sum of the two digits of a number is 6, and if the number is divided by the sum of the digits the quotient is 4. What is the number ? 19.
Page 455 - Form all the possible products of n elements each that can be formed by taking one, and only one, element from each row, and one, and only one, element from each column ; prefix to each of the products thus formed either...
Page 270 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? 24.
Page 274 - Of three numbers in geometrical progression, the sum of the first and second exceeds the third by 3, and the sum of the first and third exceeds the second by 21. What are the numbers ? 15.
Page 412 - The coefficient pt of the fourth term with its sign changed is equal to the sum of the products of the roots taken three...