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added altitude arithmetic means arithmetic progression Axiom binomial binomial formula called Clearing of fractions coefficients common factor commutative law cube root curve decimal denominator digits divided dividend division divisor E. C. Proof Elementary Course equal numbers equivalent EXERCISES Find EXERCISES Solve expressions containing factor x feet per second Find the H. C. F. Find the numbers following examples formula geometric mean geometric progression harmonic means harmonic progression Hence identity imaginary inches indeterminate equation indicated operations last term letter linear equations logarithm lower base mantissa monomial multiplying negative number obtained pair of equations pairs of numbers points polynomial positive integers positive real number powers and roots problem quadratic quotient radical expression radicand rational reduced regular tetrahedron resulting equation satisfied side solution square root Substituting tion trapezoid trinomial unknown upper base values variables velocity weight zero
Page 173 - Whence x — y is the logarithm m of — . QED n 180. Prop. 3. — The logarithm of a power of a number is the logarithm of the number multiplied by the index of the power. DEM. — Let a be the base, and x the logarithm of m.
Page 141 - The weight of a body above the earth's surface varies inversely as the square of its distance from the earth's center. If an object weighs 2000 pounds at the earth's surface, what would be its weight if it were 12,000 miles above the center of the earth, the radius of the earth being 4000 miles ? CHAPTER XI POWERS AND ROOTS 150.
Page 180 - S = vat + \gf, where g = 32.16. 21. In what time will a body fall 1000 feet if thrown downward with a velocity of 20 feet per second ? 22. With what velocity must a body be thrown downward in order that it shall fall 360 feet in 3 seconds ? 23. A stone is dropped into a well, and the sound of its striking the bottom is heard in 3 seconds. How deep is the well if sound travels 1080 feet per second ? A body thrown upward with a certain velocity will rise as far as it would have to fall to acquire this...
Page 181 - A geometric progression is a series of numbers in which any term after the first is obtained by multiplying the preceding term by a fixed number, called the common ratio. The...
Page 189 - ... 3. The sum of the exponents in each term is equal to the exponent of the binomial. 4. The coefficient of the first term is unity; of the second term, the same as the exponent of the binomial ; and the coefficient of any other term may be found by multiplying the coefficient of the next preceding term by the exponent of a in that term and dividing this product by a number one greater than the exponent of b in that term. 5. The coefficients of any pair of terms equally distant from the ends are...
Page 136 - The resistance offered by a wire to an electric current varies directly as its length and inversely as the area of its cross section.
Page 123 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions and whose denominator is the product of the denominators of the fractions. EXAMPLES,«.
Page 49 - A and В can do a piece of work in m days, В and С in n davs, and С and A in p days.