Elementary Algebra

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D. Appleton, 1908 - Algebra - 438 pages
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Page 406 - It has been found by experiment that the weight of a body varies inversely as the square of its distance from the center of the earth. If...
Page 151 - Multiplying or dividing both numerator and denominator of a fraction by the same number does not change the value of the fraction.
Page 102 - To divide a polynomial by a monomial, divide each term of the polynomial by the monomial: (Sab — 12ac) -i- 4a = 36 — 3c.
Page 79 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Page 218 - In a number of two digits the units' digit exceeds the tens' digit by 4, and when the number is divided by the sum of its digits the quotient is 4.
Page 402 - ... that the volume of a sphere varies as the cube of its radius. 20. Find the radius of a sphere whose volume is equal to the sum of the volumes of three spheres whose radii are r, /, and r".
Page 316 - Now adding (-} to the first member makes it a perfect square ( the square of x - }, since a trinomial is a perfect square when one of its terms (the middle one, ax, in this case) is twice the product of the square roots of the other two, these two being both positive (123, PAKT I.
Page 407 - ... the acceleration of a body falling freely. (See Ames's "Theory of Physics," page 59.) It is seen that the period of a pendulum varies directly as the square root of its length, and so it may be altered as desired. Further, since both the period and the length can be measured, this gives a method for the determination of the acceleration g. By swinging pendulums of all kinds of matter and measuring their periods, it has been shown that g is a constant, as stated above. Vibrations...
Page 406 - ... that the squares of the times of revolution of the planets about the sun are proportional to the cubes of their mean distances from the sun. This boy with no chance became one of the world's greatest astronomers. "When 1 found that I was black...
Page 397 - If four numbers are in proportion, the product of the means equals the product of the extremes.

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