A Second Course in Elementary Algebra

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Page 160 - 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 156 - ... 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 161 - ... 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 160 - ... 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 134 - ... 2. The sum of the sides of two squares is 7 and the sum of their areas is 25. Find the side of each square. 3. The hypotenuse of a certain right triangle is 50, and the length of one of its sides is f that of the other. Find the sides of the triangle. 4. The difference between the hypotenuse of a right triangle and the other two sides is 3 and 6 respectively. Find the sides. 5. A number consists of two digits ; the sum of their squares is 41. If each digit is multiplied by 5, the sum of these...
Page 152 - Move this (6') stake until it is exactly 6' from the first tree (or corner) stake and also 10' from the first temporary stake on the base line. The line drawn through this stake from the corner stake will be at right angles to the first (or base) line. The principle here involved is that when the sides of a triangle are in the ratio of 3 to 4 to 5 the angle opposite 5 is a right angle. 8. With this angle established, extend the new line to the opposite side of the field. 9. For planting small fields...
Page 168 - Progression (AP), is a series in which each term, after the first, is formed by adding a constant number to the preceding term.
Page 73 - The integral part of a logarithm is called its characteristic, and the decimal part is called the mantissa.
Page 63 - What is the quotient of 23 (=64) divided by 2* (=4)? A. 16=2*. 26. Hence powers of the same root may be divided by subtracting the exponent of the divisor from the exponent of the dividend. 27. Divide 315" by 315", and 82
Page 149 - In a series of equal ratios (a continued proportion), the sum of the numerators divided by the, sum of the denominators is equal to any one of the ratios.

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