This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...x can contain z only once as a factor. Again, since y may be constant when z varies, and z constant when y varies, neither dl these quantities can contain the other as a factor; nor can they contain a common variable factor. Therefore, y and a are both factors of x, and are the only factors that may vary; or x is some ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1890 Excerpt: ...x can contain z only once as a factor. Again, since y may be constant when z varies, and z constant when y varies, neither dl these quantities can contain the other as a factor; nor can they contain a common variable factor. Therefore, y and a are both factors of x, and are the only factors that may vary; or x is some constant number of times y z, as r" y z; whence x oc yz. Illustrative Examples.--1. If x oc y; and x = 6 when 1 3 y = %--, what will x eqnal when y = 4? Solution: If x ccy, x = ry, in which r is constant. Since x = 6 1 1 '12 12 when - = 2r-, 6 = r x 2; whence r---p. Therefore, x = y. 3 12 19 2 Substituting y = 4 in this equation, % = = H "5 2. If z = M + v and u ccy and v x y2; also when y = 2, i = 4, and w = 6; what is the equation between x and y? Solution: 11 u ccy and v oc. y, u = ry and v = r'yi, in which r and r' are constants. Since v = 4 and w = 6 when y = 2, 6 = r x 2 and 4 = x4; whence r = 3 and r' = 1; therefore, u = 3y and i = ys; and M + - = x = 3 3/ + y. 3. If 12 sheep cost $9G, what will 25 sheep cost at the same price per head? Solution: Let x = the cost of any number of sheep, and y = any number of sheep. Since the cost varies directly as the number, x oc y, and x = ry, in which r is constant. Since x is 96 when y is 12, 96 = r x 12, or r = 8. Therefore, x = 8y. Substituting 25 for y, x = 8x25--200, the cost in dollars. 4. The attraction of bodies varies inversely as the square of the distance they are apart. If the body A attracts the body B with a force of 10 pounds when they are 5 feet apart, with what force does it attract it when they are 25 feet apart? Solution: Let x = the force of attraction at any distance, and y = any distance measured in feet. 1 r Now, x oc-; or x = in which r is constant. y y Cl...
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