Algebra Volume 1 ; an elementary text-book, for the higher classes of secondary schools and for colleges

9781236244222: Algebra Volume 1 ; an elementary text-book, for the higher classes of secondary schools and for colleges
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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. 1904 Excerpt: ...T/P. Example 1. If s oc f when/ is constant, and s a/ when t is constant, and 2s=f when 1 = 1, find the relation connecting,?,/, I. It follows by a slight extension of 20 (5) that, when/and I both vary, s:ft1. Hence s = afp, where a is a constant, which we have to determine. Now, when 1 = 1, s=J/, hence /=/l2, that is, kf=af; in other words, we must have a= J. The relation required is, therefore, s=fp. Example 2. The thickness of a grindstone is unaltered in the using, but its radius gradually diminishes. By how much must its radius diminish before the half of its mass is worn away? Given that the mass varies directly as the square of the radius when the thickness remains unaltered. Let m denote the mass, r the radius, then by data, m=ars, where a is constant. Let now r become r', and, in consequence, m become km, then hn=ar'1, hence ar12 _ Ji rcr1 m' r'2 that is, =4; whence--=--r. r V It follows, therefore, that the radius of the stone must be diminished in the ratio 1: y/2. Example 3. A and B are partners in a business in which their interests are in the ratio a: b. They admit C to the partnership, without altering the whole amount of capital, in such a way that tho interests of the threo partners in the business are then equal. C contributes c to the capital of the firm. 280 EXERCISES XVIII CHAP. XIII (11.) A watch loses 2h minutes per day. It is set right on the 15th March at 1 P.m.: what will the proper time be when it indicates 9 A.m. on the 20th April 1 (12.) A small disc is placed between two infinitely small sources of radiant heat of equal intensity, at a point on the line joining them equidistant from the two. It is then moved parallel to itself through a distance a/2/2 towards one of the two sources, a being the di...

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