Algebra for Colleges and Schools

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Macmillan Company, 1897 - Algebra - 516 pages
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Page 292 - Given that the area of a circle varies as the square of its radius...
Page 161 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 166 - The coefficient of any term may be found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing this product by the number of the term.
Page 177 - The sixth root of an expression is found by taking the cube root of the square root, or the square root of the cube root.
Page 283 - In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d.
Page 283 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 316 - From 7 Englishmen and 4 Americans a committee of 6 is to be formed: in how many ways can this be done, (1) when the committee contains exactly 2 Americans, (2) at least 2 Americans...
Page 386 - ... continued through the season of 1900 and a few more facts were established which add to our knowledge of the disease. EFFECTS OF THE DISEASE AND APPEARANCE OF AFFECTED PARTS. >A brief discussion of the work of the fungus and the appearance of cankered limbs will not be out of place at this time; but for a fuller discussion of the subject the reader is referred to the former bulletin.
Page 315 - From 12 books in how many ways can a selection of 5 be made, (1) when one specified book is always included, (2) when one specified book is always excluded ? (1) Since the specified book is to be included in every selection, we have only to choose 4 out of the remaining 11. Hence the number of ways...
Page 254 - At what price per dozen did she sell them at first ? 20. Two rectangles contain the same area, 480 square yards. The difference of their lengths is 10 yards, and of their breadths 4 yards ; find their sides. 21. There is a number between 10 and 100 ; when multiplied by the digit on the left the product is 280 ; if the sum of the digits be multiplied by the same digit the product is 55 : required the number.

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