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Extra resources for An introduction to Grobner bases

Sample text

3 , 3 8 d. -40 10 e. -1 -2 , 10 5 f. 8 0 Solution a. Since the signs are different or unlike, the quotient is negative and b. Since the signs are the same, the quotient is positive and c. e. 3 3 , 3 = 8 8 # 1 1 = 3 8 -1 -2 1 , = 10 5 10 # - 5 1 = 2 4 d. -40 = -4 10 f. 8 is undefined. 0 20 = -5. -4 -9 = 3. -3 PRACTICE 5 -16 8 54 d. -9 a. Divide. -15 -3 1 3 e. , a- b 12 4 b. c. f. 2 , 4 3 0 -7 With sign rules for division, we can understand why the positioning of the negative sign in a fraction does not change the value of the fraction.

A. Complete the table below. 88. - 7y 2 y 1x y x 10 x Cost per Bookshelf 43 + 0 51 - 12 0 86. 4x - 10y 2 10 97. The algebraic expression Number of Bookshelves 1 -22 + 3 2120 - 20 7 b. As the radius of a circle increases (see the table), does its area increase or decrease? Explain your answer. Evaluate each expression when x = 9 and y = -2. See Example 12. 89. pr 3 2 4 3 87. - 3y 2 r Area 81. 3 5 - 2 + 531 - 21 - 2 + 5246 82. 2 5 - 1 + 337 - 41- 10 + 12246 83. Radius -2 0 3 - 9 0 - 0 -5 0 31- 2 + 12 a.

A. 3y -1 7 -a b - 3y 9x - 2y d. d. - 9x 2y a b Find the value of the expression when x1 = 2 , x2 = 4 , y1 = - 3 , y2 = 2. y2 - y1 105. 106. 21x2 - x1 2 2 + 1y2 - y1 2 2 x2 - x1 Integrated Review 29 Each circle below represents a whole, or 1. Determine the unknown fractional part of each circle. 108. Q ﬂ Z £ ~ 109. Most of Mauna Kea, a volcano on Hawaii, lies below sea level. If this volcano begins at 5998 meters below sea level and then rises 10,203 meters, find the height of the volcano above sea level.