Accretion Discs, Jets and High Energy Phenom. in by Beskin et al.,

By Beskin et al.,

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Y ϭ 8 Ϫ 3x 53. y ϭ Ίx ϩ 4 54. y ϭ Ί2x Ϫ 1 55. y ϭ 3x Ϫ 7 56. y ϭ Ϫ x ϩ 10 57. y ϭ 2x3 Ϫ 4x 2 58. y ϭ x 4 Ϫ 25 59. y2 ϭ 6 Ϫ x 60. y 2 ϭ x ϩ 1 Խ Խ Խ y 2 4 6 y 4 4 2 2 −2 84. x ϭ y 2 Ϫ 5 Խ Խ ԽԽ 89. Endpoints of a diameter: ͑0, 0͒, ͑6, 8͒ 90. Endpoints of a diameter: ͑Ϫ4, Ϫ1͒, ͑4, 1͒ In Exercises 91– 96, find the center and radius of the circle, and sketch its graph. 92. x 2 ϩ y 2 ϭ 16 2 16 96. ͑x Ϫ 2͒2 ϩ ͑ y ϩ 3͒2 ϭ 9 97. Depreciation A manufacturing plant purchases a new molding machine for $225,000.

3x ϩ x 2 Ϫ 1 ϭ 0 2t 2 2 In Exercises 55– 68, solve the quadratic equation by factoring. 2 23 109. 28x Ϫ 49x 2 ϭ 4 113. ͑ y Ϫ 5͒2 ϭ 2y 2 Solving Equations ϪxϪ1ϭ0 95. 16x 2 ϩ 8x Ϫ 3 ϭ 0 96. 25x 2 Ϫ 20x ϩ 3 ϭ 0 97. 2 ϩ 2x Ϫ x 2 ϭ 0 98. x 2 Ϫ 10x ϩ 22 ϭ 0 ϭ0 3 130. x2 ϩ 3x Ϫ 4 ϭ 0 2 132. a 2x 2 Ϫ b 2 ϭ 0, a and b are real numbers 133. 3x ϩ 4 ϭ 2x2 Ϫ 7 134. 4x 2 ϩ 2x ϩ 4 ϭ 2x ϩ 8 In Exercises 135–152, find all solutions of the equation. Check your solutions in the original equation. 135. 4x4 Ϫ 18x 2 ϭ 0 136.

3x ϩ 4 Ϫ6 h 90. ͑z Ϫ 2͒ ϩ 0 ϭ z Ϫ 2 92. ͑z ϩ 5͒x ϭ z и x ϩ 5 и x 93. x ϩ ͑ y ϩ 10͒ ϭ ͑x ϩ y͒ ϩ 10 95. 3͑t Ϫ 4͒ ϭ 3 и t Ϫ 3 и 4 и 7͒12 ϭ 1 и 12 ϭ 12 In Exercises 97–104, perform the operation(s). ) 103. 5 3 16 ϩ 16 5 1 5 8 Ϫ 12 ϩ 6 12 Ϭ 14 100. 2x x Ϫ 3 4 104. 98. 102. 5 0. aϩb a b c c c ϭ ϩ , then ϭ ϩ . c c c aϩb a b Խ Խ ԽԽ ԽԽ Consider u ϩ v and u ϩ v , where (a) Are the values of the expressions always equal? If not, under what conditions are they unequal? 0001 In Exercises 113 and 114, use the real numbers A, B, and C shown on the number line.

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