A Beginner's Guide to the Stars by Maud King Murphy

By Maud King Murphy

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Find an expression in terms of the time t (in hours) giving the distance between the two ships. b. Using the expression obtained in part (a), find the distance between the two ships 2 hr after leaving port. 2 1 B (400, 300) x (miles) A (0, 0) Q(x, 0) 1000 38. MINIMIZING SHIPPING COSTS Refer to the figure for Exer- cise 37. Suppose a fleet of 100 automobiles are to be shipped from an assembly plant in town A to town D. They may be shipped either by freight train along Route 1 at a cost of 22¢/mile per automobile or by truck along Route 2 at a cost of 21¢/mile per automobile.

318 ϩ 8 Ϫ 21y ϩ 1x Ϫ 1y 2 4 In Exercises 119–126, perform the indicated operations and simplify each expression. 119. (x2 ϩ y2)x Ϫ xy(2y) 120. 2kr(R Ϫ r) Ϫ kr 2 8 2 16 16 84. x2 ϩ x ϩ x2 Ϫ x Ϫ 2x ϩ 2 9 3 3 3 121. 2(x Ϫ 1)(2x ϩ 2)3[4(x Ϫ 1) ϩ (2x ϩ 2)] 85. (x ϩ 8)(x Ϫ 2) 86. (5x ϩ 2)(3x Ϫ 4) 122. 5x2(3x2 ϩ 1)4(6x) ϩ (3x2 ϩ 1)5(2x) 87. (a ϩ 5)2 88. (3a Ϫ 4b)2 89. (x ϩ 2y)2 90. (6 Ϫ 3x)2 91. (2x ϩ y)(2x Ϫ y) 92. (3x ϩ 2)(2 Ϫ 3x) 93. (x2 Ϫ 1)(2x) Ϫ x2(2x) 94. 1x 1/2 1 1 ϩ 12 ¢ x Ϫ1/2≤ Ϫ 1x1/2 Ϫ 1 2¢ x Ϫ1/2≤ 2 2 123.

If it is true, explain why it is true. If it is false, give an example to show why it is false. 139. 5, where y is the number of families with an income of x or more dollars. a. How many families in this city have an income of $30,000 or more? b. How many families have an income of $60,000 or more? 140. If b2 Ϫ 4ac Ͼ 0, then ax2 ϩ bx ϩ c ϭ 0 (a real roots. 0) has two 141. If b2 Ϫ 4ac Ͻ 0, then ax2 ϩ bx ϩ c ϭ 0 (a real roots. 0) has no 142. 21a ϩ b 2 1b Ϫ a2 ϭ 2b2 Ϫ a2 for all real numbers a and b.

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