By Richard L. Burden, J. Douglas Faires

The hot 7th version of Burden and Faires' well-respected Numerical research offers a beginning in glossy numerical-approximation innovations. Explaining how, why, and while the options could be anticipated to paintings, the 7th version areas a good better emphasis on construction readers' instinct to assist them comprehend why the ideas provided paintings as a rule, and why, in a few occasions, they fail. utilized difficulties from different parts, resembling engineering and actual, computing device, and organic sciences, are supplied so readers can know the way numerical equipment are utilized in real-life occasions. The 7th variation has been up to date and now addresses the evolving use of expertise, incorporating it each time applicable.

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**Example text**

X2 Ϫ 2x Ϫ 15 111. 3x2 Ϫ 6x Ϫ 24 112. 3x2 Ϫ 4x Ϫ 4 113. 12x2 Ϫ 2x Ϫ 30 114. (x ϩ y)2 Ϫ 1 115. 9x2 Ϫ 16y2 116. 8a2 Ϫ 2ab Ϫ 6b2 117. x6 ϩ 125 118. x3 Ϫ 27 78. 3(2a Ϫ b) Ϫ 4(b Ϫ 2a) 79. x Ϫ {2x Ϫ [Ϫx Ϫ (1 Ϫ x)]} 80. 3x2 Ϫ {x2 ϩ 1 Ϫ x[x Ϫ (2x Ϫ 1)]} ϩ 2 1 1 81. ¢ Ϫ 1 ϩ e≤ Ϫ ¢Ϫ Ϫ 1 ϩ eϪ1≤ 3 3 3 1 1 1 82. Ϫ y Ϫ x ϩ 100 ϩ x ϩ y Ϫ 120 4 4 2 4 1 3 83. 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.

1 ϩ e≤ Ϫ ¢Ϫ Ϫ 1 ϩ eϪ1≤ 3 3 3 1 1 1 82. Ϫ y Ϫ x ϩ 100 ϩ x ϩ y Ϫ 120 4 4 2 4 1 3 83. 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.

A cable is to be laid connecting the relay station with the experimental station. 00 per running foot, find the total cost for laying the cable. y (feet) M(0, 3000) x (feet) O Q(2000, 0) S(10,000, 0) FIGURE 14 Cable connecting relay station S to experimental station M Solution The length of cable required on land is given by the distance from S to Q. This distance is (10,000 Ϫ 2000), or 8000 feet. Next, we see that the length of cable required underwater is given by the distance from M to Q. 55 feet.