Elementary Mathematics from an Advanced Standpoint. Vol. 1 by Felix Klein

By Felix Klein

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Com. An accounting firm determines that the value V (in dollars) of a copier t years after its purchase is V ϭ Ϫ300t ϩ 1500. Describe the practical significance of the y-intercept and slope of this line. com Copyright 2012 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.

Use the steps following to determine whether the set of points ͭA͑2, 3͒, B͑2, 6͒, C͑6, 3͒ͮ and the set of points ͭA͑8, 3͒, B͑5, 2͒, C͑2, 1͒ͮ are collinear. x (a) ͑x0, y0͒ (c) x (b) ͑Ϫ2x0, y0͒ ͑x0, 12 y0͒ (d) ͑Ϫx0, Ϫy0͒ 59. Proof Prove that the diagonals of the parallelogram in the figure intersect at their midpoints. y (b, c) (a + b, c) (0, 0) (a, 0) x 54. Think About It What is the y-coordinate of any point on the x-axis? What is the x-coordinate of any point on the y-axis? Copyright 2012 Cengage Learning.

Y ϭ 3 Ϫ 2x 59. y ϭ x 2 Ϫ 4x ϩ 3 2x 61. y ϭ xϪ1 2 58. y ϭ 3x Ϫ 1 60. y ϭ x 2 ϩ x Ϫ 2 4 62. y ϭ 2 x ϩ1 Sketching the Graph of a Circle In Exercises 77–82, find the center and radius of the circle. Then sketch the graph of the circle. x 2 ϩ y 2 ϭ 25 ͑x Ϫ 1͒2 ϩ ͑ y ϩ 3͒2 ϭ 9 ͑x Ϫ 12 ͒2 ϩ ͑y Ϫ 12 ͒2 ϭ 94 ͑x Ϫ 2͒2 ϩ ͑ y ϩ 3͒2 ϭ 169 78. x 2 ϩ y 2 ϭ 16 80. x 2 ϩ ͑ y Ϫ 1͒ 2 ϭ 1 83. Depreciation A hospital purchases a new magnetic resonance imaging (MRI) machine for $500,000. The depreciated value y (reduced value) after t years is given by y ϭ 500,000 Ϫ 40,000t, 0 Յ t Յ 8.

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