64. Highway Design A section of highway connecting two hillsides with grades of 6% and 4% is to be built between two points that are separated by a horizontal distance of 2000 feet (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. At points A and B, the slope of the model must match the grade of the hillside. (b) Use a graphing utility to graph the model. (c) Use a graphing utility to graph the derivative of the model. (d) Determine the grade at the steepest part of the transitional section of the highway.
64. Highway Design A section of highway connecting two hillsides with grades of 6% and 4% is to be built between two points that are separated by a horizontal distance of 2000 feet (see figure). At the point where the two hillsides come together, there is a 50-foot difference in elevation. Highway B(1000, 90) A(-1000, 60) 6% grade 4% grade 50 ft Not drawn to scale (a) Design a section of highway connecting the hillsides modeled by the function f(x) = ax³ + bx² + cx + d, -1000 s xs 1000. At points A and B, the slope of the model must match the grade of the hillside. (b) Use a graphing utility to graph the model. (c) Use a graphing utility to graph the derivative of the model. (d) Determine the grade at the steepest part of the transitional section of the highway.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
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ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
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Chapter3: Graphing Linear Functions
Section3.5: Graphing Linear Equations In Slope-intercept From
Problem 44E
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Transcribed Image Text:64. Highway Design A section of highway connecting two
hillsides with grades of 6% and 4% is to be built between two
points that are separated by a horizontal distance of 2000 feet
(see figure). At the point where the two hillsides come
together, there is a 50-foot difference in elevation.
Highway
B(1000, 90)
A(-1000, 60)
6% grade
4% grade
50 ft
Not drawn to scale
(a) Design a section of highway connecting the hillsides
modeled by the function
f(x) = ax³ + bx² + cx + d, -1000 s xs 1000.
At points A and B, the slope of the model must match the
grade of the hillside.
(b) Use a graphing utility to graph the model.
(c) Use a graphing utility to graph the derivative of the model.
(d) Determine the grade at the steepest part of the transitional
section of the highway.
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