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A surveyor needs to work out the area of the old window shown in the diagram below. Based on a coordinate system with the origin in the bottom left-hand corner of the window, the points A, B, C, and D have coordinates (0, 6), (1, 8.5), (2, 9.4) and (3, 10). a) Use the trapezoidal rule to find an approximation for the area of the window. b) A mathematician suggests to the surveyor that the might that a more accurate result if he fits a cubic curve through the four points (use the cubic regression in your calculator to find the function). Find the area of the window using this method. Show the cubic function as well as all the work you entered in the calculator to find the answer. c) Find the difference between the two values as a percentage of the area found by the second method.

A surveyor needs to work out the area of the old window shown in the diagram below. Based on a coordinate system with the origin in the bottom left-hand corner of the window, the points A, B, C, and D have coordinates (0, 6), (1, 8.5), (2, 9.4) and (3, 10). a) Use the trapezoidal rule to find an approximation for the area of the window. b) A mathematician suggests to the surveyor that the might that a more accurate result if he fits a cubic curve through the four points (use the cubic regression in your calculator to find the function). Find the area of the window using this method. Show the cubic function as well as all the work you entered in the calculator to find the answer. c) Find the difference between the two values as a percentage of the area found by the second method.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CT: Test
Problem 8CT: Determine whether the statement is true or false. a A right circular cone has exactly two bases. b...
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A surveyor needs to work out the area of the old window shown in the diagram below. Based on a coordinate system with the origin in the bottom left-hand corner of the window, the points A, B, C, and 10 9 B. D have coordinates (0, 6), (1, 8.5), (2, 9.4) and (3, 10). a) Use the trapezoidal rule to find an approximation for the area of 7 the window. 6 b) A mathematician suggests to the surveyor that the might that a more accurate result if he fits a cubic curve through the four points (use the cubic regression in your calculator to find the function). Find the area of the window using this method. Show the cubic function as well as all the work you entered in the calculator to 5 3 find the answer. 1 c) Find the difference between the two values as a percentage of the area found by the second method. 2 3 4 5
Transcribed Image Text:A surveyor needs to work out the area of the old window shown in the diagram below. Based on a coordinate system with the origin in the bottom left-hand corner of the window, the points A, B, C, and 10 9 B. D have coordinates (0, 6), (1, 8.5), (2, 9.4) and (3, 10). a) Use the trapezoidal rule to find an approximation for the area of 7 the window. 6 b) A mathematician suggests to the surveyor that the might that a more accurate result if he fits a cubic curve through the four points (use the cubic regression in your calculator to find the function). Find the area of the window using this method. Show the cubic function as well as all the work you entered in the calculator to 5 3 find the answer. 1 c) Find the difference between the two values as a percentage of the area found by the second method. 2 3 4 5
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