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.

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Description: You may use a calculator to fully solve this problem A surveyor needs to work out the area of the old window shown inthe diagram below. Based on a coordinate system with the origin inthe bottom left-hand corner of the window, the points A, B, C, and1

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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You may use a calculator to fully solve this problem

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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