The cross-sectional view of a tunnel is shown on the axes below. The line [AB] represents a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above the horizontal ground is modelled by y=-0.1x³ +0.8x², 2 ≤x≤8, relative to an origin O. 8 E D 6 4 B A 2 2 6 8 10 Point A has coordinates (2, 0), point B has coordinates (2, 2.4), and point C has coordinates (8,0). dy (a) (i) Find dr (ii) Hence find the maximum height of the tunnel. When x = 4 the height of the tunnel is 6.4m and when x = 6 the height of the tunnel is 7.2 m. These points are shown as D and E on the diagram, respectively. (b) Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel. (c) (i) Write down the integral which can be used to find the cross-sectional area of the tunnel. (ii) Hence find the cross-sectional area of the tunnel. с
The cross-sectional view of a tunnel is shown on the axes below. The line [AB] represents a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above the horizontal ground is modelled by y=-0.1x³ +0.8x², 2 ≤x≤8, relative to an origin O. 8 E D 6 4 B A 2 2 6 8 10 Point A has coordinates (2, 0), point B has coordinates (2, 2.4), and point C has coordinates (8,0). dy (a) (i) Find dr (ii) Hence find the maximum height of the tunnel. When x = 4 the height of the tunnel is 6.4m and when x = 6 the height of the tunnel is 7.2 m. These points are shown as D and E on the diagram, respectively. (b) Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of the tunnel. (c) (i) Write down the integral which can be used to find the cross-sectional area of the tunnel. (ii) Hence find the cross-sectional area of the tunnel. с
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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![The cross-sectional view of a tunnel is shown on the axes below. The line [AB] represents
a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above
the horizontal ground is modelled by y = -0.1xr' + 0.8x², 2 <x < 8, relative to an origin O.
8
E
D
6
4
В
2
A
4
8
10
Point A has coordinates (2, 0), point B has coordinates (2, 2.4), and point C has
coordinates (8,0).
dy
Find
dr
(а)
(i)
(ii)
Hence find the maximum height of the tunnel.
When x = 4 the height of the tunnel is 6.4m and when x = 6 the height of the tunnel is 7.2 m.
These points are shown as D and E on the diagram, respectively.
(b)
Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of
the tunnel.
(i)
Write down the integral which can be used to find the cross-sectional area of
the tunnel.
(c)
(ii)
Hence find the cross-sectional area of the tunnel.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6de38f42-50ea-4ffb-a93e-7630affffeb6%2Fd1350cd6-28ba-4f77-b5ed-15f617dae1d9%2F39m7s64_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The cross-sectional view of a tunnel is shown on the axes below. The line [AB] represents
a vertical wall located at the left side of the tunnel. The height, in metres, of the tunnel above
the horizontal ground is modelled by y = -0.1xr' + 0.8x², 2 <x < 8, relative to an origin O.
8
E
D
6
4
В
2
A
4
8
10
Point A has coordinates (2, 0), point B has coordinates (2, 2.4), and point C has
coordinates (8,0).
dy
Find
dr
(а)
(i)
(ii)
Hence find the maximum height of the tunnel.
When x = 4 the height of the tunnel is 6.4m and when x = 6 the height of the tunnel is 7.2 m.
These points are shown as D and E on the diagram, respectively.
(b)
Use the trapezoidal rule, with three intervals, to estimate the cross-sectional area of
the tunnel.
(i)
Write down the integral which can be used to find the cross-sectional area of
the tunnel.
(c)
(ii)
Hence find the cross-sectional area of the tunnel.
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