dy Find dr - 6.3% +1-6x (а) () (ii) Hence find the maximum height of the tunnel.
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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Question
![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 = -0.1x' +0.8x², 2<x<8, relative to an origin O.
y.
8 -
D.
6.
4
B
2
A
C
4
6.
8.
10
Point A has coordinates (2,0), point B has coordinates (2,2.4), and point C has
coordinates (8,0).
(i)
dy
= - 0.3 +1.6x
(a)
Find
dr
mox -0.3X
2 +1.6x=0
x:5.33(3510
(ii)
Hence find the maximum height of the tunnel.
When x = 4 the height of the tunnel is 6.4 m 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. ydx a i
Write down the integral which can be used to find the cross-sectional area of
(i)
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%2Fdf7c064b-a2d8-4c79-b34d-8abb1adec9ff%2F887a6fdc-d1dd-4031-af5f-e108b79987e0%2F3kgrge_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 = -0.1x' +0.8x², 2<x<8, relative to an origin O.
y.
8 -
D.
6.
4
B
2
A
C
4
6.
8.
10
Point A has coordinates (2,0), point B has coordinates (2,2.4), and point C has
coordinates (8,0).
(i)
dy
= - 0.3 +1.6x
(a)
Find
dr
mox -0.3X
2 +1.6x=0
x:5.33(3510
(ii)
Hence find the maximum height of the tunnel.
When x = 4 the height of the tunnel is 6.4 m 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. ydx a i
Write down the integral which can be used to find the cross-sectional area of
(i)
the tunnel.
(c)
(ii)
Hence find the cross-sectional area of the tunnel.
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