3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine function. The high and low points of this part differ by 24 meters and cover a horizontal distance of 40 meters from the high point to the low point. The low point is 6 meters below ground in a tunnel. Let y repre- sent the number of meters the track is above or below ground, and let x repre- sent the number of meters the track is horizontally from the high point. a. Sketch this situation. b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an equation for which the coefficient of x is in radians per meter. c. What is the length of a vertical support girder at the high point? At a dis- tance of 6 meters horizontally from the high point? At a distance of 20 meters horizontally from the high point? d. Measured horizontally, how far from the high point does the roller coaster enter the tunnel?
3. An amusement park is planning a new roller coaster. Part of it is to have the shape of the cosine function. The high and low points of this part differ by 24 meters and cover a horizontal distance of 40 meters from the high point to the low point. The low point is 6 meters below ground in a tunnel. Let y repre- sent the number of meters the track is above or below ground, and let x repre- sent the number of meters the track is horizontally from the high point. a. Sketch this situation. b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an equation for which the coefficient of x is in radians per meter. c. What is the length of a vertical support girder at the high point? At a dis- tance of 6 meters horizontally from the high point? At a distance of 20 meters horizontally from the high point? d. Measured horizontally, how far from the high point does the roller coaster enter 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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Transcribed Image Text:+
3. An amusement park is planning a new
roller coaster. Part of it is to have the
shape of the cosine function. The high
and low points of this part differ by 24
meters and cover a horizontal distance
of 40 meters from the high point to the
low point. The low point is 6 meters
below ground in a tunnel. Let y repre-
sent the number of meters the track is
above or below ground, and let x repre-
sent the number of meters the track is
horizontally from the high point.
a. Sketch this situation.
b. The equation y = 12 cos (4.5x) + 6 models the situation when x and y are in
meters and 4.5 is in degrees per meter. Rewrite y = 12 cos (4.5x) + 6 as an
equation for which the coefficient of x is in radians per meter.
c. What is the length of a vertical support girder at the high point? At a dis-
tance of 6 meters horizontally from the high point? At a distance of 20
meters horizontally from the high point?
d. Measured horizontally, how far from the high point does the roller coaster
enter the tunnel?
a. Make and label a general sketch of the graph of each function rule below. In
each case, a > 1.
a
y
y = a*
y
x2
äx²
y = a sinx
1
y = ax³
y = a cos x
b. Describe one characteristic of the graph of each function that sets it apart
from the graphs of the other functions.
c. Without sketching, explain how the graphs you drew in Part a would be dif-
ferent if 0 < a < 1 and if a <0.
inimell
@y=
S
pascoa
didepap
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