3. sin 2m 5. 17 20 M(x) KER 27 (2x+ 1)m 2m sin 10 * 17 xS 13 11(2x 20 37 33 7. 13

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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RMIT Classification: Trusted
Hence, show that the function M(x) is smooth at x = 13 (i.e. the two relevant adjacent
expressions defining the piecewise function have the same gradient at this location).
iii.
b.
Show, by explicit calculations, that this model predicts the shortest time required for a vehicle
to pass through the junction during daytime from 7:00 a.m. to 3:00 p.m, happens at 12:30 p.m.
That is showing M(x) has a minimum at this time within the time period indicated. In doing so,
be sure to check all relevant pieces of the hybrid function, as well as showing evidence
supporting it being a minimum turning point.
RMIT Classification: Trusted
Hence, determine the predicted waiting time required at 12:30 p.m. Give answer accurate to
C.
the nearest 0.01 minute.
19
Transcribed Image Text:RMIT Classification: Trusted Hence, show that the function M(x) is smooth at x = 13 (i.e. the two relevant adjacent expressions defining the piecewise function have the same gradient at this location). iii. b. Show, by explicit calculations, that this model predicts the shortest time required for a vehicle to pass through the junction during daytime from 7:00 a.m. to 3:00 p.m, happens at 12:30 p.m. That is showing M(x) has a minimum at this time within the time period indicated. In doing so, be sure to check all relevant pieces of the hybrid function, as well as showing evidence supporting it being a minimum turning point. RMIT Classification: Trusted Hence, determine the predicted waiting time required at 12:30 p.m. Give answer accurate to C. the nearest 0.01 minute. 19
22:59
Question 11
Consultant: Dr Lore
In this paper, the modelling of the traffic flow (measured by the average time required for a vehicle to
pass through the intersection) at the Hoppers Crossing railway junction is based on the assumptions
that the morning and afternoon/evening peak periods are of different lengths and that the traffic
volume during daytime is in general higher than that of night time even during off-peak hours.
The proposed model is based on the following piecewise function:
Osxs
M(x) =27 1(2x + 1)" 2
KER
10 sin9
J 17
<IS 13
13 <xS 24
where M(x) is the average time (in minutes) required for a vehicle to pass through the junction, and
x is the number of hours after 7:00 a.m, in the morning.
It can be shown that M(x) is a smooth function everywhere for x E (0,24) by checking the derivative
function M'(x) at various points of interest.
Find sin +쥐, xER
a.l.
i.
Find
XER
Transcribed Image Text:22:59 Question 11 Consultant: Dr Lore In this paper, the modelling of the traffic flow (measured by the average time required for a vehicle to pass through the intersection) at the Hoppers Crossing railway junction is based on the assumptions that the morning and afternoon/evening peak periods are of different lengths and that the traffic volume during daytime is in general higher than that of night time even during off-peak hours. The proposed model is based on the following piecewise function: Osxs M(x) =27 1(2x + 1)" 2 KER 10 sin9 J 17 <IS 13 13 <xS 24 where M(x) is the average time (in minutes) required for a vehicle to pass through the junction, and x is the number of hours after 7:00 a.m, in the morning. It can be shown that M(x) is a smooth function everywhere for x E (0,24) by checking the derivative function M'(x) at various points of interest. Find sin +쥐, xER a.l. i. Find XER
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