Question

The traffic flow rate (cars per hour) across an intersection is r ( t ) = 500 + 800 t − 180 t^2 , where t is in hours, and t =0 is 6am. How many cars pass through the intersection between 6 am and 10 am?

Answer #1

9) A company is considering expanding their production
capabilities with a new machine that costs $37,000 and has a
projected lifespan of 6 years. They estimate the increased
production will provide a constant $6,000 per year of additional
income. Money can earn 0.9% per year, compounded continuously.
Should the company buy the machine?
(a) Yes, the present value of the machine is greater than the
cost by
(b) No, the present value of the machine is less than the cost...

Cars pass an intersection at a rate of 18 per hour. What is the
probability that we have to wait at least 5 minutes before the next
car passes?

Oil leaked from a tank at a rate of r(t) liters per hour. Values
of the rate at 2-hour intervals are given in the table below.
time (hours)r(t) (liters per hour)
0
2
4
6
8
10
12
8.7
7.6
6.8
6.2
5.7
5.3
5.0
(a) Use a Left Hand Sum with n=3 subdivisions to give an
approximation on the total amount of oil lost over the time
interval from t=0 to t=12 hours. Include units in your
answer.
(b)...

You work on a traffic management team for the city. There has
been a proposal to add a new lane to a road near a busy
intersection. As part of the research into whether or not to build
the new lane, the team would like to know how many cars, on
average, pass through this intersection at peak hour each day (5 pm
to 6 pm). Your colleague has developed the hypothesis that the
population mean is 887. You intend...

Oil leaked from a tank at a rate of r(t)
liters per hour. The rate decreased as time passed, and values of
the rate at two hour time intervals are shown in the table. Find
lower and upper estimates for the total amount of oil that leaked
out.
V
≈
L (lower estimate)
V
≈
L (upper estimate)
t
(h)
0
2
4
6
8
10
r(t) (L/h)
8.8
7.9
6.8
6.2
5.6
5.3

A data set of traffic stream characteristics, such as space mean
speed (u: miles per hour), density (k: vehicles per mile) and
traffic flow rate (q: vehicles per hour), was collected for a
freeway lane. The data reveals a relationship between flow rate (q)
and density (k) as calibrated below:
q=66*(k-k^2/160)
Where, q = flow rate of the lane (vehicles per hour); k =
density of the lane (vehicles per mile). Answer the following
questions:
(1)Determine the free-flow space mean...

The output of a factory is changing at the rate
Q′(t) =
3t3 + 5t2 + 4t +
7
units per hour, where t is the number of hours after the
morning shift begins at 7:00 AM. How many units are produced
between 9:00 AM and 11:00 AM?

Water leaks from a tank at a rate of
115−2?2‾‾‾‾‾‾‾‾√115−2t2
liters/ hour, where ?t is the number of hours after 7am. How
much water is lost between 9:30 am and 11:30 am?

A forest fire covers 1200 acres at time t=0. The fire is growing
at a rate of 8√t acres per hour, where t is in hours. How many
acres are covered 28 hours later?

Wage rate is $10 per hour for a consumer, and he is choosing
earning of $10 per hour and taking leisure of 1 hour together.
a. Derive the mathematical equation and
draw the corresponding graph for daily income-leisure
constraint.
b. Draw the corresponding indifference
curve between earning and leisure.
c. How many hours will this
consumer work and how much will this consumer earn?

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