Question

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?

Answer #1

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)...

A tank initally contains 10 liters of blue paint. Then red paint
enters the tank at a rate of 3 liters/hour while blue paint enters
the tank at a rate of 2 listers/hour.
(a) How many liters of red paint are in the tank after t hours?
_______ liters
(b) How many total liters of paint are in the tank after t
hours? _______ liters
(c) What is the percentage of red paint in the tank after t
hours? _______%...

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 tank that holds 2000 liters initially contains 150 liters of
water into which 30 grams of salt has been dissolved. Water is
flowing into the tank at a rate of 20 liters/minute with a
concentration of sin^2(πt) at any time, t. The liquid is well
mixed, and flows out at a rate of 10 liters/minute. Set up, do not
solve, a 1st order IVP to find the amount of salt in the tank at
any time, t, after t...

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?

The traffic flow rate (cars per hour) across an intersection is
r(t)=200+800t−240t^2, where t is in hours, and t=0 is 6am. How many
cars pass through the intersection between 6 am and 8 am?

A tank originally contains 120 liters of water with 5 grams of
salt in solution. Beginning at t=0, water containing 0.4 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

A tank originally contains 130 liters of water with 10 grams of
salt in solution. Beginning at t=0, water containing 0.1 grams of
salt per liter flows into the tank at a rate of 2 liters per minute
and the uniform mixture drains from the tank at a rate of 2 liters
per minute. Letting t be time in minutes and Q be the amount of
salt in the tank at time t measured in grams, formulate an initial
value...

Water is draining from a large tank. After tmin, there
are150000-7500t +t2 litres of water in the tank.
a) Determine the average rate at which the water empties from
the tank in the interval between 5 and 10 minutes.
b) Determine the average rate at which the water empties from
the tank in the interval between 9 and 10 min.
c) Estimate the rate at which the water runs out after exactly
10 min.
d) How much water is in...

A 24 gallon tank is filled with pure water. Water which has a
concentration of 6g of salt per gallon flows into the tank at a
rate of 2 gallons/min, and the mixture is stirred to a uniform
concentration. Water also leaks from the tank at the same rate, 2
gallons/min.
Find a differential equation describing the rate of change of salt
in the tank.
Hint: The concentration of salt in the tank is
S(t)/24, where
S(t) is the total...

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