Larson_Calculus_10e ch06sec04
MULTIPLE CHOICE
1. Solve the first order linear differential equation.
a.
b.
c.
d.
e.
2. Solve the first-order linear differential equation .
a.
b.
c.
d.
e.
3. Solve the first order linear differential equation.
a.
b.
c.
d.
e.
4. Find the particular solution of the differential equation that satisfies the initial
condition .
a.
b.
c.
d.
e.
5. Find the particular solution of the differential equation that satisfies the boundary
condition .
a.
b.
c.
d.
e.
6. Find the particular solution of the differential equation that satisfies the boundary
condition .
a.
b.
c.
d.
e.
7. Find the particular solution of the differential equation that satisfies the boundary
condition .
a.
b.
c.
d.
e.
8. A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time
distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is
withdrawn at the same rate. Find the amount of concentrate Q in the solution as a function of t.
a.
b.
c.
d.
e.
9. A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time ,
distilled water is added to the tank at a rate of 10 gallons per minute, and the well-stirred solution is
withdrawn at the same rate. Find the time at which the amount of concentrate in the tank reaches 15
pounds. Round your answer to one decimal place.
a.
18.3 min
b.
3.6 min
c.
20.4 min
d.
10.2 min
e.
5.1 min
10. A 300-gallon tank is full of a solution containing 35 pounds of concentrate. Starting at time ,
distilled water is added to the tank at a rate of 30 gallons per minute, and the well-stirred solution is
withdrawn at the same rate. Find the quantity of the concentrate in the solution as .
a.
1
b.
35
c.
36
d.
0
e.
30
11. A 300-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of
concentrate per gallon enters the tank at the rate of 8 gallons per minute, and the well-stirred mixture is
withdrawn at the rate of 6 gallons per minute. At what time will the tank be full?
a.
150 minutes
b.
76 minutes
c.
75 minutes
d.
301 minutes
e.
600 minutes
12. A 200-gallon tank is half full of distilled water. At time , a solution containing 0.5 pound of
concentrate per gallon enters the tank at the rate of 5 gallons per minute, and the well-stirred mixture is
withdrawn at the rate of 3 gallons per minute. At the time the tank is full, how many pounds of
concentrate will it contain? Round your answer to two decimal places.
a.
11.61 lbs
b.
64.64 lbs
c.
71.34 lbs
d.
49.39 lbs
e.
82.32 lbs
13. Suppose an eight-pound object is dropped from a height of 5000 feet, where the air resistance is
proportional to the velocity. Write the velocity as a function of time if its velocity after 7 seconds is
approximately –75 feet per second. Use a graphing utility or a computer algebra system. Round
numerical answers in your answer to four places.
0.8018
d.
e.
14. Assume an object weighing 7 pounds is dropped from a height of 9,000 feet, where the air resistance is
proportional to the velocity. Round numerical answers in your answer to two places.
(i) Write the velocity as a function of time if the object’s velocity after 6 seconds is 3.50 feet per
second.
(ii) What is the limiting value of the velocity function?
a.
(i) ; (ii) 0
b.
(i) ; (ii) 0
c.
(i) ; (ii) 3.5000
d.
(i) ; (ii) 3.5000
e.
(i) ; (ii) limit does not exist
15. Solve the Bernoulli differential equation .
a.
b.
c.
d.
e.
16. Find the particular solution of the differential equation passing through the point
.
a.
b.
c.
d.
e.