CALCULUS WITH APPLICATIONS
11th Edition
ISBN: 2818440028601
Author: Lial
Publisher: XX SUPPLY
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Chapter R.2, Problem 29E
To determine
To factor: The polynomial
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2. A tank with a capacity of 650 gal. originally contains 200 gal of water with 100 lb. of salt in
solution. Water containing 1 lb. of salt per gallon is entering at a rate of 4 gal/min, and the
mixture is allowed to flow out of the tank at a rate of 3 gal/min.
a. Find the amount of salt in the tank at any time prior to the instant when the tank
begins to overflow (650 gallons).
b. Find the concentration (in pounds per gallon) of salt in the tank when the tank hits
400 gallons.
D.E. for mixture problems:
dv
dt=11-12
dA
A(t)
dt
- Suppose that you have the differential equation:
dy
= (y - 2) (y+3)
dx
a. What are the equilibrium solutions for the differential equation?
b. Where is the differential equation increasing or decreasing? Show how you know.
Showing them on the drawing is not enough.
c. Where are the changes in concavity for the differential equation? Show how you
know. Showing them on the drawing is not enough.
d. Consider the slope field for the differential equation. Draw solution curves given the
following initial conditions:
i. y(0) = -5
ii. y(0) = -1
iii. y(0) = 2
5. Suppose that a mass of 5 stretches a spring 10. The mass is acted on by an external force
of F(t)=10 sin () and moves in a medium that gives a damping coefficient of ½. If the mass
is set in motion with an initial velocity of 3 and is stretched initially to a length of 5. (I
purposefully removed the units- don't worry about them. Assume no conversions are
needed.)
a) Find the equation for the displacement of the spring mass at time t.
b) Write the equation for the displacement of the spring mass in phase-mode form.
c) Characterize the damping of the spring mass system as overdamped, underdamped or
critically damped. Explain how you know.
D.E. for Spring Mass Systems
k
m* g = kLo
y" +—y' + — —±y = —±F(t), y(0) = yo, y'(0) = vo
m
2
A₁ = √c₁² + C₂²
Q = tan-1
Chapter R Solutions
CALCULUS WITH APPLICATIONS
Ch. R.1 - YOUR TURN 1 Perform the operation
Ch. R.1 - YOUR TURN 2 Perform the operation .
Ch. R.1 - Prob. 3YTCh. R.1 - Prob. 4YTCh. R.1 - Perform the indicated operations.
1.
Ch. R.1 - Prob. 2ECh. R.1 - Prob. 3ECh. R.1 - Prob. 4ECh. R.1 - Perform the indicated operations.
5.
Ch. R.1 - Perform the indicated operations.
6.
Ch. R.1 - Perform the indicated operations.
7.
Ch. R.1 - Prob. 8ECh. R.1 - Prob. 9ECh. R.1 - Prob. 10ECh. R.1 - Prob. 11ECh. R.1 - Prob. 12ECh. R.1 - Prob. 13ECh. R.1 - Prob. 14ECh. R.1 - Prob. 15ECh. R.1 - Prob. 16ECh. R.1 - Prob. 17ECh. R.1 - Prob. 18ECh. R.1 - Prob. 19ECh. R.1 - Prob. 20ECh. R.1 - Prob. 21ECh. R.1 - Prob. 22ECh. R.1 - Prob. 23ECh. R.1 - Prob. 24ECh. R.1 - Prob. 25ECh. R.1 - Prob. 26ECh. R.2 - YOUR TURN 1 Factor
Ch. R.2 - YOUR TURN 2 Factor
Ch. R.2 - YOUR TURN 3 Factor
Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Prob. 12ECh. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Prob. 17ECh. R.2 - Prob. 18ECh. R.2 - Prob. 19ECh. R.2 - Prob. 20ECh. R.2 - Prob. 21ECh. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Prob. 29ECh. R.2 - Prob. 30ECh. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.3 - YOUR TURN 1 Write in lowest terms .
Ch. R.3 - YOUR TURN 2 Perform each of the following...Ch. R.3 - Prob. 1ECh. R.3 - Prob. 2ECh. R.3 - Prob. 3ECh. R.3 - Prob. 4ECh. R.3 - Prob. 5ECh. R.3 - Prob. 6ECh. R.3 - Prob. 7ECh. R.3 - Prob. 8ECh. R.3 - Prob. 9ECh. R.3 - Prob. 10ECh. R.3 - Prob. 11ECh. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Prob. 16ECh. R.3 - Prob. 17ECh. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Perform the indicated operations.
20.
Ch. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Prob. 28ECh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.4 - YOUR TURN 1 Solve .
Ch. R.4 - Prob. 2YTCh. R.4 - Prob. 3YTCh. R.4 - Prob. 4YTCh. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Prob. 3ECh. R.4 - Prob. 4ECh. R.4 - Prob. 5ECh. R.4 - Prob. 6ECh. R.4 - Prob. 7ECh. R.4 - Prob. 8ECh. R.4 - Prob. 9ECh. R.4 - Prob. 10ECh. R.4 - Prob. 11ECh. R.4 - Prob. 12ECh. R.4 - Prob. 13ECh. R.4 - Prob. 14ECh. R.4 - Prob. 15ECh. R.4 - Prob. 16ECh. R.4 - Prob. 17ECh. R.4 - Prob. 18ECh. R.4 - Prob. 19ECh. R.4 - Prob. 20ECh. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Prob. 23ECh. R.4 - Prob. 24ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 26ECh. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Prob. 29ECh. R.4 - Prob. 30ECh. R.4 - Prob. 31ECh. R.4 - Prob. 32ECh. R.4 - Prob. 33ECh. R.4 - Prob. 34ECh. R.4 - Prob. 35ECh. R.4 - Prob. 36ECh. R.4 - Prob. 37ECh. R.5 - YOUR TURN 1 Solve 3z – 2 > 5z + 7.
Ch. R.5 - YOUR TURN 2 Solve 3y2 16y + 12.
Ch. R.5 - Prob. 3YTCh. R.5 - Prob. 1ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 3ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Prob. 7ECh. R.5 - Prob. 8ECh. R.5 - Prob. 9ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 11ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 13ECh. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Prob. 19ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 21ECh. R.5 - Prob. 22ECh. R.5 - Prob. 23ECh. R.5 - Solve each inequality and graph the...Ch. R.5 - Solve each inequality and graph the...Ch. R.5 - Prob. 26ECh. R.5 - Prob. 27ECh. R.5 - Solve each inequality. Graph each solution.
28.
Ch. R.5 - Prob. 29ECh. R.5 - Solve each inequality. Graph each solution.
30.
Ch. R.5 - Prob. 31ECh. R.5 - Solve each inequality. Graph each solution.
32.
Ch. R.5 - Prob. 33ECh. R.5 - Prob. 34ECh. R.5 - Prob. 35ECh. R.5 - Prob. 36ECh. R.5 - Prob. 37ECh. R.5 - Solve each inequality. Graph each solution.
38.
Ch. R.5 - Prob. 39ECh. R.5 - Solve each inequality. Graph each solution.
40.
Ch. R.5 - Prob. 41ECh. R.5 - Solve each inequality. Graph each solution.
42.
Ch. R.5 - Prob. 43ECh. R.5 - Prob. 44ECh. R.5 - Prob. 45ECh. R.5 - Solve each inequality.
46.
Ch. R.5 - Prob. 47ECh. R.5 - Prob. 48ECh. R.5 - Prob. 49ECh. R.5 - Prob. 50ECh. R.5 - Solve each inequality.
51.
Ch. R.5 - Solve each inequality.
52.
Ch. R.5 - Prob. 53ECh. R.5 - Prob. 54ECh. R.6 - YOUR TURN 1 Find
Ch. R.6 - YOUR TURN 2 Simplify
Ch. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 1ECh. R.6 - Evaluate each expression. Write all answers...Ch. R.6 - Prob. 3ECh. R.6 - Prob. 4ECh. R.6 - Prob. 5ECh. R.6 - Prob. 6ECh. R.6 - Prob. 7ECh. R.6 - Evaluate each expression. Write all answers...Ch. R.6 - Prob. 9ECh. R.6 - Prob. 10ECh. R.6 - Prob. 11ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 13ECh. R.6 - Prob. 14ECh. R.6 - Prob. 15ECh. R.6 - Prob. 16ECh. R.6 - Prob. 17ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 19ECh. R.6 - Simplify each expression. Assume that all...Ch. R.6 - Prob. 21ECh. R.6 - Prob. 22ECh. R.6 - Prob. 23ECh. R.6 - Simplify each expression, writing the answers as a...Ch. R.6 - Prob. 25ECh. R.6 - Prob. 26ECh. R.6 - Prob. 27ECh. R.6 - Prob. 28ECh. R.6 - Prob. 29ECh. R.6 - Write each number without exponents.
30.
Ch. R.6 - Prob. 31ECh. R.6 - Prob. 32ECh. R.6 - Prob. 33ECh. R.6 - Prob. 34ECh. R.6 - Prob. 35ECh. R.6 - Write each number without exponents.
36.
Ch. R.6 - Prob. 37ECh. R.6 - Prob. 38ECh. R.6 - Prob. 39ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 41ECh. R.6 - Prob. 42ECh. R.6 - Prob. 43ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 45ECh. R.6 - Prob. 46ECh. R.6 - Prob. 47ECh. R.6 - Prob. 48ECh. R.6 - Prob. 49ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 51ECh. R.6 - Factor each expression.
52.
Ch. R.6 - Prob. 53ECh. R.6 - Prob. 54ECh. R.6 - Prob. 55ECh. R.6 - Factor each expression.
56.
Ch. R.7 - Prob. 1YTCh. R.7 - Prob. 2YTCh. R.7 - Prob. 3YTCh. R.7 - Prob. 1ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 3ECh. R.7 - Prob. 4ECh. R.7 - Prob. 5ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Prob. 9ECh. R.7 - Prob. 10ECh. R.7 - Prob. 11ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 13ECh. R.7 - Prob. 14ECh. R.7 - Prob. 15ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 17ECh. R.7 - Prob. 18ECh. R.7 - Prob. 19ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 21ECh. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Simplify each root, if possible.
24.
Ch. R.7 - Prob. 25ECh. R.7 - Prob. 26ECh. R.7 - Prob. 27ECh. R.7 - Prob. 28ECh. R.7 - Prob. 29ECh. R.7 - Prob. 30ECh. R.7 - Prob. 31ECh. R.7 - Prob. 32ECh. R.7 - Prob. 33ECh. R.7 - Prob. 34ECh. R.7 - Prob. 35ECh. R.7 - Prob. 36ECh. R.7 - Prob. 37ECh. R.7 - Prob. 38ECh. R.7 - Prob. 39ECh. R.7 - Prob. 40ECh. R.7 - Prob. 41ECh. R.7 - Prob. 42ECh. R.7 - Prob. 43ECh. R.7 - Prob. 44E
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