Using the same set of axes, graph R , C , and P , the total-revenue, total-cost, and total-profit functions. R ( x ) = 50 x − 0.5 x 2 , C ( x ) = 10 x + 3
Using the same set of axes, graph R , C , and P , the total-revenue, total-cost, and total-profit functions. R ( x ) = 50 x − 0.5 x 2 , C ( x ) = 10 x + 3
Solution Summary: The author explains how to graph the total revenue function, total-cost function and profit function.
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot
mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external
force of 4 cos 2t lb.
a. Set-up the differential equation and initial value problem for the system.
b. Write the function in phase-amplitude form.
C.
Determine the transient solution to the system. Show your work.
d. Determine the steady state of this system. Show your work.
e.
Is the system underdamped, overdamped or critically damped? Explain what this
means for the system.
4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a
capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge
60
to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the
following questions
a. Find the function that models the charge of this circuit.
b. Is the circuit underdamped, overdamped or critically damped?
Chapter 2 Solutions
Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)
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