EBK BUSINESS MATH
11th Edition
ISBN: 8220103633802
Author: NOBLE
Publisher: RENT PEARS
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Chapter 4, Problem 4PT
To determine
The returned check service charge for the bank's statement of D.G.Hernandez Equipment.
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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
Chapter 4 Solutions
EBK BUSINESS MATH
Ch. 4.1 - Prob. 1-1SCCh. 4.1 - Prob. 1-2SCCh. 4.1 - Prob. 1-3SCCh. 4.1 - Prob. 1-4SCCh. 4.1 - Prob. 1-5SCCh. 4.1 - Prob. 2-1SCCh. 4.1 - Prob. 2-2SCCh. 4.1 - Prob. 2-3SCCh. 4.1 - Prob. 2-4SCCh. 4.1 - Prob. 1SE
Ch. 4.1 - Prob. 2SECh. 4.1 - Prob. 3SECh. 4.1 - Prob. 4SECh. 4.1 - Prob. 5SECh. 4.1 - Prob. 6SECh. 4.1 - Prob. 7SECh. 4.1 - Prob. 8SECh. 4.1 - Prob. 9SECh. 4.1 - Prob. 10SECh. 4.1 - Prob. 11SECh. 4.1 - Prob. 12SECh. 4.2 - Prob. 1-1SCCh. 4.2 - Prob. 1-2SCCh. 4.2 - Prob. 1-3SCCh. 4.2 - Prob. 1-4SCCh. 4.2 - Prob. 1-5SCCh. 4.2 - Prob. 1-6SCCh. 4.2 - Prob. 1-7SCCh. 4.2 - Prob. 1-8SCCh. 4.2 - Prob. 1-10SCCh. 4.2 - Prob. 1SECh. 4.2 - Prob. 2SECh. 4.2 - Prob. 3SECh. 4.2 - Prob. 4SECh. 4.2 - Prob. 5SECh. 4 - Prob. 1ESCh. 4 - Prob. 2ESCh. 4 - Prob. 3ESCh. 4 - Prob. 4ESCh. 4 - Prob. 5ESCh. 4 - Prob. 6ESCh. 4 - Prob. 7ESCh. 4 - Prob. 8ESCh. 4 - Prob. 9ESCh. 4 - Prob. 10ESCh. 4 - Prob. 11ESCh. 4 - Prob. 12ESCh. 4 - Prob. 13ESCh. 4 - Prob. 14ESCh. 4 - Prob. 15ESCh. 4 - Prob. 16ESCh. 4 - Prob. 17ESCh. 4 - Prob. 18ESCh. 4 - Prob. 19ESCh. 4 - Prob. 20ESCh. 4 - Prob. 21ESCh. 4 - Prob. 22ESCh. 4 - Prob. 23ESCh. 4 - Prob. 24ESCh. 4 - Prob. 25ESCh. 4 - Prob. 26ESCh. 4 - Prob. 27ESCh. 4 - Prob. 28ESCh. 4 - Prob. 29ESCh. 4 - Prob. 30ESCh. 4 - Prob. 1PTCh. 4 - Prob. 2PTCh. 4 - Prob. 3PTCh. 4 - Prob. 4PTCh. 4 - Prob. 5PTCh. 4 - Prob. 6PTCh. 4 - Prob. 7PTCh. 4 - Prob. 8PTCh. 4 - Prob. 9PTCh. 4 - Prob. 10PTCh. 4 - Prob. 11PTCh. 4 - Prob. 1CTCh. 4 - Prob. 2CTCh. 4 - Prob. 3CTCh. 4 - Prob. 4CTCh. 4 - Prob. 5CTCh. 4 - Prob. 6CTCh. 4 - Prob. 7CTCh. 4 - Prob. 8CTCh. 4 - Prob. 9CTCh. 4 - Prob. 10CTCh. 4 - Prob. 1CPCh. 4 - Prob. 2CPCh. 4 - Prob. 1CS1Ch. 4 - Prob. 2CS1Ch. 4 - Prob. 3CS1Ch. 4 - Prob. 4CS1Ch. 4 - Prob. 1CS2Ch. 4 - Prob. 2CS2Ch. 4 - Prob. 3CS2Ch. 4 - Prob. 4CS2
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- 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-1arrow_forward4. Given the following information determine the appropriate trial solution to find yp. Do not solve the differential equation. Do not find the constants. a) (D-4)2(D+ 2)y = 4e-2x b) (D+ 1)(D² + 10D +34)y = 2e-5x cos 3xarrow_forward9.7 Given the equations 0.5x₁-x2=-9.5 1.02x₁ - 2x2 = -18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the system's condition? (d) Solve by the elimination of unknowns. (e) Solve again, but with a modified slightly to 0.52. Interpret your results.arrow_forward
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- 11.9 Recall from Prob. 10.8, that the following system of equations is designed to determine concentrations (the e's in g/m³) in a series of coupled reactors as a function of amount of mass input to each reactor (the right-hand sides are in g/day): 15c3cc33300 -3c18c26c3 = 1200 -4c₁₂+12c3 = 2400 Solve this problem with the Gauss-Seidel method to & = 5%.arrow_forward9.8 Given the equations 10x+2x2-x3 = 27 -3x-6x2+2x3 = -61.5 x1 + x2 + 5x3 = -21.5 (a) Solve by naive Gauss elimination. Show all steps of the compu- tation. (b) Substitute your results into the original equations to check your answers.arrow_forwardTangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations).arrow_forward
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