University Calculus: Early Transcendentals (3rd Edition)
3rd Edition
ISBN: 9780321999580
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter A.8, Problem 22E
To determine
The six solutions of the equation
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A cylindrical chemical storage tank with a capacity of 950m3 is going to be constructed in a warehouse that is 11m by 14m with a height of 10m. The specifications call for the case to be made of sheet metal that costs $90/m2, the top to be made from sheet metal that costs $45/m2 and the wall to be made of sheet metal that costs $80/m2. If you want to minimize the cost to make the storage house, how much would you end up spending to build the tank?
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Chapter A.8 Solutions
University Calculus: Early Transcendentals (3rd Edition)
Ch. A.8 - Prob. 1ECh. A.8 - Prob. 2ECh. A.8 - Prob. 3ECh. A.8 - Prob. 4ECh. A.8 - Prob. 5ECh. A.8 - Prob. 6ECh. A.8 - Prob. 7ECh. A.8 - Prob. 8ECh. A.8 - Prob. 9ECh. A.8 - Prob. 10E
Ch. A.8 - Prob. 11ECh. A.8 - Prob. 12ECh. A.8 - Prob. 13ECh. A.8 - Prob. 14ECh. A.8 - Prob. 15ECh. A.8 - Prob. 16ECh. A.8 - Prob. 17ECh. A.8 - Prob. 18ECh. A.8 - Prob. 19ECh. A.8 - Prob. 20ECh. A.8 - Prob. 21ECh. A.8 - Prob. 22ECh. A.8 - Prob. 23ECh. A.8 - Prob. 24ECh. A.8 - Prob. 25ECh. A.8 - Prob. 26ECh. A.8 - Prob. 27ECh. A.8 - Prob. 28ECh. A.8 - Prob. 29ECh. A.8 - Prob. 30E
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- Consider the sequence below: 1 1 1 (a) Express this sequence as a recurrence relation (b) Express this sequence in the form {a}=1 (c) Does this sequence converge or diverge? Justify your answer. Consider the sequence below: 1 1 1 1, 4' 9' 16' (a) Express this sequence in the form {ak}=1 (b) Does this sequence converge or diverge? Justify your answer. Consider the sequence below: 345 2. 4' 9' 16' ·} (a) Express this sequence in the form {a}1 (b) Does this sequence converge or diverge? Justify your answer.arrow_forwardUse the growth rate of sequences theorem to find the limit or state it divergesarrow_forwardcalculate the maximum value of the directional derivativearrow_forward
- 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) dtarrow_forward- 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) = 2arrow_forward5. 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_forward
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