FIRST CRSE.IN DIFF.EQUAT..-ACCESS
11th Edition
ISBN: 9781337652469
Author: ZILL
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.1, Problem 37E
How High?—Linear Air Resistance Repeat Problem 36, but this time assume that air resistance is proportional to instantaneous velocity. It stands to reason that the maximum height attained by the cannonball must be less than that in part (b) of Problem 36. Show this by supposing that the constant of proportionality is k = 0.0025. [Hint: Slightly modify the differential equation in Problem 35.]
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
1) Suppose continuous random variable X has sample space S = [1, ∞) and a pdf of the
form f(x) = Ce-(2-1)/2. What is the expected value of X?
A sequence X = (xn) is said to be a contractive sequence if there is a constant 0 < C < 1 so
that
for all n = N.
-
|Xn+1 − xn| ≤ C|Xn — Xn−1|
-
1) Find the equation of the tangent line to the graph y=xe at the point (1, 1).
Chapter 3 Solutions
FIRST CRSE.IN DIFF.EQUAT..-ACCESS
Ch. 3.1 - The population of a community is known to increase...Ch. 3.1 - Suppose it is known that the population of the...Ch. 3.1 - The population of a town grows at a rate...Ch. 3.1 - The population of bacteria in a culture grows at a...Ch. 3.1 - The radioactive isotope of lead, Pb-209, decays at...Ch. 3.1 - Initially 100 milligrams of a radioactive...Ch. 3.1 - Determine the half-life of the radioactive...Ch. 3.1 - Consider the initial-value problem dA/dt = kA,...Ch. 3.1 - When a vertical beam of light passes through a...Ch. 3.1 - When interest is compounded continuously, the...
Ch. 3.1 - Carbon Dating Archaeologists used pieces of burned...Ch. 3.1 - The Shroud of Turin, which shows the negative...Ch. 3.1 - Newtons Law of Cooling/Warming A thermometer is...Ch. 3.1 - A thermometer is taken from an inside room to the...Ch. 3.1 - A small metal bar, whose initial temperature was...Ch. 3.1 - Two large containers A and B of the same size are...Ch. 3.1 - A thermometer reading 70 F is placed in an oven...Ch. 3.1 - At t = 0 a sealed test tube containing a chemical...Ch. 3.1 - A dead body was found within a closed room of a...Ch. 3.1 - The rate at which a body cools also depends on its...Ch. 3.1 - A tank contains 200 liters of fluid in which 30...Ch. 3.1 - Solve Problem 21 assuming that pure water is...Ch. 3.1 - A large tank is filled to capacity with 500...Ch. 3.1 - In Problem 23, what is the concentration c(t) of...Ch. 3.1 - Solve Problem 23 under the assumption that the...Ch. 3.1 - Determine the amount of salt in the tank at time t...Ch. 3.1 - A large tank is partially filled with 100 gallons...Ch. 3.1 - In Example 5 the size of the tank containing the...Ch. 3.1 - A 30-volt electromotive force is applied to an...Ch. 3.1 - Prob. 30ECh. 3.1 - A 100-volt electromotive force is applied to an...Ch. 3.1 - A 200-volt electromotive force is applied to an...Ch. 3.1 - An electromotive force E(t)={120,0t200,t20 is...Ch. 3.1 - An LR-series circuit has a variable inductor with...Ch. 3.1 - Air Resistance In (14) of Section 1.3 we saw that...Ch. 3.1 - How High?No Air Resistance Suppose a small...Ch. 3.1 - How High?Linear Air Resistance Repeat Problem 36,...Ch. 3.1 - Skydiving A skydiver weighs 125 pounds, and her...Ch. 3.1 - Rocket Motion Suppose a small single-stage rocket...Ch. 3.1 - Rocket MotionContinued In Problem 39 suppose of...Ch. 3.1 - Evaporating Raindrop As a raindrop falls, it...Ch. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Constant-Harvest model A model that describes the...Ch. 3.1 - Drug Dissemination A mathematical model for the...Ch. 3.1 - Memorization When forgetfulness is taken into...Ch. 3.1 - Heart Pacemaker A heart pacemaker, shown in Figure...Ch. 3.1 - Sliding Box (a) A box of mass m slides down an...Ch. 3.1 - Sliding Box—Continued
In Problem 48 let s(t) be...Ch. 3.1 - What Goes Up (a) It is well known that the model...Ch. 3.2 - The number N(t) of supermarkets throughout the...Ch. 3.2 - The number N(t) of people in a community who are...Ch. 3.2 - A model for the population P(t) in a suburb of a...Ch. 3.2 - Census data for the United States between 1790 and...Ch. 3.2 - (a) If a constant number h of fish are harvested...Ch. 3.2 - Investigate the harvesting model in Problem 5 both...Ch. 3.2 - Repeat Problem 6 in the case a = 5, b = 1, h = 7.Ch. 3.2 - (a) Suppose a = b = 1 in the Gompertz differential...Ch. 3.2 - Two chemicals A and B are combined to form a...Ch. 3.2 - Solve Problem 9 if 100 grams of chemical A is...Ch. 3.2 - Leaking cylindrical tank A tank in the form of a...Ch. 3.2 - Leaking cylindrical tank—continued When friction...Ch. 3.2 - Leaking Conical Tank A tank in the form of a...Ch. 3.2 - Inverted Conical Tank Suppose that the conical...Ch. 3.2 - Air Resistance A differential equation for the...Ch. 3.2 - How High?Nonlinear Air Resistance Consider the...Ch. 3.2 - That Sinking Feeling (a) Determine a differential...Ch. 3.2 - Solar Collector The differential equation...Ch. 3.2 - Tsunami (a) A simple model for the shape of a...Ch. 3.2 - Evaporation An outdoor decorative pond in the...Ch. 3.2 - Doomsday equation Consider the differential...Ch. 3.2 - Doomsday or extinction Suppose the population...Ch. 3.2 - Skydiving A skydiver is equipped with a stopwatch...Ch. 3.2 - Prob. 27ECh. 3.2 - Old Man River In Figure 3.2.8(a) suppose that the...Ch. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Time Drips By The clepsydra, or water clock, was a...Ch. 3.2 - (a) Suppose that a glass tank has the shape of a...Ch. 3.2 - Prob. 35ECh. 3.3 - We have not discussed methods by which systems of...Ch. 3.3 - In Problem 1 suppose that time is measured in...Ch. 3.3 - Use the graphs in Problem 2 to approximate the...Ch. 3.3 - Construct a mathematical model for a radioactive...Ch. 3.3 - Potassium-40 Decay The chemical element potassium...Ch. 3.3 - Potassium-Argon Dating The knowledge of how K-40...Ch. 3.3 - Consider two tanks A and B, with liquid being...Ch. 3.3 - Use the information given in Figure 3.3.6 to...Ch. 3.3 - Two very large tanks A and B are each partially...Ch. 3.3 - Three large tanks contain brine, as shown in...Ch. 3.3 - Consider the Lotka-Volterra predator-prey model...Ch. 3.3 - Show that a system of differential equations that...Ch. 3.3 - Determine a system of first-order differential...Ch. 3.3 - Prob. 16ECh. 3.3 - SIR Model A communicable disease is spread...Ch. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Mixtures Solely on the basis of the physical...Ch. 3.3 - Newtons Law of Cooling/Warming As shown in Figure...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - Answer Problems 1 and 2 without referring back to...Ch. 3 - Prob. 3RECh. 3 - Air containing 0.06% carbon dioxide is pumped into...Ch. 3 - tzi the Iceman In September of 1991 two German...Ch. 3 - Prob. 6RECh. 3 - Prob. 7RECh. 3 - Suppose a cell is suspended in a solution...Ch. 3 - Suppose that as a body cools, the temperature of...Ch. 3 - According to Stefans law of radiation the absolute...Ch. 3 - Suppose an RC-series circuit has a variable...Ch. 3 - A classical problem in the calculus of variations...Ch. 3 - A model for the populations of two interacting...Ch. 3 - Initially, two large tanks A and B each hold 100...Ch. 3 - Prob. 15RECh. 3 - When all the curves in a family G(x, y, c1) = 0...Ch. 3 - Prob. 17RECh. 3 - Prob. 18RECh. 3 - Prob. 19RECh. 3 - Sawing Wood A long uniform piece of wood (cross...Ch. 3 - Solve the initial-value problem in Problem 20 when...Ch. 3 - Prob. 22RE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- 2) Find the maximum value of f(x, y) = x - y on the circle x² + y² - 4x - 2y - 4 = 0.arrow_forwardBlue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production cycle. Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs. (This supplier has the capacity to deliver as many hot tub shells as Howie needs.) Howie installs the same type of pump into both hot tubs. He will have only 200 pumps available during his next production cycle. From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required. Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing. Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing. Howie expects to have 1,566 production labor hours and 2,880 feet of tubing available during the next production cycle. Howie earns a profit of…arrow_forward7. From a point 20 m away on a level ground, the angle of elevation to the bottom of a the top of the window is 32°. Calculate the window is 27° and the angle of elevatim height of the window. (3 marks) 32 SOUCAHTOA Rom Coso-Adj opponite 1270 H X Hyp Tant=OPP Adj 20 # Zom Adjacent CoS2E 20 XHX Tanz 20 20 K -0.0445503261 -1.764201788 0-044550326 60044550320 (1 mark) 3960 8. All odd numbers from 1 to 10 are arranged in descending order to form a number. (i) Write the number. 35798. 97531 31 (ii) Write the total value of the second digit of the number formed in (a) (i) FA 7X1000-7000 이 (1 mark) 9. A cylinder has a diameter of 28 cm and the height is 18 cm. Calculate its volume. 2 22 × 14 × 14 × 18 -110880m 3 (3 marks) 10. The figure below shows a right pyramid with AB = 3 cm, BC = 5 cm, and AV VC = VD = 4 cm. Draw its net. V 3+ 12 7/18 (2/20 2105 SSS 20arrow_forward
- No chatgpt pls will upvotearrow_forwardFind an nfa that accepts the language L(aa (a + b)). Create and test the NFA in Jflap. Test the strings: aab, ab, aaaa, aaaab, baab, aa, abbbb, a, b, 1. Submit the Jflap diagram and the Jflap test cases. 4. Find an nfa that accepts the language L (aa* (a+b)).arrow_forwardCVE, AVM, AC, ¬SA¬ME A Fitch Style proof for this argumentarrow_forward
- 13:26 ... ← Robert F. Blitzer - Thinkin... 0,04 61 KB/d 目 polygons to create a fraudulent tessellation with discrepancies that are too subtle for the eye to notice. In Exercises 45-46, you will use mathematics, not your eyes, to observe the irregularities. B A 45. Find the sum of the angle measures at vertex A. Then explain why the tessellation is a fake. 46. Find the sum of the angle measures at vertex B. Then explain why the tessellation is a fake. =et at If se Fic SECTION 10.3 Polygons, Perimeter, and Tessellations 645 61. I find it helpful to think of a polygon's perimeter as the length of its boundary. 62. If a polygon is not regular, I can determine the sum of the measures of its angles, but not the measure of any one of its angles. 63. I used floor tiles in the shape of regular pentagons to completely cover my kitchen floor. In Exercises 64-65, write an algebraic expression that represents the perimeter of the figure shown. is be 64. le a b C 2/ If se nyarrow_forwardnot use ai please don'tarrow_forwardpls helparrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY