CALCULUS+ITS APPLICATIONS(LL)-W/MYMATH.
14th Edition
ISBN: 9780134465333
Author: Goldstein
Publisher: PEARSON
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Chapter 10.4, Problem 14E
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CALCULUS+ITS APPLICATIONS(LL)-W/MYMATH.
Ch. 10.1 - Show that any function of the form y=Aet3/3, where...Ch. 10.1 - If the function f(t) is a solution of the...Ch. 10.1 - Prob. 3CYUCh. 10.1 - Show that the function f(t)=32et212 is a solution...Ch. 10.1 - Show that the function f(t)=t212 is a solution of...Ch. 10.1 - Show that the function f(t)=5e2t satisfies...Ch. 10.1 - Show that the function f(t)=(et+1)1 satisfies...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Is the constant function f(t)=3 a solution of the...
Ch. 10.1 - Prob. 8ECh. 10.1 - Find a constant solution of y=t2y5t2.Ch. 10.1 - Prob. 10ECh. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Savings Account Let f(t) be the balance in a...Ch. 10.1 - Spread of News A certain piece of news is being...Ch. 10.1 - Paramecium Growth Let f(t) be the size of...Ch. 10.1 - Rate of Net Investment Let f(t) denote the amount...Ch. 10.1 - Newtons Law of Cooling A cool object is placed in...Ch. 10.1 - Carbon Dioxide Diffusion in Lungs during Breath...Ch. 10.1 - Slope Field The slope field in Fig4(a) suggests...Ch. 10.1 - Prob. 23ECh. 10.1 - On the slope field in Fig5(a), or a copy of it,...Ch. 10.1 - Prob. 25ECh. 10.1 - On the slope field in Fig4(a), or a copy of it,...Ch. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Technology Exercise Consider the differential...Ch. 10.1 - Technology Exercise The function f(t)=50001+49et...Ch. 10.2 - Solve the initial-value problem y=5y,y(0)=2, by...Ch. 10.2 - Solve y=ty,y(1)=4.Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Solve the following differential equations:...Ch. 10.2 - Prob. 15ECh. 10.2 - Prob. 16ECh. 10.2 - Prob. 17ECh. 10.2 - Prob. 18ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 23ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 25ECh. 10.2 - Prob. 26ECh. 10.2 - Solve the following differential equations with...Ch. 10.2 - Solve the following differential equations with...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Probability of AccidentsLet t represent the total...Ch. 10.2 - Amount of Information LearnedIn certain learning...Ch. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Rate of DecompositionWhen a certain liquid...Ch. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.3 - Using an integrating factor, solve y+y=1+et.Ch. 10.3 - Find an integrating factor for the differential...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for an equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Find an integrating factor for the equation:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the equation using an integrating factor:...Ch. 10.3 - Solve the initial value problem: y+2y=1,y(0)=1.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem: y=2(10y),y(0)=1.Ch. 10.3 - Solve the initial value problem: y+y=e2t,y(0)=1.Ch. 10.3 - Solve the initial value problem: tyy=1,y(1)=1,t0.Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Solve the initial value problem:...Ch. 10.3 - Consider the initial value problem...Ch. 10.4 - Solutions can be found following the section...Ch. 10.4 - A Retirement Account refer toExample 1 a. How fast...Ch. 10.4 - Prob. 2ECh. 10.4 - A Retirement Account A person planning for her...Ch. 10.4 - A Savings Account A person deposits 10,000 in bank...Ch. 10.4 - Prob. 5ECh. 10.4 - Prob. 6ECh. 10.4 - Aperson took out a loan of 100,000 from a bank...Ch. 10.4 - Car Prices in 2012 The National Automobile Dealers...Ch. 10.4 - New Home Prices in 2012 The Federal Housing...Ch. 10.4 - Answer parts (a), (b), and (c) of Exercise 9 if...Ch. 10.4 - Prob. 11ECh. 10.4 - Find the demand function if the elasticity of...Ch. 10.4 - Temperature of a Steel Rod When a red-hot steel...Ch. 10.4 - Prob. 14ECh. 10.4 - Determining the Time of Death A body was found in...Ch. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Prob. 18ECh. 10.4 - Prob. 19ECh. 10.4 - Radioactive Decay Radium 226 is a radioactive...Ch. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 22ECh. 10.4 - In Exercises 2125, solving the differential...Ch. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Technology Exercise Therapeutic Level of a Drug A...Ch. 10.5 - Consider the differential equation y=g(y) where...Ch. 10.5 - Prob. 2CYUCh. 10.5 - Prob. 3CYUCh. 10.5 - Prob. 4CYUCh. 10.5 - Exercise 1-6 review concepts that are important in...Ch. 10.5 - Prob. 2ECh. 10.5 - Prob. 3ECh. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 11ECh. 10.5 - Prob. 12ECh. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - One or more initial conditions are given for each...Ch. 10.5 - Prob. 18ECh. 10.5 - Prob. 19ECh. 10.5 - Prob. 20ECh. 10.5 -
Ch. 10.5 - Prob. 22ECh. 10.5 - Prob. 23ECh. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 -
Ch. 10.5 - Prob. 27ECh. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - Prob. 31ECh. 10.5 - Prob. 32ECh. 10.5 - Prob. 33ECh. 10.5 - , where , and
Ch. 10.5 - Prob. 35ECh. 10.5 - Prob. 36ECh. 10.5 - Growth of a plant Suppose that, once a sunflower...Ch. 10.5 - Prob. 38ECh. 10.5 - Technology Exercises
Draw the graph of, and use...Ch. 10.5 - Technology Exercises Draw the graph of...Ch. 10.6 - Refer to Example 4, involving the flow of...Ch. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 2ECh. 10.6 - In Exercises 1- 4, you are given a logistic...Ch. 10.6 - Prob. 4ECh. 10.6 - Answer part (a) in Example 2, if the pond was...Ch. 10.6 - Prob. 6ECh. 10.6 - Social Diffusion For information being spread by...Ch. 10.6 - Gravity At one point in his study of a falling...Ch. 10.6 - Autocatalytic Reaction In an autocatalytic...Ch. 10.6 - Drying A porous material dries outdoors at a rate...Ch. 10.6 - Movement of Solutes through a Cell Membrane Let c...Ch. 10.6 - Bacteria Growth An experimenter reports that a...Ch. 10.6 - Chemical Reaction Suppose that substance A is...Ch. 10.6 - War Fever L. F. Richardson proposed the following...Ch. 10.6 - Capital Investment Model In economic theory, the...Ch. 10.6 - 16. Evans Price Adjustment Model Consider a...Ch. 10.6 - Fish Population with Harvesting The fish...Ch. 10.6 - Continuous Annuity A continuous annuity is a...Ch. 10.6 - Savings Account with Deposits A company wishes to...Ch. 10.6 - Savings Account A company arranges to make...Ch. 10.6 - Amount of CO2 in a Room The air in a crowded room...Ch. 10.6 - Elimination of a Drug from the Bloodstream A...Ch. 10.6 - Elimination of a Drug A single dose of iodine is...Ch. 10.6 - Litter in a Forest Show that the mathematical...Ch. 10.6 - Population Model In the study of the effect of...Ch. 10.7 - Prob. 1CYUCh. 10.7 - Prob. 2CYUCh. 10.7 - Prob. 1ECh. 10.7 - Prob. 2ECh. 10.7 - Prob. 3ECh. 10.7 - Prob. 4ECh. 10.7 - Prob. 5ECh. 10.7 - Prob. 6ECh. 10.7 - Use Eulers method with n=4 to approximate the...Ch. 10.7 - Let be the solution of , Use Euler’s method with...Ch. 10.7 - Prob. 9ECh. 10.7 - Prob. 10ECh. 10.7 - Suppose that the consumer Products Safety...Ch. 10.7 -
12. Rate of evaporation The Los Angeles plans to...Ch. 10.7 - Prob. 13ECh. 10.7 - The differential equation y=0.5(1y)(4y) has five...Ch. 10.7 - Prob. 15ECh. 10.7 - Prob. 16ECh. 10 - What is a differential equation?Ch. 10 - Prob. 2CCECh. 10 - Prob. 3CCECh. 10 - Prob. 4CCECh. 10 - Prob. 5CCECh. 10 - Prob. 6CCECh. 10 - Prob. 7CCECh. 10 - Prob. 8CCECh. 10 - Prob. 9CCECh. 10 - Prob. 10CCECh. 10 - Prob. 11CCECh. 10 - Prob. 12CCECh. 10 - Describe Eulers method for approximating the...Ch. 10 - Prob. 1RECh. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Solve the differential equation in Exercises 1-10....Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Let P(t) denote the price in dollars of a certain...Ch. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Prob. 15RECh. 10 - Prob. 16RECh. 10 - Prob. 17RECh. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Sketch the solutions of the differential equations...Ch. 10 - Sketch the solutions of the differential equations...Ch. 10 - Prob. 22RECh. 10 - Prob. 23RECh. 10 - Prob. 24RECh. 10 - Prob. 25RECh. 10 - Suppose that in a chemical reaction, each gram of...Ch. 10 - Prob. 27RECh. 10 - Prob. 28RECh. 10 - Let f(t) be the solution to y=2e2ty,y(0)=0. Use...Ch. 10 - Prob. 30RECh. 10 - Prob. 31RECh. 10 - Prob. 32RE
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- Keplers Third Law Keplers Third Law of planetary motion states that the square of the period T of a planet the time it takes for the planet to make a complete revolution about the sun is directly proportional to the cube of its average distance d from the sun. a Express Keplers Third Law as an equation. b Find the constant of proportionality by using the fact that for our planet the period is about 365 days and the average distance is about 93 million miles. c The planet Neptune is about 2.79109 mi from the sun. Find the period of Neptune.arrow_forwardKepler’s Third Law Kepler’s Third Law of planetary motion states that the square of the period T of a planet (the time it takes fur the planet to make a complete resolution about the sun) is directly proportional to the cube of its average distance d from the sun. (a) Express Kepler’s Third Law as an equation. (b) Find the constant of proportionality by using the Fact that for our planet the period is about 365 days and the average distance is about 93 million miles (c) The planet Neptune is about 2.79109 mi from the sun. Find the period of Neptune.arrow_forwardHubbles Constant Astronomers believe that the universe is expanding and that stellar objects are moving away from us at a radial velocity V proportional to the distance D from Earth to the object. a. Write V as a function of D using H as the constant of proportionality. b. The equation in part a was first discovered by Edwin Hubble in 1929 and is known as Hubbles law. The constant of proportionality H is known as Hubbles constant. The currently accepted value of Hubbles constant is 70 kilometers per second per megaparsec. One megaparsec is about 3.0861019 kilometers. With these units for H, the distance D is measured in megaparsecs, and the velocity V is measured in kilometers per second. The galaxy G2237+305 is about 122.7 megaparsecs from Earth. How fast is G2237+305 receding from Earth? c. One important feature of Hubbles constant is that scientists use it to estimate the age of the universe. The approximate relation is y=1012H Where y is time in years. Hubbles constant is extremely difficult to measure, and Edwin Hubbles best estimate in 1929 was about 530 kilometers per second per megaparsec. What is the approximate age of the universe when this value of H is used? d. The calculation in part c would give scientists some concern, since Earth is thought to be about 4.6 billion years old. What estimate of the age of the universe does the more modern value of 70 kilometers per second per megaparsec give?arrow_forward
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