Explanation Given information: Object A and B are placed in a warm bath at temperature T 0 = 40 ° C . Object A has initial temperature − 20 ° C and cooling constant k = 0.004 s − 1 . Object B has initial temperature 0 o C and cooling constant k = 0.002 s − 1 . Formula used: Newton’s law of cooling: y ' = − k ( y − T 0 ) , y ( t ) is the temperature of object, T 0 is ambient temperature and k is cooling constant. The solution to the equation of form y ' = − k ( y − T 0 ) is y ( t ) = T 0 + C e k t , Calculation: A : y 1 ' = − k 1 ( y 1 − T 0 ) B : y 2 ' = − k 2 ( y 2 − T 0 ) From given information, we have T 0 = 40 ° C y 1 ( 0 ) = − 20 ° C k 1 = 0.004 s − 1 y 2 ( 0 ) = 0 ° C k 2 = 0.002 s − 1 A : y 1 ' = − 0.004 ( y 1 − 40 ) The solution is y 1 ( t ) = 40 + C e 0.004 t S i n c e y 1 ( 0 ) = − 20 ° C ⇒ 40 + C e 0 = − 20 ⇒ C = − 20 − 40 ⇒ C = − 60 The solution becomes y 1 ( t ) = 40 − 60 e 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 10.2, Problem 11E

To determine

To plot:The temperatures of A and B for 0≤t≤1000 and to find the time after that the objects has the same temperature.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.2, Problem 10E

Chapter 10.2, Problem 12E

Students have asked these similar questions

The population of a certain kind of insect change directly proportional to its present population at any given time "t". If a culture of 12 insect grows to 93 after 10 days, determine the population of insect after 47 days. (unit not needed)

Chapter 10 Solutions

CALCULUS (CLOTH)

Ch. 10.1 - Prob. 1PQ Ch. 10.1 - Prob. 2PQ Ch. 10.1 - Prob. 3PQ Ch. 10.1 - Prob. 4PQ Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E

Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - Prob. 44E Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - Prob. 48E Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 56E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - Prob. 59E Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Prob. 62E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 64E Ch. 10.1 - Prob. 65E Ch. 10.1 - Prob. 66E Ch. 10.1 - Prob. 67E Ch. 10.1 - Prob. 68E Ch. 10.1 - Prob. 69E Ch. 10.1 - Prob. 70E Ch. 10.1 - Prob. 71E Ch. 10.2 - Prob. 1PQ Ch. 10.2 - Prob. 2PQ Ch. 10.2 - Prob. 3PQ Ch. 10.2 - Prob. 4PQ Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.3 - Prob. 1PQ Ch. 10.3 - Prob. 2PQ Ch. 10.3 - Prob. 3PQ Ch. 10.3 - Prob. 4PQ Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - Prob. 22E Ch. 10.3 - Prob. 23E Ch. 10.3 - Prob. 24E Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.4 - Prob. 1PQ Ch. 10.4 - Prob. 2PQ Ch. 10.4 - Prob. 3PQ Ch. 10.4 - Prob. 1E Ch. 10.4 - Prob. 2E Ch. 10.4 - Prob. 3E Ch. 10.4 - Prob. 4E Ch. 10.4 - Prob. 5E Ch. 10.4 - Prob. 6E Ch. 10.4 - Prob. 7E Ch. 10.4 - Prob. 8E Ch. 10.4 - Prob. 9E Ch. 10.4 - Prob. 10E Ch. 10.4 - Prob. 11E Ch. 10.4 - Prob. 12E Ch. 10.4 - Prob. 13E Ch. 10.4 - Prob. 14E Ch. 10.4 - Prob. 15E Ch. 10.4 - Prob. 16E Ch. 10.4 - Prob. 17E Ch. 10.4 - Prob. 18E Ch. 10.5 - Prob. 1PQ Ch. 10.5 - Prob. 2PQ Ch. 10.5 - Prob. 3PQ Ch. 10.5 - Prob. 4PQ Ch. 10.5 - Prob. 1E Ch. 10.5 - Prob. 2E Ch. 10.5 - Prob. 3E Ch. 10.5 - Prob. 4E Ch. 10.5 - Prob. 5E Ch. 10.5 - Prob. 6E Ch. 10.5 - Prob. 7E Ch. 10.5 - Prob. 8E Ch. 10.5 - Prob. 9E Ch. 10.5 - Prob. 10E Ch. 10.5 - Prob. 11E Ch. 10.5 - Prob. 12E Ch. 10.5 - Prob. 13E Ch. 10.5 - Prob. 14E Ch. 10.5 - Prob. 15E Ch. 10.5 - Prob. 16E Ch. 10.5 - Prob. 17E Ch. 10.5 - Prob. 18E Ch. 10.5 - Prob. 19E Ch. 10.5 - Prob. 20E Ch. 10.5 - Prob. 21E Ch. 10.5 - Prob. 22E Ch. 10.5 - Prob. 23E Ch. 10.5 - Prob. 24E Ch. 10.5 - Prob. 25E Ch. 10.5 - Prob. 26E Ch. 10.5 - Prob. 27E Ch. 10.5 - Prob. 28E Ch. 10.5 - Prob. 29E Ch. 10.5 - Prob. 30E Ch. 10.5 - Prob. 31E Ch. 10.5 - Prob. 32E Ch. 10.5 - Prob. 33E Ch. 10.5 - Prob. 34E Ch. 10.5 - Prob. 35E Ch. 10.5 - Prob. 36E Ch. 10.5 - Prob. 37E Ch. 10.5 - Prob. 38E Ch. 10.5 - Prob. 39E Ch. 10.5 - Prob. 40E Ch. 10.5 - Prob. 41E Ch. 10.5 - Prob. 42E Ch. 10.5 - Prob. 43E Ch. 10.5 - Prob. 44E Ch. 10.5 - Prob. 45E Ch. 10.5 - Prob. 46E Ch. 10.5 - Prob. 47E Ch. 10.5 - Prob. 48E Ch. 10.5 - Prob. 49E Ch. 10 - Prob. 1CRE Ch. 10 - Prob. 2CRE Ch. 10 - Prob. 3CRE Ch. 10 - Prob. 4CRE Ch. 10 - Prob. 5CRE Ch. 10 - Prob. 6CRE Ch. 10 - Prob. 7CRE Ch. 10 - Prob. 8CRE Ch. 10 - Prob. 9CRE Ch. 10 - Prob. 10CRE Ch. 10 - Prob. 11CRE Ch. 10 - Prob. 12CRE Ch. 10 - Prob. 13CRE Ch. 10 - Prob. 14CRE Ch. 10 - Prob. 15CRE Ch. 10 - Prob. 16CRE Ch. 10 - Prob. 17CRE Ch. 10 - Prob. 18CRE Ch. 10 - Prob. 19CRE Ch. 10 - Prob. 20CRE Ch. 10 - Prob. 21CRE Ch. 10 - Prob. 22CRE Ch. 10 - Prob. 23CRE Ch. 10 - Prob. 24CRE Ch. 10 - Prob. 25CRE Ch. 10 - Prob. 26CRE Ch. 10 - Prob. 27CRE Ch. 10 - Prob. 28CRE Ch. 10 - Prob. 29CRE Ch. 10 - Prob. 30CRE Ch. 10 - Prob. 31CRE Ch. 10 - Prob. 32CRE Ch. 10 - Prob. 33CRE Ch. 10 - Prob. 34CRE Ch. 10 - Prob. 35CRE Ch. 10 - Prob. 36CRE Ch. 10 - Prob. 37CRE Ch. 10 - Prob. 38CRE Ch. 10 - Prob. 39CRE Ch. 10 - Prob. 40CRE Ch. 10 - Prob. 41CRE Ch. 10 - Prob. 42CRE Ch. 10 - Prob. 43CRE Ch. 10 - Prob. 44CRE Ch. 10 - Prob. 45CRE Ch. 10 - Prob. 46CRE Ch. 10 - Prob. 47CRE Ch. 10 - Prob. 48CRE Ch. 10 - Prob. 49CRE Ch. 10 - Prob. 50CRE Ch. 10 - Prob. 51CRE Ch. 10 - Prob. 52CRE

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?

Recommended textbooks for you

College Algebra
Algebra
ISBN:9781938168383
Author:Jay Abramson
Publisher:OpenStax
College Algebra
Algebra
ISBN:9781337282291
Author:Ron Larson
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning

College Algebra

Algebra

ISBN:9781938168383

Author:Jay Abramson

Publisher:OpenStax

College Algebra

Algebra

ISBN:9781337282291

Author:Ron Larson

Publisher:Cengage Learning

Functions and Change: A Modeling Approach to Coll...

Algebra

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:9781133382119

Author:Swokowski

Publisher:Cengage

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

Trigonometry (MindTap Course List)

Trigonometry

ISBN:9781337278461

Author:Ron Larson

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

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

To plot: The temperatures of A and B for 0 ≤ t ≤ 1000 and to find the time after that the objects has the same temperature.

Solution Summary: The author plots the temperatures of A and B for a long run of t and to find the time after that the objects have the same temperature.

Concept explainers

Videos

To plot:The temperatures of A and B for 0≤t≤1000 and to find the time after that the objects has the same temperature.

Want to see the full answer?

Chapter 10 Solutions