Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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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…

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Question

Chapter 3.4, Problem 25E

To determine

To calculate: The rate dy/dt.

Expert Solution

Answer to Problem 25E

dydt=(t12−1)m/h.

Explanation of Solution

Given information:A tank is given and depth of y fluid in the tank at t hours is y=6(1−t12)2m .Using this we will find the solution of given questions.

Calculation:For finding rate at which water level is changing.

y=6(1−t12)2mdydt=12(1−t12)*−112dydt=(t12−1)m/h

To determine

To calculate: When is the fluid level in the tank filling fastest/ slowest.

Expert Solution

Answer to Problem 25E

Fastest at t=0h and slowest between at t=10h to t=12h.

Explanation of Solution

Given information:A tank is given and depth of y fluid in the tank at t hours is y=6(1−t12)2m .Using this we will find the solution of given questions.

Calculation:

If you see the graph in (c) part of question, we found at t=0h tank is filling fastest and then decrease means tank is filling slowest between t=10h to t=12h .

To determine

To draw: The graph of y and dy/dt

Expert Solution

Answer to Problem 25E

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.4, Problem 25E , additional homework tip 1

Explanation of Solution

Given information:A tank is given and depth of y fluid in the tank at t hours is y=6(1−t12)2m .Using this we will find the solution of given questions.

Calculation:

See the graph carefully.

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 3.4, Problem 25E , additional homework tip 2

Red graph shows dy/dt (rate of change in depth of fluid) and black graph shows y (depth of fluid).Water level is filling fastest when depth of water is 6m at t=0 and velocity is −1m/h and then after filling rate is slow, In between t=10h to t=12h , we can say filling rate of water in tank is slow. And filling rate is 0 at t=12h.

Chapter 3.4, Problem 24E

Chapter 3.4, Problem 26E

Chapter 3 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 3.1 - Prob. 1QR Ch. 3.1 - Prob. 2QR Ch. 3.1 - Prob. 3QR Ch. 3.1 - Prob. 4QR Ch. 3.1 - Prob. 5QR Ch. 3.1 - Prob. 6QR Ch. 3.1 - Prob. 7QR Ch. 3.1 - Prob. 8QR Ch. 3.1 - Prob. 9QR Ch. 3.1 - Prob. 10QR

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The rate d y / d t .

Concept explainers

Videos

To calculate: The rate dy/dt.

Answer to Problem 25E

Explanation of Solution

To calculate: When is the fluid level in the tank filling fastest/ slowest.

Answer to Problem 25E

Explanation of Solution

To draw: The graph of y and dy/dt

Answer to Problem 25E

Explanation of Solution

Chapter 3 Solutions

Additional Math Textbook Solutions