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The height of a certain hill (in feet) is given byh ( x ,

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 12P Chapter 1

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 12P

The height of a certain hill (in feet) is given by

h ( x , y ) = 10(2xy − 3x2 − 4y2 − 18x + 28y + 12),

where y is the distance (in miles) north, x the distance east of South Hadley.

(a) Where is the top of the hill located?

(b) How high is the hill?

(c) How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In what direction is the slope steepest, at that point?

Step-by-Step Solution:

a.)

Step 1 of 3</p>

We have to find the location of the top of the hill.

The location of the top of the hill can be found by solving the expression,

                                                           

                                    

 

The height  (in feet) of the certain hill is given by,

 

where  is the distance (in miles) north,

            the distance east of South Hadley.

Substituting for  in

                                 

 

         

Solve above two equations to get the values of  and ,

Therefore, the top of the hill is located at 3 miles north, 2 miles west of South Hadley.

b.)

Step 2 of 3</p>

We have to find the height of the hill.

The height of the hill can be found by substituting as -2 and as 3 in the expression for h,

 

Therefore,

               

                   

                     feet

Therefore, the height of the  hill is 720 feet.

c.)

Step 3 of 3

Chapter 1, Problem 12P is Solved
Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. The answer to “The height of a certain hill (in feet) is given byh ( x , y ) = 10(2xy ? 3x2 ? 4y2 ? 18x + 28y + 12),where y is the distance (in miles) north, x the distance east of South Hadley.(a) Where is the top of the hill located?(b) How high is the hill?(c) How steep is the slope (in feet per mile) at a point 1 mile north and one mile east of South Hadley? In what direction is the slope steepest, at that point?” is broken down into a number of easy to follow steps, and 87 words. The full step-by-step solution to problem: 12P from chapter: 1 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. Since the solution to 12P from 1 chapter was answered, more than 252 students have viewed the full step-by-step answer. This full solution covers the following key subjects: mile, Hill, Hadley, feet, South. This expansive textbook survival guide covers 12 chapters, and 550 solutions. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4.

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