Imagine you are invited to a birthday party and you arrive late. The room is crowded and you can't find your friend, but you can visually see that the distribu- tion of people in the room is given by the scalar function 5(cos(3)+cos(3)) where x and y are the coordinates of the Cartesian coordinate system centered in the middle of the room (note: here x and y are measured in meters, in other words they are dimensionless). The space is a square room with side length 6 meters, spanning the area -3 m < x < 3m, -3 m < y < 3m. Calculate the gradient of the distribution function. Assuming that you arrive from the door which is in the corner of the room, and people are gathered around your friend, use your result to determine your friend's position. Where is your friend? Explain briefly how you arrived at your answer.
Imagine you are invited to a birthday party and you arrive late. The room is crowded and you can't find your friend, but you can visually see that the distribu- tion of people in the room is given by the scalar function 5(cos(3)+cos(3)) where x and y are the coordinates of the Cartesian coordinate system centered in the middle of the room (note: here x and y are measured in meters, in other words they are dimensionless). The space is a square room with side length 6 meters, spanning the area -3 m < x < 3m, -3 m < y < 3m. Calculate the gradient of the distribution function. Assuming that you arrive from the door which is in the corner of the room, and people are gathered around your friend, use your result to determine your friend's position. Where is your friend? Explain briefly how you arrived at your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Imagine you are invited to a birthday party and you arrive late. The room is
crowded and you can't find your friend, but you can visually see that the distribu-
tion of people in the room is given by the scalar function 5(cos(3) + cos(½)) where
x and y are the coordinates of the Cartesian coordinate system centered in the
middle of the room (note: here x and y are measured in meters, in other words
they are dimensionless). The space is a square room with side length 6 meters,
spanning the area −3 m < x < 3m, −3 m < y < 3m.
Calculate the gradient of the distribution function.
Assuming that you arrive from the door which is in the corner of the room, and
people are gathered around your friend, use your result to determine your friend's
position. Where is your friend? Explain briefly how you arrived at your answer.
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Follow-up Question
Hello, can you give a more definite answer? For example, "Using the distribution function, determine where the tables are." and "Using the gradient, determine the path how to find your way there?" and "Visualize the gradient
Thank you very much, this question is very important to me, please.... I'll definitely give an upvote right away when the answer is done
Transcribed Image Text:After finding your friend, you search for the buffet place. Again it is crowded. You
want to know where the food tables are located (there are multiple tables). Assume
that people are gathered at the food tables, and the distribution in the room has
changed and is now given by the scalar function x² + y². Using the distribution
function, determine where the tables are. Using the gradient, determine the path
how to find your way there? Visualize the gradient vector.
Solution
by Bartleby ExpertFollow-up Question
Transcribed Image Text:After finding your friend, you search for the buffet place. Again it is crowded. You
want to know where the food tables are located (there are multiple tables). Assume
that people are gathered at the food tables, and the distribution in the room has
changed and is now given by the scalar function x² + y². Using the distribution
function, determine where the tables are. Using the gradient, determine the path
how to find your way there? Visualize the gradient vector.
Solution
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