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Calculus Volume 1 | 18th Edition | ISBN: 9781938168024 | Authors: Openstax ISBN: 9781938168024 2035

Solution for problem 203 Chapter 5.3

Calculus Volume 1 | 18th Edition

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Calculus Volume 1 | 18th Edition | ISBN: 9781938168024 | Authors: Openstax

Calculus Volume 1 | 18th Edition

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Problem 203

A point on an ellipse with major axis length 2a and minor axis length 2b has the coordinates \((a \cos \theta, b \sin \theta)\), \(0 \leq \theta \leq 2 \pi\).

(a) Show that the distance from this point to the focus at (-c, 0) is \(d(\theta)=a+c \cos \theta\), where \(c=\sqrt{a^{2}-b^{2}}\)

(b) Use these coordinates to show that the average distance \(\bar{d}\) from a point on the ellipse to the focus at (-c, 0), with respect to angle \(\theta\), is a.

Text Transcription:

(a cos theta, b sin theta)

0 leq theta leq 2 pi

d(theta)=a+c cos theta

c=sqrt a^2-b^2

bar d

theta

Step-by-Step Solution:
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Module #18-­‐ Basic concepts of sensation and perception Sunday, February 28, 2016 5:55 PM -­ Heather Sellersc 'urious mix of "perfect vision" and face blindness: the distinction between sensation and perception ○ Sensation: the process by which our sensory receptors and nervous system receive and represent stimulus energies from our environment (sensory receptors detect information→nervous system transmits the information to her brain) [normal] ○ Perception: the process of organizing and interpreting sensory information, enabling us to recognize meaningful objects and events [almost normal] ○ Bottom -­‐up processing: analysis that begins with the sensory receptors and works up to the brain's integration of sensory information [build up from smallest pieces of sensory info/detect lines, angels, colors…] ○ Top-­‐down processing: constructs perceptions from the sensory input by drawing on our experience and expectations [perception that's driven by perception/ the brain applies what y

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Chapter 5.3, Problem 203 is Solved
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Textbook: Calculus Volume 1
Edition: 18
Author: Openstax
ISBN: 9781938168024

This full solution covers the following key subjects: . This expansive textbook survival guide covers 51 chapters, and 2890 solutions. This textbook survival guide was created for the textbook: Calculus Volume 1, edition: 18. Calculus Volume 1 was written by Aimee Notetaker and is associated to the ISBN: 9781938168024. Since the solution to 203 from 5.3 chapter was answered, more than 202 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 203 from chapter: 5.3 was answered by Aimee Notetaker, our top Calculus solution expert on 03/25/22, 03:16PM. The answer to “?A point on an ellipse with major axis length 2a and minor axis length 2b has the coordinates \((a \cos \theta, b \sin \theta)\), \(0 \leq \theta \leq 2 \pi\).(a) Show that the distance from this point to the focus at (-c, 0) is \(d(\theta)=a+c \cos \theta\), where \(c=\sqrt{a^{2}-b^{2}}\)(b) Use these coordinates to show that the average distance \(\bar{d}\) from a point on the ellipse to the focus at (-c, 0), with respect to angle \(\theta\), is a.Text Transcription:(a cos theta, b sin theta)0 leq theta leq 2 pid(theta)=a+c cos thetac=sqrt a^2-b^2bar dtheta” is broken down into a number of easy to follow steps, and 93 words.

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