
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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The graph of the equation x Superscript 2 divided by 3 Baseline plus y Superscript 2 divided by 3 Baseline equals 5 Superscript 2 divided by 3 is one of a family of curves called astroids because of their starlike appearance (as shown in the accompanying figure). Find the length of this particular astroid by finding the length of half the first-quadrant portion, y equals left parenthesis 5 Superscript 2 divided by 3 Baseline minus x Superscript 2 divided by 3 Baseline right parenthesis Superscript 3 divided by 2, StartFraction 5 StartRoot 2 EndRoot Over 4 EndFraction
less than or equalsxless than or equals5, and multiplying by 8.

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The graph of the equationxy5is one of a family of curves called astroids because of their starlike appearance (as
shown in the accompanying figure). Find the length of this particular astroid by finding the length of half the first-quadrant portion,
2/3 2/313/2 5/2
, Sxs 5, and multiplying by 8
The length of the given astroid is
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