A parabolic satellite dish is 2 m wide and 1 / 2 m deep. Its axis of symmetry is tilted 30 degrees from the vertical. a. Set up, but do not evaluate, a triple integral in rectangular coordinates that gives the amount of water the satellite dish will hold. (Hint: Put your coordinate system so that the satellite dish is in “standard position” and the plane of the water level is slanted.) (Caution: The limits of integration are not “nice.”) b. What would be the smallest tilt of the satellite dish so that it holds no water?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A parabolic satellite dish is 2 m wide
and 1 / 2 m deep. Its axis of symmetry is tilted 30 degrees from the
vertical.
a. Set up, but do not evaluate, a triple integral in rectangular coordinates
that gives the amount of water the satellite dish will
hold. (Hint: Put your coordinate system so that the satellite
dish is in “standard position” and the plane of the water level
is slanted.) (Caution: The limits of integration are not “nice.”)
b. What would be the smallest tilt of the satellite dish so that it
holds no water?

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