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EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z 8 - x? - y?. Leaves at z = 8-x- y z= 8 - x -y? The curve of intersection D (-2,0,4) (2, 0, 4) + 3y Enters at z =x + 3y? 2,0.0) Enters at y= -V(4-x/2 (x, y) +2y = 4 (2,0, 0) Leaves at y= V(4 - x)/2 18

EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z 8 - x? - y?. Leaves at z = 8-x- y z= 8 - x -y? The curve of intersection D (-2,0,4) (2, 0, 4) + 3y Enters at z =x + 3y? 2,0.0) Enters at y= -V(4-x/2 (x, y) +2y = 4 (2,0, 0) Leaves at y= V(4 - x)/2 18

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.1: The Graphing Method
Problem 24WE
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EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z = 8 - x? Mt Leaves at z = 8 - x - y? z = 8 - x -y? The curve of intersection D (-2,0, 4) (2, 0, 4) Enters at z = x + 3y? Enters at T-2,0.0) y=-V(4 -x)/2 +2y? = 4 (2,0, 0) Leaves at y = V(4 -2 18
Transcribed Image Text:EXAMPLE 1 Finding a Volume Find the volume of the region D enclosed by the surfaces z = x? + 3y? and z = 8 - x? Mt Leaves at z = 8 - x - y? z = 8 - x -y? The curve of intersection D (-2,0, 4) (2, 0, 4) Enters at z = x + 3y? Enters at T-2,0.0) y=-V(4 -x)/2 +2y? = 4 (2,0, 0) Leaves at y = V(4 -2 18
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