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y? +x = 2, 2r + 3y +3: 6, = 0, y=0, 2=0 TOke the surfaes and obtam valmes fo X, Y and z qnd compore to The XZ projection of the solid is compound by two regions R1 and R2 , those regions are determined by the points (x,2): A) R :0

y? +x = 2, 2r + 3y +3: 6, = 0, y=0, 2=0 TOke the surfaes and obtam valmes fo X, Y and z qnd compore to The XZ projection of the solid is compound by two regions R1 and R2 , those regions are determined by the points (x,2): A) R :0

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...
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Consider the solid in the first octant, limited by the surfaces y² + x=2, 2x+3y +3z=6₁ x = 0, y = 0, z=0 The XZ projection of the solid is compound by two regions R1 and R2, those regions are determined by the points (x,z): Take the surfaces and obtain values Por X, Y and Z and compare to y R₂:0≤x≤2A2-3-√√2-x≤x≤2- R₂:0≤x≤2 A √2-x≤²≤2-²/3 y R₂:0≤x≤2^2- +√2-x≤z≤2-² A) R₁ :0≤x≤2A0≤ ≤2-2-√√2-x B) R₁ :0≤x≤ 2 A 0 ≤ ≤ √√2-x y C) R₁ :0≤x≤2/0≤2≤2-2+√2-x D) R₁:0≤x≤ 2 A 0≤ ≤-√2-x y R₂:0≤x≤2A-√2-x≤x≤2-²/3
Transcribed Image Text:Consider the solid in the first octant, limited by the surfaces y² + x=2, 2x+3y +3z=6₁ x = 0, y = 0, z=0 The XZ projection of the solid is compound by two regions R1 and R2, those regions are determined by the points (x,z): Take the surfaces and obtain values Por X, Y and Z and compare to y R₂:0≤x≤2A2-3-√√2-x≤x≤2- R₂:0≤x≤2 A √2-x≤²≤2-²/3 y R₂:0≤x≤2^2- +√2-x≤z≤2-² A) R₁ :0≤x≤2A0≤ ≤2-2-√√2-x B) R₁ :0≤x≤ 2 A 0 ≤ ≤ √√2-x y C) R₁ :0≤x≤2/0≤2≤2-2+√2-x D) R₁:0≤x≤ 2 A 0≤ ≤-√2-x y R₂:0≤x≤2A-√2-x≤x≤2-²/3
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