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On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1- (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): Cross sections with a fixed give? Cross sections with y fixed give ? Cross sections with z fixed give? (b) For (ii) (z 1- (x² + y²)): Cross sections with a fixed give ? Cross sections with y fixed give ? Cross sections with z fixed give ?

On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1- (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): Cross sections with a fixed give? Cross sections with y fixed give ? Cross sections with z fixed give? (b) For (ii) (z 1- (x² + y²)): Cross sections with a fixed give ? Cross sections with y fixed give ? Cross sections with z fixed give ?

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.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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The choices for the second set of drop down boxes are:

a horizontal line in a plane parallel to the yz-plane

an empty set, or one or two vertical lines-in a plane parallel to the yz-plane

a vertical line in a plane parallel to the yz-plane

two vertical lines in a plane parallel to the yz-plane

a line in a plane parallel to the yz-plane

an upward opening parabola in a plane parallel to the yz-plane

a downward opening parabola in plane parallel to the yz-plane

a circle centered on the origin in a plane parallel to the yz-plane

a point in a plane parallel to the yz-plane

 an empty set, or a circle centered on the origin in a plane parallel to the yz-plane

On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1 - (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): - Cross sections with a fixed giv✔? Cross sections with y fixed give Cross sections with z fixed give (b) For (ii) (z = 1 − (x² + y²)): Cross sections with a fixed giv Cross sections with y fixed give Cross sections with z fixed give a horizontal line in a plane parallel to the yz-plane an empty set, or one or two vertical lines in a plane parallel to the yz-plane a vertical line in a plane parallel to the yz-plane two vertical lines in a plane parallel to the yz-plane a line in a plane parallel to the yz-plane an upward opening parabola in a plane parallel to the yz-plane a downward opening parabola in a plane parallel to the yz-plane a circle centered on the origin in a plane parallel to the yz-plane a point in a plane parallel to the yz-plane an empty set, or a circle centered on the origin in a plane parallel to the yz-plane
Transcribed Image Text:On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1 - (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): - Cross sections with a fixed giv✔? Cross sections with y fixed give Cross sections with z fixed give (b) For (ii) (z = 1 − (x² + y²)): Cross sections with a fixed giv Cross sections with y fixed give Cross sections with z fixed give a horizontal line in a plane parallel to the yz-plane an empty set, or one or two vertical lines in a plane parallel to the yz-plane a vertical line in a plane parallel to the yz-plane two vertical lines in a plane parallel to the yz-plane a line in a plane parallel to the yz-plane an upward opening parabola in a plane parallel to the yz-plane a downward opening parabola in a plane parallel to the yz-plane a circle centered on the origin in a plane parallel to the yz-plane a point in a plane parallel to the yz-plane an empty set, or a circle centered on the origin in a plane parallel to the yz-plane
On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1 - (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): Cross sections with a fixed give? Cross sections with y fixed give? Cross sections with z fixed give ? (b) For (ii) (z = 1 − (x² + y²)): Cross sections with a fixed give ? Cross sections with y fixed give? Cross sections with z fixed give? C
Transcribed Image Text:On a piece of paper, sketch each of the following surfaces: (i) 1 = x² + y² (ii) z = 1 - (x² + y²) Use your graphs to fill in the following descriptions of cross-sections of the surfaces. (a) For (i) (1 = x² + y²): Cross sections with a fixed give? Cross sections with y fixed give? Cross sections with z fixed give ? (b) For (ii) (z = 1 − (x² + y²)): Cross sections with a fixed give ? Cross sections with y fixed give? Cross sections with z fixed give? C
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