QUERY24

course MTH 272

05/09, 1830

assignment #024024.

Applied Calculus II

05-08-2010

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16:42:47

Query problem 7.2.52 (was 7.2.48) identify quadric surface z^2 = x^2 + y^2/2.

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RESPONSE -->

z^2 = x^2 + y^2/2

x^2 + y^2/2 -z^2=0

Elliptic cone

confidence rating #$&* 2

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16:43:38

What is the name of this quadric surface, and why?

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RESPONSE -->

Elliptic Cone

Equation matches form for elliptic cone with all variables squared, one being subtracted, and equaling zero.

confidence rating #$&* 2

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16:46:34

Give the equation of the xz trace of this surface and describe its shape, including a justification for your answer.

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RESPONSE -->

xz-trace (y=0):

x^2 + (0^2)/2 - z^2=0

x^2 - z^2=0

For this equation to work, z and x must be equal. I think that this trace may only be a single point instead of a shape, particularly since the equation is set equal to zero.

confidence rating #$&* 1

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16:48:15

Describe in detail the z = 2 trace of this surface.

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RESPONSE -->

x^2 + y^2/2 - z^2 =0

x^2 +y^2/2 =z^2

x^2 + y^2/2 = 4

x^2/4 + y^2/8=1

Ellipse

confidence rating #$&* 2

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