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anonymous
 5 years ago
Determine the type of solid
0 <= theta <= pi/2; r <= z <= 7
Would this be a quarter of a cone or a quarter of a paraboloid?
anonymous
 5 years ago
Determine the type of solid 0 <= theta <= pi/2; r <= z <= 7 Would this be a quarter of a cone or a quarter of a paraboloid?

This Question is Closed

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Think about what happens along the xaxis. There \[ r =\sqrt{x^2 + y^2} = \sqrt{x^2 + 0^2} = x \] Hence if \( z = x \), is that consistent with a cone or a paraboloid?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I still don't understand...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So would this be looking like a cone? Since parabolas are curvy, which doesn't closely represent x? Whereas, a cone on a 2D graph would look like x??

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2You have that r <= z <= 7 Hence x <= z <= 7 Now at the boundary of the object, r = z, or along the xaxis z = r = x. If the object were a cone, would we expect the cross section along the xaxis to be ... what? A straight line, a parabola, what? If the object were a paraboloid, what would you expect of the crosssection? A straight line, parabola or something else? Given that z = x, is that straight line, parabola or something else? Therefore is your shape consistent with a cone or a paraboloid.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Therefore is your shape consistent with a cone or a paraboloid?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It would have to be more consistent with a cone.

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2Yes, because z = x is a straight line for x > 0 and a different straight line for x < 0

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2and a cone has straight edges along the xaxis, while a paraboloid does not.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thanks James! I don't know how you're so boss at calculus, but I really appreciate your help and detailed explanations :)

JamesJ
 5 years ago
Best ResponseYou've already chosen the best response.2I'm a fallen angel. Had a few millennia practicing conic sections.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you a professor???

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I love you man. All I have to say :).
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