A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 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
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.0I still don't understand...

anonymous
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.2Therefore is your shape consistent with a cone or a paraboloid?

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

JamesJ
 4 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
 4 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
 4 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
 4 years ago
Best ResponseYou've already chosen the best response.2I'm a fallen angel. Had a few millennia practicing conic sections.

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I love you man. All I have to say :).
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.