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anonymous

  • 5 years ago

Identify the surface for each of the following equations. (a) r=5 (b) r^2 + z^2=100 (c) z=r

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  1. anonymous
    • 5 years ago
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    I'm thinking you're working in cylindrical coordinates. If you are, then r=5 means "r=5 no matter what theta or z is". If this is the case, you'd have a cylinder of radius 5, extending from -infinity to +infinity. The second one you can look at by considering the definition of the transformation of coordinates from rectilinear to cylindrical, namely,\[x=r \cos \theta \]\[y= r \sin \theta \]\[z=z\]Then\[r^2+z^2=(x^2+y^2)+z^2=100\]This is just a sphere of radius 10. The last one you can use the definitions again to find\[z=r \rightarrow z=\sqrt{x^2+y^2} \]which is a circular cone.

  2. anonymous
    • 5 years ago
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    I only took the positive square root since you have to consider the fact that, with the definitions, r>0, so the representation of r in the Cartesian space must be positive also.

  3. anonymous
    • 5 years ago
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    thank you soo much :)

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