Mathematics: Find a parametrization of the portion of the plane x + y + z = 5 that is contained inside the following. inside the cylinder x^2 + y^2 = 16 inside the cylinder y^2 + z^2 = 16

Find a parametrization of the portion of the plane

paaoolav

11.01.2022

Inside

Set

$\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=5-x(u,v)-y(u,v)=5-u(\cos v+\sin v)\end{cases}$

with $0\le u\le4$ and $0\le v\le2\pi$ .

Inside

Same as above, but swap z(u,v) with x(u,v) , so that

$\begin{cases}x(u,v)=5-u(\cos v+\sin v)\\y(u,v)=u\sin v\\z(u,v)=u\cos v\end{cases}$

again with $0\le u\le4$ and $0\le v\le2\pi$ .

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Adones5104

17.06.2022

Unless the people that don't are eliminated or die, all the people would still remain

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