Results for this submission

$\backslash$table$[[$Entered$,$Answer Preview,Result,$],[2**cos(t)i+2^{**}sin(t)j+5k,2cos(t)vec(i)+2sin(t)vec(j)+5$vec$(k),$incorrect,Make sure that your parameterization traverses the curve in the correct direction.$],[0,0,$incorrect,$],[6\mathrm{.}28319,2,$incorrect,$],[150\mathrm{.}796,48,$incorrect,$]]$

At least one of the answers above is NOT correct.

$(1$ point$)$ Let $S$ be an opened cylindrical can standing on the $xy-$plane. $(S$ has a bottom and sides, but no top.$)$ The side of $S$ is given by $x^2+y^2=4,$ and its height is $5.$

$($a$)$ Give a parametric equation, vec$(r)(t)$ for the rim, $C.$

vec

$,$ with $t$

$($For this problem, enter your vector equation with angle$-$bracket notation: $.)$

$($b$)$ If $S$ is oriented outward and downward, find ${\displaystyle \underset{S}{\overset{\phantom{}}{}}}(grad(-6$yvec$(i)+6$xvec$(j)+5$zvec$(k)))*dvec(A).$

${\displaystyle \underset{S}{\overset{\phantom{}}{}}}(grad(-6$yvec$(i)+6$xvec$(j)+5$zvec$(k)))*dvec(A)=$

$$