$$\text { Find the center of mass of the wire that lies along the curve } r \text { and has density } \delta \text {. }$$

$$\text { Find the center of mass of the wire that lies along the curve } r \text { and has density } \delta \text {. }$$
- $r ( t ) = ( 5 \cos 3 t ) i + ( 5 \sin 3 t ) j + 15 t k , 0 \leq t \leq 2 \pi ; \delta ( x , y , z ) = 3 ( 1 + \sin 3 t \cos 3 t )$

A) $\left( 0,0 , \frac { 3 } { 2 } \pi \right)$
B) $\left( 0,0 , \frac { 15 } { 2 } \pi \right)$
C) $\left( 0,0 , \frac { 5 } { 4 } ( 12 \pi - 1 ) \right)$
D) $\left( 0,0 , \frac { 3 } { 2 } ( \pi + 1 ) \right)$