Find the Coordinates of the Centroid of the Curve $x = 5 \cos t + 5 t \sin t , y = 5 \sin t - 5 t \cos t , 0 \leq t \leq \pi$

question 37

Multiple Choice

Find the coordinates of the centroid of the curve.
-Find the coordinates of the centroid of the curve $x = 5 \cos t + 5 t \sin t , y = 5 \sin t - 5 t \cos t , 0 \leq t \leq \pi$ .

• A) \(( \bar { x } , \bar { y } ) = \left( \frac { 60 } { \pi } - \frac { 120 } { \pi ^ { 2 } } , \frac { 120 } { \pi ^ { 2 } } - 10 \right)\)
• B) \(( \bar { x } , \bar { y } ) = \left( 10 - \frac { 60 } { \pi } , \frac { 30 } { \pi ^ { 2 } } \right)\)
• C) \(( \bar { x } , \bar { y } ) = \left( 10 - \frac { 120 } { \pi ^ { 2 } } , \frac { 15 } { \pi } \right)\)
• D) \(( \bar { x } , \bar { y } ) = \left( 10 - \frac { 60 } { \pi ^ { 2 } } , \frac { 30 } { \pi } \right)\)

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Definitions:

Temporal

Relates to the aspect of time or the timing of events, as well as to the temporal bone area adjacent to the temples on the human skull.

Sphenoid

A complex bone at the base of the skull, which contributes to the formation of the orbit, the nasal cavity, and several important foramina.

Occipital

Pertaining to the back part of the skull, primarily associated with the visual processing region of the brain.

Ethmoid

A spongy, cubed bone located at the top of the nasal cavity and at the front of the floor of the cranium, crucial for nasal support and olfaction.