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:

Kinesthesia

The sense of movement and body position, often referred to as muscle memory or the ability to feel movements of the limbs and body.

Precognition

The purported psychic ability to see or know about events before they happen, which remains a controversial and largely scientifically unproven concept.

Psychokinesis

Is the supposed ability to move or manipulate objects with the mind without physical interaction.

Clairvoyance

The alleged psychic ability to gain information about an object, person, location, or physical event through means other than the known human senses.