Find the Coordinates of the Centroid of the Curve $x = e ^ { 5 t } \cos 5 t , y = e ^ { 5 t } \sin 5 t , 0 \leq t \leq \frac { \pi } { 10 }$

question 41

Multiple Choice

Find the coordinates of the centroid of the curve.
-Find the coordinates of the centroid of the curve $x = e ^ { 5 t } \cos 5 t , y = e ^ { 5 t } \sin 5 t , 0 \leq t \leq \frac { \pi } { 10 }$ .

• A) \(( \bar { x } , \bar { y } ) = \left( \frac { e ^ { \pi + 2 } } { 5 \left( e ^ { \pi / 2 } - 1 \right) } , \frac { 2 e ^ { \pi } - 1 } { 5 \left( e ^ { \pi / 2 } - 1 \right) } \right)\)
• B) \(( \bar { x } , \bar { y } ) = \left( \frac { e ^ { \pi } - 2 } { 5 \left( e ^ { \pi } - 1 \right) } , \frac { 2 e ^ { \pi } + 1 } { 5 \left( e ^ { \pi } - 1 \right) } \right)\)
• C) \(( \bar { x } , \bar { y } ) = \left( \frac { 2 e ^ { \pi } - 1 } { e ^ { \pi / 2 } - 1 } , \frac { e ^ { \pi + 1 } } { e ^ { \pi / 2 } - 1 } \right)\)
• D) \(( \bar { x } , \bar { y } ) = \left\{ \frac { e ^ { \pi } - 2 } { 5 \left( e ^ { \pi / 2 } - 1 \right) } , \frac { 2 e ^ { \pi } + 1 } { 5 \left( e ^ { \pi / 2 } - 1 \right) } \right)\)

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A statement positing no difference or no effect, which researchers aim to test against the alternative hypothesis.