Use a Computer Algebra System and the Result "The Centroid $A$

question 57

Multiple Choice

Use a computer algebra system and the result "The centroid of the region having area $A$ bounded by the simple closed path $C$ is $\bar { x } = \frac { 1 } { 2 A } \int _ { C } x ^ { 2 } d y , \bar { y } = - \frac { 1 } { 2 A } \int _ { C } y ^ { 2 } d x ^ { \prime \prime }$ to find the centroid of the region bounded by the graphs of $y = \sqrt { 196 - x ^ { 2 } }$ and $y = 0$ .

• A) \(\left( 0 , \frac { 56 } { 3 \pi } \right)\)
• B) \(( 28 \pi , 0 )\)
• C) \(( 0,56 \pi )\)
• D) \(\left( 0 , \frac { 14 } { 3 \pi } \right)\)
• E) \(\left( \frac { 56 } { 3 \pi } , 0 \right)\)

---

Definitions:

Threshold

The point or level at which something begins or changes.

Dendrites

The branched extensions of a neuron that receive signals from other neurons.

Insulate Neurons

The process of covering neurons with myelin, a fatty substance that speeds up the transmission of electrical signals along nerve cells.

Integrate Information

The process of combining data from different sources and making sense of it, often to form a comprehensive understanding or to make decisions.