Let $D$ Be a Region Bounded by a Simple Closed Path $C$

question 103

Multiple Choice

Let $D$ be a region bounded by a simple closed path $C$ in the $x y$ . Then the coordinates of the centroid $( \bar { x } , \bar { y } )$ of $D$ are $\bar { x } = \frac { 1 } { 2 A } \oint _ { C } x ^ { 2 } d y , \bar { y } = - \frac { 1 } { 2 A } \oint _ { C } y ^ { 2 } d x$ where $A$ is the area of $D$ .
Find the centroid of the triangle with vertices $( 0,0 ) , ( 5,0 )$ and $( 0,10 )$ .

• A) \(\left( \frac { 1 } { 8 } , \frac { 1 } { 8 } \right)\)
• B) \(\left( \frac { 10 } { 3 } , \frac { 10 } { 3 } \right)\)
• C) \(\left( \frac { 1 } { 10 } , \frac { 1 } { 5 } \right)\)
• D) \(\left( \frac { 5 } { 3 } , - \frac { 10 } { 3 } \right)\)
• E) \(\left( \frac { 1 } { 8 } , \frac { 1 } { 64 } \right)\)

---

Definitions:

Conflict Theories

A sociological perspective that views human society as an arena of inequality that generates conflict and social change.

Functionalist Theories

Sociological perspectives that interpret society as a structure with interrelated parts designed to meet the biological and social needs of individuals who make up that society.

Social Structure

Social structure refers to the organized pattern of social relationships and social institutions that together compose society, shaping behaviors and interactions among its members.

Social Control Theory

A theory in sociology that suggests that people's relationships, commitments, values, norms, and beliefs encourage them not to break the law.