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

question 20

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) \(\left( \frac { 1 } { 8 } , \frac { 1 } { 64 } \right)\)

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Definitions:

Alleles

Alternative forms of a gene that occur at a specific locus on a chromosome, contributing to genetic diversity.

Gene

A unit of hereditary information composed of DNA, which resides on chromosomes and influences specific characteristics.

Mendel's Research

The foundational genetic studies conducted by Gregor Mendel, which established the principles of inheritance through the breeding of pea plants.

Pea Plants

The plants used by Gregor Mendel in his pioneering experiments on genetics, contributing to the foundation of modern genetics.