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

question 102

Short Answer

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 $( 0,0 ) , ( 8,0 )$ and $( 0,16 )$ .

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Definitions:

Hormone-Receptor Complex

When a hormone binds to its corresponding receptor on a cell, initiating a specific cellular response.

Binds DNA

Refers to proteins or molecules that attach to DNA, influencing its function and regulation.

Calcium Ions

Positively charged atoms of calcium, playing vital roles in various physiological processes, including muscle contraction and neurotransmission.

Calmodulin

A calcium-binding messenger protein present in all eukaryotic cells, involved in various cellular processes by interacting with other proteins.