Solve the Problem $\frac { x } { 10 } + \frac { y } { 2 } + \frac { z } { 9 } = 1$

question 381

Multiple Choice

Solve the problem.
-Find the center of mass of a tetrahedron of constant density bounded by the coordinate planes and the plane $\frac { x } { 10 } + \frac { y } { 2 } + \frac { z } { 9 } = 1$ .

• A) \(\bar { x } = 5 , \bar { y } = 1 , \bar { z } = \frac { 9 } { 2 }\)
• B) \(\bar { x } = \frac { 20 } { 3 } , \bar { y } = \frac { 4 } { 3 } , \bar { z } = 6\)
• C) \(\bar { x } = \frac { 10 } { 3 } , \bar { y } = \frac { 2 } { 3 } , \bar { z } = 3\)
• D) \(\bar { x } = \frac { 5 } { 2 } , \bar { y } = \frac { 1 } { 2 } , \bar { z } = \frac { 9 } { 4 }\)

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Definitions:

Modern Synthesis

Modern Synthesis is a scientific theory that combines Darwin's theory of natural selection with Mendelian genetics, serving as the foundation of contemporary evolutionary biology.

Population Genetics

The study of genetic variability in a population and of the forces that act on it.

Theory of Evolution

A scientific explanation for the diversity of life on Earth, proposing that species change over time through natural selection and genetic variation.

Acquired Traits

Characteristics or changes that are gained after birth due to environmental influences or personal actions, not determined by genes and therefore not inheritable.