Use the Barycentric Coordinates with Respect to S to Determine $$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } \right\}$$

question 22

Multiple Choice

Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.
- $$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } \right\}$$
Barycentric coordinates: $\left( 0,0 , \frac { 3 } { 8 } , \frac { 5 } { 8 } \right)$

• A) Face
• B) Inside
• C) Outside
• D) Edge

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Definitions:

Homothetic Preferences

A situation in consumer theory where a consumer's preference structure can be represented by a utility function that is proportionally scalable.

Engel Curve

A graphical representation that shows the relationship between income and the demand for a good or service, keeping all other factors constant.

Utility Function

A mathematical representation of how a consumer ranks different baskets of goods according to their level of satisfaction.

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Refers to individuals or households that earn a significantly higher amount of money compared to the average income levels within a specific geographic region or within a particular demographic.