Find the Average Value of F(x, Y, Z) Over the Given

question 435

Multiple Choice

Find the average value of F(x, y, z) over the given region.
- $F ( x , y , z ) = x ^ { 2 } y ^ { 6 } z ^ { 9 }$ over the cube in the first octant bounded by the coordinate planes and the planes $x = 1$ , $y = 1 , z = 1$

• A) \(\frac { 1 } { 192 }\)
• B) \(\frac { 1 } { 84 }\)
• C) \(\frac { 1 } { 108 }\)
• D) \(\frac { 1 } { 210 }\)

---

Definitions:

Standard of Living

The level of wealth, comfort, material goods, and necessities available to a certain socioeconomic class or geographic area.

Public Good

A good that is non-excludable and non-rivalrous, meaning that one person's consumption does not reduce its availability to others and people cannot be prevented from using it.

Communist Governments

Government systems where the state owns and controls all major aspects of the economy, aiming for classless society and elimination of private property.

Circular Flow Diagram

A visual model of the economy that shows how dollars flow through markets among households and firms.