Plane $2 x + 4 y + 2 z = 12$

question 35

Multiple Choice

$\text { Let } \mathbf { F } ( x , y , z ) = ( 2 x - y ) \mathbf { i } - ( 2 y - z ) \mathbf { j } + z \mathbf { k } \text { and let } S \text { be the surface bounded by the }$ plane $2 x + 4 y + 2 z = 12$ and the coordinates planes. Verify the Divergence Theorem by evaluating $\iint_{S} \mathbf{F} \cdot \mathbf{N} d s$ as a surface integral and as a triple integral.

• A) 43
• B) 36
• C) 6
• D) 18
• E) 23

---

Definitions:

Standards-based Learning

An educational approach that sets clear, measurable learning goals or standards for what students should know and be able to do.

Place-based Learning

An educational approach that utilizes the local community and environment as a starting point to teach concepts in various subjects.

Ecological Health

Ecological health refers to the overall condition of an ecosystem based on factors like biodiversity, productivity, and the ability of the environment to sustain life and processes.

Nearby State Park

A state-managed public park located in close proximity to a person's residence, offering outdoor activities and natural beauty.