Use a Computer Algebra System to Compute the Flux Of \mathbf

question 48

Multiple Choice

Use a computer algebra system to compute the flux of $\mathbf { F }$ across $S . S$ is the surface of the cube cut from the first octant by the planes
$x = \frac { \pi } { 2 } , y = \frac { \pi } { 2 } , z = \frac { \pi } { 2 }$
$$\mathbf { F } ( x , y , z ) = 5 \sin x \cos ^ { 2 } y \mathbf { i } + 5 \sin ^ { 3 } y \cos ^ { 4 } z \mathbf { j } + 5 \sin ^ { 5 } z \cos ^ { 6 } x \mathbf { k }$$

• A) \(5 \pi ^ { 2 }\)
• B) \(95 \pi ^ { 2 }\)
• C) \(\frac { 5 \pi ^ { 2 } } { 64 }\)
• D) \(\frac { 95 \pi ^ { 2 } } { 64 }\)
• E) \(\frac { 95 \pi ^ { 2 } } { 32 }\)

---

Definitions:

Government Operation

Activities carried out by the government, including regulation, provision of public services, and maintenance of law and order.

Average Costs

The total costs divided by the total output produced, a measure of cost efficiency for production.

Social Welfare

A concept concerning the well-being, health, and economic security of society as a whole.

Synergies

The increased effectiveness or efficiencies created when two or more elements or companies work together.