Find the Flux $\vec { F }$ Of Through $S$ $\iint _ { S } \vec { F } \cdot \vec { N } d S$

question 37

Multiple Choice

Find the flux $\vec { F }$ of through $S$ , $\iint _ { S } \vec { F } \cdot \vec { N } d S$ , where $\vec { N }$ is the upward unit normal vector to S. $\overrightarrow { \mathbf { F } } ( x , y , z ) = 2 z \hat { \mathbf { i } } - 8 \hat { \mathbf { j } } + y \hat { \mathbf { k } }$
$S : x + y + z = 9$ , first octant

• A) \(- \frac { 81 } { 2 }\)
• B) \(\frac { 81 } { 2 }\)
• C) \(\frac { 99 } { 2 }\)
• D) \(\frac { 93 } { 2 }\)
• E) \(- \frac { 87 } { 2 }\)

Understand the liabilities and duties of bailors and bailees in various scenarios.

Recognize the implications of bailment contracts, including the impact of exemption clauses.

Assess the liability in cases of damage or loss of bailed goods.

Evaluate the legal protections for goods under bailment agreements.

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