Show That $\mathbf { F }$ Is Conservative, and Find a Function

question 41

Multiple Choice

Show that $\mathbf { F }$ is conservative, and find a function $f$ such that $\mathbf { F } = \nabla f$ , and use the result to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ , where $C$ is any curve from $A \left( x _ { 0 } , y _ { 0 } , z _ { 0 } \right)$ to $B \left( x _ { 1 } , y _ { 1 } , z _ { 1 } \right)$ .
$\mathbf { F } ( x , y , z ) = 21 x ^ { 2 } y \mathbf { i } + \left( 7 x ^ { 3 } + 15 y ^ { 2 } z ^ { 2 } \right) \mathbf { j } + 10 y ^ { 3 } z \mathbf { k } ; A ( 0,0,0 )$ and $B ( - 1,0 , - 3 )$

• A) 0
• B) \(- 154\)
• C) \(- 107\)
• D) \(- 89\)

Identify the factors that influence the classification of workers as employees or independent contractors.

Understand the concept and implications of employment-at-will and fixed-term employment agreements.

Identify legitimate reasons for discrimination in hiring under specific circumstances.

Recognize the different types of employment agreements and their characteristics.

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