Find the Flux of the Vector Field F Across the Surface

question 173

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathrm { F } = \mathrm { x } ^ { 5 } \mathrm { y } ^ { 2 } \mathrm { i } + \mathrm { yj } - \mathrm { zk } ; \mathrm { S }$ is the portion of the parabolic cylinder $\mathrm { z } = 4 - \mathrm { y } ^ { 2 }$ for which $\mathrm { z } \geq 0$ and $2 \leq \mathrm { x } \leq 10$ ; direction is outward (away from the $x$ -y plane)

• A) -128
• B) 128
• C) 0
• D) 64

---

Definitions:

Transformational Leadership

A style of leadership that inspires and stimulates followers to exceed their own interests for a collective purpose.

Intellectual Stimulation

The aspect of leadership that involves encouraging followers to be innovative and creative, challenging their own beliefs and valuing those which are rational.

Social Exchange Relationship-based

A perspective viewing relationships in terms of the exchange of resources, benefits, and supports, where the balance of give-and-take is considered crucial for relationship stability.

Leader-member Exchange (LMX)

A theory describing how leaders develop relationships with team members, leading to different levels of influence and outcomes for members.