Identify the Surface with the Vector Equation (Hint: First Consider

question 33

Short Answer

Identify the surface with the vector equation $\mathbf { r } ( u , v ) = \cos u \sin v \mathbf { i } + \sin u \sin v \mathbf { j } + \cos v \mathbf { k } , 0 \leq u \leq 2 \pi , 0 \leq v \leq \frac { \pi } { 2 }$ . (Hint: First consider $x ^ { 2 } + y ^ { 2 }$ .)

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Definitions:

Achievement Motivation

A psychological drive or ambition for success and accomplishment in tasks, influencing one’s persistence, effort, and goal-setting behavior.

Elective Course

A class that students can choose to take as part of their curriculum, which is not required for their major or degree program.

Bidirectional Relationship

A relationship where both entities influence each other, often seen in interactions between individuals, systems, or variables.

Levels of Motivation

Variations in the intensity and type of motivation that individuals experience, which can affect behavior and achievement in different contexts such as work, learning, and personal goals.