Solve the Problem $z = x ^ { 2 } + y ^ { 2 }$

question 214

Multiple Choice

Solve the problem.
-Find the average height of the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ above the annular region $36 \leq x ^ { 2 } + y ^ { 2 } \leq 49$ in the $x y - p l a n e$ .

• A) 67
• B) \(\frac { 183 } { 2 }\)
• C) \(\frac { 121 } { 2 }\)
• D) \(\frac { 85 } { 2 }\)

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Definitions:

Regular School System

Denotes the traditional educational setup designed for the majority of students, including standard curriculum, schedules, and grading practices.

Equilibrium

A state of balance or stability within a system, achieved through equal action of opposing forces or factors.

Self-awareness

The conscious knowledge of one's own character, feelings, motives, and desires, enabling introspection and understanding of one's self.

Expressing

The process of conveying thoughts, feelings, or information to others, whether through verbal language, writing, or other forms of communication.