Find the Area of the Surface $z = 25 - x ^ { 2 } - y ^ { 2 }$

question 28

Multiple Choice

Find the area of the surface.
The part of the surface $z = 25 - x ^ { 2 } - y ^ { 2 }$ that lies above the $x y$ -plane.

• A) \(( \sqrt { 626 } - 626 )\)
• B) \(\frac { 2 } { 75 } ( 626 \sqrt { 626 } + 1 )\)
• C) \(\frac { 2 } { 75 } \pi ( 626 \sqrt { 626 } - 1 )\)
• D) \(\frac { 2 } { 75 } ( \sqrt { 626 } + 1 )\)
• E) \(\pi ( 626 \sqrt { 626 } - 1 )\)

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Definitions:

Cooperation

A process where two or more entities work together towards a common goal, often leading to mutual benefit.

Competition

A situation in which two or more parties strive for a goal that cannot be shared or are vying for the same objective or resource.

Individualist Cultures

Societies that emphasize personal achievement, autonomy, and individual rights over collective goals and social responsibilities.

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Societies that prioritize the goals, needs, and views of the group over those of the individual, emphasizing strong familial and community ties.