Find the Center and Radius of the Sphere $$2 x ^ { 2 } + 2 y ^ { 2 } + 2 z ^ { 2 } - x + y - z = 9$$

question 212

Multiple Choice

Find the center and radius of the sphere.
- $$2 x ^ { 2 } + 2 y ^ { 2 } + 2 z ^ { 2 } - x + y - z = 9$$

• A) \(\left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } , - \frac { 1 } { 4 } \right) , \mathrm { a } = \frac { 75 } { 8 }\)
• B) \(\left( \frac { 1 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right) , \mathrm { a } = \frac { 5 \sqrt { 6 } } { 4 }\)
• C) \(\left( \frac { 1 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right) , \mathrm { a } = \frac { 5 \sqrt { 6 } } { 2 }\)
• D) \(\left( \frac { 1 } { 4 } , - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right) , \mathrm { a } = \frac { 5 \sqrt { 3 } } { 4 }\)

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Definitions:

Pretend Play

A form of play in which children use their imagination to create scenarios, roles, and activities, essential for cognitive and social development.

Egocentrism

A cognitive trait where an individual is unable to understand or assume any perspective other than their own.

Operations

Procedures carried out in the execution of a task, workflow, or within a functional area of a business or study.

Intuitive Thought

A cognitive process that occurs without analytical reasoning, often based on experiences and immediate perceptions.