Find the Center and Radius of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$

question 52

Multiple Choice

Find the center and radius of the sphere. $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - 5 x = 0$

• A)Center: \(\left( \frac { 5 } { 2 } , 0,0 \right)\) Radius: \(\frac { 5 } { 2 }\)
• B)Center: \(\left( 0 , \frac { 3 } { 2 } , 0 \right)\) Radius: \(\frac { 3 } { 2 }\)
• C)Center: \(\left( 0 , \frac { 3 } { 2 } , \frac { 1 } { 2 } \right)\) Radius: \(\frac { \sqrt { 10 } } { 2 }\)
• D)Center: \(\left( \frac { 1 } { 2 } , 0,0 \right)\) Radius: \(\frac { 1 } { 2 }\)
• E)Center: \(\left( \frac { 5 } { 2 } , 0,1 \right)\) Radius: \(\frac { \sqrt { 29 } } { 2 }\)

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Definitions:

Hippocampus

A major component of the brain of humans and other vertebrates, playing crucial roles in the consolidation of information from short-term memory to long-term memory, and in spatial memory that enables navigation.

Cerebral Cortex

The outer layer of the cerebrum in the brain, playing a key role in memory, attention, perception, cognition, awareness, thought, language, and consciousness.

Basal Ganglia

A group of structures in the brain involved in coordinating movement, as well as aspects of learning and memory.

Cerebellum

The cerebellum is a section of the brain at the back of the skull in vertebrates, which coordinates and regulates muscular activity.