Write one or more inequalities that describe the set of points. -The exterior of the sphere of radius 5 centered at the point (-2, -3, -5) A) $( x + 2 ) ^ { 2 } + ( x + 3 ) ^ { 2 } + ( x + 5 ) ^ { 2 } 25$ B) $( x - 2 ) ^ { 2 } + ( x - 3 ) ^ { 2 } + ( x - 5 ) ^ { 2 }

Question

Write one or more inequalities that describe the set of points.
-The exterior of the sphere of radius 5 centered at the point (-2, -3, -5) 
A) $( x + 2 ) ^ { 2 } + ( x + 3 ) ^ { 2 } + ( x + 5 ) ^ { 2 } > 25$
B) $( x - 2 ) ^ { 2 } + ( x - 3 ) ^ { 2 } + ( x - 5 ) ^ { 2 } < 25$
C) $( x - 2 ) ^ { 2 } + ( x - 3 ) ^ { 2 } + ( x - 5 ) ^ { 2 } \geq 25$
D) $( x + 2 ) ^ { 2 } + ( x + 3 ) ^ { 2 } + ( x + 5 ) ^ { 2 } < 25$

Quizplus · Accepted Answer

CThe correct inequalities describe points outside the sphere centered at (-2, -3, -5) with radius 5. Option A correctly adjusts the center coordinates and sets the inequality for points outside the sphere (> 25). Option C incorrectly uses 'x' for all dimensions but correctly sets the inequality for points outside or on the surface of the sphere ($\geq 25$). However, since the variable notation is consistent across all options and might be a typographical error, considering the structure of the inequality, it aligns with the logic for describing points outside the sphere.

Write One or More Inequalities That Describe the Set of Points