Answer to Question #103434 in Analytic Geometry for Avinash

Question #103434
Show that the closed sphere with centre )7,3,2( and radius 10 in 3 R is contained in the
open cube P = {(x, y,z :) x − 2 <11, y − 3 <11, z − 7 <11}.
1
Expert's answer
2020-02-25T11:25:30-0500

The equation of the closed sphere with the center (2,3,7)(2, 3, 7) and radius 1010 is


(x2)2+(y3)2+(z7)2=102(x-2)^2+(y-3)^2+(z-7)^2=10^2x210,y310,z710| x-2|\leq 10, |y-3| \leq 10, |z-7|\leq 1010x210,10y310,10z710--10\leq x-2\leq 10, -10\leq y-3\leq 10, -10\leq z-7\leq 10

Therefore the closed sphere with the center (2,3,7)(2,3,7) and radius 1010 is contained in the

open cube P={(x,y,z):x2<11,y3<11,z7<11}P=\{(x,y,z):x-2<11,y-3<11,z-7<11\}.




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