find the distance between the spheres x^2+y^2+z^2=4 and x^2+y^2+z^2=4x+4y+4z-11. Please show me the steps so I can understand what I am doing. Thank you:)

Question

amistre64 · Answer

the distance between the spheres is the distance between there centers minus their radiuses

amistre64 · Answer

can you tell me the center and radius for the first one?

anonymous · Answer

c:= (0,0,0) r:=2 for the second c:=(2,2,2) r:= 1

anonymous · Answer

I am not sure if I am correct

amistre64 · Answer

the first one is good, lets see if i can agree with the second; I like the center of it ...

amistre64 · Answer

3(-4) = -12

r^2 -12 =-11; r^2 = 1 .... yep

amistre64 · Answer

since the zero sqaured is trivial; lets find the distance as:$$d=\sqrt{2^2+2^2+2^2}$$and subtract 3 from it

anonymous · Answer

d=1

amistre64 · Answer

sqrt(12) not equal 1

amistre64 · Answer

|dw:1347204206799:dw|

anonymous · Answer

oh, that is what I am doing wrong. I am skipping a four and going right to 16. So it is 2sqrt(3) but why subtract 3

amistre64 · Answer

we dont want the distance from centers; we want the distance from outside to outside; to get to the outside of the spheres, we have to move 2 on one of them, and 1 onthe other; for a total of -3 from the centers

anonymous · Answer

I see. The answer is then 2sqrt(3)-3. Thank you very much for your help.

amistre64 · Answer

youre welcome