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ChrisS
 4 years ago
Would someone mind checking this for me?
Find the center and radius of the sphere given by the equation
\[3x ^{2}+3y^{2}+3z^{2}+2y2z=9\]
\[x^{2}+y^{2}+\frac{2}{3}y+z^{2}\frac{2}{3}z=3\ (regroup\ and\ divide\ by\ 3)\]
\[x^{2}+y^{2}+\frac{2}{3}y+\frac{1}{9}+z^{2}\frac{2}{3}z+\frac{1}{9}=3\frac{1}{9}\frac{1}{9}\ (Complete\ the\ \Square)\]
\[x^{2}+(y+\frac{1}{3})^{2}+(z\frac{1}{3})^{2}=\frac{25}{9}\]
\[Center\ (0,\frac{1}{3},\frac{1}{3}),\ radius\ \frac{5}{3}\]
ChrisS
 4 years ago
Would someone mind checking this for me? Find the center and radius of the sphere given by the equation \[3x ^{2}+3y^{2}+3z^{2}+2y2z=9\] \[x^{2}+y^{2}+\frac{2}{3}y+z^{2}\frac{2}{3}z=3\ (regroup\ and\ divide\ by\ 3)\] \[x^{2}+y^{2}+\frac{2}{3}y+\frac{1}{9}+z^{2}\frac{2}{3}z+\frac{1}{9}=3\frac{1}{9}\frac{1}{9}\ (Complete\ the\ \Square)\] \[x^{2}+(y+\frac{1}{3})^{2}+(z\frac{1}{3})^{2}=\frac{25}{9}\] \[Center\ (0,\frac{1}{3},\frac{1}{3}),\ radius\ \frac{5}{3}\]

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amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=3x%5E2+%2B3y%5E2+%2B3z%5E2+%2B2y%E2%88%922z%3D9+

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0centers good, radius seems off a bit

dumbcow
 4 years ago
Best ResponseYou've already chosen the best response.2looks pretty good. the only thing i see is when you complete the square you should have added 2/9 to right side

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0i tend to divide off the 3 after i complete the square parts to avoid fractions

ChrisS
 4 years ago
Best ResponseYou've already chosen the best response.0right... I subtracted it instead of added... thanks!

ChrisS
 4 years ago
Best ResponseYou've already chosen the best response.0so my radius should be \[\frac{\sqrt{29}}{3}\]

ChrisS
 4 years ago
Best ResponseYou've already chosen the best response.0awesome. thanks to you both :)
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