Question 1092167
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Write the equation of a sphere of the radius of 7 units and centered at the point (6,9,4):

{{{(x-6)^2 + (y-9)^2 + (z-4)^2}}} = {{{7^2}}}

and substitute there x = 8 and z = 10. You will get

{{{(8-6)^2 + (y-9)^2 + (10-4)^2}}} = 49,   or

{{{2^2 + (y-9)^2 + 6^2}}} = 49,   or

{{{(y-9)^2}}} = 49 - 4 - 36 = 9.

Then take the square root of both sides to get

y - 9 = +/- {{{sqrt(9)}}} = +/- 3.

So, "y" may have only TWO values y = 9+3 = 12  or/and  y = 9-3 = 6.


Of them, the largest is y = 12 units.
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Solved.