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anonymous
 one year ago
Calculus III:
Find an equation of a sphere if one of its diameters has endpoints
(3, 5, 6) and (5, 7, 8).
anonymous
 one year ago
Calculus III: Find an equation of a sphere if one of its diameters has endpoints (3, 5, 6) and (5, 7, 8).

This Question is Closed

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2HI!! this is not as hard as it looks

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2find the center first, the average in each coordinate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anticipation is killing me...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry! Working through some other homework problems. Which equations do we use for that?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2just like the midpoint in two dimensions take the average in each coordinate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So (x1  x2, y1  y2, z1  z2)?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2add up and divide by two

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2"no" i meant just like finding the midpoint of \((3,5)\) and \((7,11)\) in two dimensions add and divide by two in each coordinate in my example the midpoint would be \((5,8)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0( (3+5)/2, (5+7)/2, (6+8)/2) = (4, 6, 7)?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2before we continue, do you remember how to find the equation of a circle given two endpoints of the diameter? this is identical, except with one extra coordinate

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2the equation is going to be \[(x4)^2+(y6)^2+(z7)^2=r^2\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2because the center is \((4,6,7)\)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2equation for a circle with radius \(r\) and center \((h,k)\) is \[(xh)^2+(yk)^2=r^2\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2this is exactly the same, but with one more coordinate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, so it's like the other problems we've had, but backwards! So we add these values squared and take the square root to find r?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2maybe i am not sure what exactly you mean we got the center, we need the radius

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2actually we don't need the radius, we just need the square of the radius, so forget the square root business

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2same distance formula as with two points, only now each point has three coordinates instead of two

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2square of the distance between \((3, 5, 6) \) and \( (4, 6, 7)\) is \[((43)^2+(65)^2+(76)^2\] a pretty easy calculation in this case

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2for the actual distance it would be \[\sqrt{(43)^2+(65)^2+(76)^2}\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2you get 3 pretty much instantly right?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2final answer:\[(x4)^2+(y6)^2+(z7)^2=3\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2a nice picture http://www.wolframalpha.com/input/?i=%28x4%29%5E2%2B%28y6%29%5E2%2B%28z7%29%5E2%3D3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh, I see. Thank you so much for explaining it to me! :)

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[\huge \color\magenta\heartsuit\]
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