alexisbreton
09.12.2019 •
Mathematics
The plane x + y + 2z = 12 intersects the paraboloid z = x2 + y2 in an ellipse. find the points on the ellipse that are nearest to and farthest from the origin. nearest point (x, y, z) = farthest point (x, y, z) =
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Ответ:
The distance between a point and the origin is . But since , both and have the same critical points, so we can consider instead the squared distance, .
We're looking for the extrema of subject to and . The Lagrangian is
with critical points where the partial derivatives vanish:
From the first two equations, it follows that .
Then in the last two equations,
If , then ; if , then .
So there are two critical points, and .
Let . We have a minimum distance of and maximum distance of .
Ответ:
answer:
The shape below is transformed to another shape.
Shape C D E F G H
Which shape could be its image?
Shape C D E F G H
Shape G prime H prime C prime D prime E prime F prime
Shape G prime C E D prime F H prime
Shape C prime D prime E prime F prime G prime H prime
Mark this and returnp