PokeVideoPlayer v23.9-app.js-020924_
0143ab93_videojs8_1563605 licensed under gpl3-or-later
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Video Format : (720p) openh264 ( https://github.com/cisco/openh264) mp4a.40.2 | 44100Hz
Audio Format: 140 ( High )
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Date : 1729825899424 - unknown on Apple WebKit
Mystery text : U2Q5eTlGdmI5R2cgaSAgbG92ICB1IGV1LXByb3h5LnBva2V0dWJlLmZ1bg==
143 : true
804 Views • Aug 14, 2023 • Click to toggle off description
Views : 804
Genre: Education
License: Standard YouTube License
Uploaded At Aug 14, 2023 ^^
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Rating : 5 (0/36 LTDR)
100.00% of the users lieked the video!!
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User score: 100.00- Masterpiece Video
RYD date created : 2024-06-04T16:22:13.540589Z
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@MichaelRothwell1
1 year ago
This is a beautifully simple solution to this constrained optimization problem.
However, I think we need to show that the limit of 6 can actually be achieved, which of course it can, with (x, y)=(3, 3) [and the lower limit can be achieved with (x, y)=(-3, -3)].
This problem can also be understood visually, by considering the family of lines of the form x+y=k, where we want to find the largest k such that x+y=k intersects the constraint curve x²+y²=18. Naturally, the extreme values of k will occur when x+y=k just touches, i.e. is tangential to, x²+y²=18. Although this can be solved using calculus, it can also be seen by symmetry that this occurs when x=y, so when (x, y)=(3, 3), which gives the maximum and when (x, y)=(-3, - 3), which gives the minimum.
A general method for solving this kind of problem is to use Lagrange multipliers.
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