In this video I go over further into Polar Coordinates and this time look at Example 12 Question A which revisits the Limaçons curves from Example 11 but now I take an analytical approach as opposed to the graphical approach from the previous example. Question A looks at the “loop” which I showed occurred for values of c that are larger than 1 or less than -1, i.e. the absolute value of c is greater than 1, in the Limaçon formula r = 1 + c sin ϴ. We are asked to prove this is the case, and thus I go over an VERY extensive analytical proof by first showing that the requirement for the loop is to have two angles where the coordinates are at the origin, and between them the r-values are negative. I show that this is only possible when |c| is greater than 1. This is an extremely detailed proof video, but if you follow along the whole thing you will be that much more knowledgeable about mathematics in general, so make sure to watch this video! I will be going over Question B in the next video so #StayTuned! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvRsaO7qUm_nIAzIXw View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-12-limacons-analytical-proof-part-1-question-a Related Videos: Polar Coordinates: Example 11: Limaçons + Cochlea + Archimedean Screw: https://youtu.be/GByUVHGAMe0 Polar Coordinates: Example 10: Graphing r = sin(8ϴ/5): https://youtu.be/m-A35NDX7b0 Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk Polar Coordinates: Example 9: Cardioid: Part 4: https://youtu.be/R6UtQD8tUF0 Polar Coordinates: Example 9: Cardioid: Part 3: Question B: https://youtu.be/-TZHaTjHfb8 Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs Polar Coordinates: Example 3: Cartesian to Polar Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE Polar Coordinates: https://youtu.be/-KAdZL-N4ok Parametric Equations and Polar Coordinates: h ... https://www.youtube.com/watch?v=90XjQVkLBVY

In this video I go over further on the Malaysian Airlines Flight MH370 alleged teleportation videos, and this time double down on the duplicate frame by showing that the UFO orb rotates the WRONG direction at the 45th second frame! In my previous video I showed that the supposed MH370 thermal plane footage likely involved a copy and paste job for one of the frames, which is unlike any typical video compression techniques, and this video further confirms it. Going frame by frame on the orb, it maintains its rotational motion throughout the video except at the 45 second frame, where is rotates abruptly the wrong direction before abruptly rotating back in the next frame. At the 47 second frame, the duplicate frame shows proper orb motion with no abrupt changes. Thus the 47th frame is likely the correct frame while the 45th frame is the edited frame. Note also that the first "stereoscopic satellite 3D" plane footage involves the plane, orbs, and clouds moving every 5th frame while the mouse moves every frame besides duplicating every 5th frame. In the thermal video, it too doubles every 5th frame. If you know why this is or have further information on it, please let me know! Links to all the references and videos used are listed below: - MES Livestream 11: Emergency MH370 Broadcast: https://www.youtube.com/live/C2vv4FjSh6o - MH370 Teleportation Video Fakery: Duplicate Frames (NOT Video Compression): https://youtu.be/tazw6CAcrKo - Duplicate frames MES Links telegram post: https://t.me/meslinks/21496 - Mick West tweet: https://twitter.com/MickWest/status/1726385274534679014 - @ophello tweet: https://twitter.com/ophello/status/1726828364600840534 - NOT video compression: https://twitter.com/528vibes/status/1726567372968898691 - NOT video motion vector compression: https://www.securitylinkindia.com/technology-paper/2019/07/15/video-compression-and-its-significance3/ - Camtasia video editing file: https://1drv.ms/u/s!As32ynv0LoaIirhfhyD_2K1OSVA5vw - GIMP photoshop file: https://1drv.ms/u/s!As32ynv0LoaIirhguJ36QTkDgImkVA - MH370 videos on MES Links telegram: https://t.me/meslinks/21412 - May 19, 2014: Satellite Video: Airliner and UFOs by RegicideAnon: http://web.archive.org/web/20170606182854/https://youtube.com/watch?v=5Ok1A1fSzxY - Download link: https://web.archive.org/web/20140526071334oe_... - MES local download: https://1drv.ms/v/s!As32ynv0LoaIirhd1lFnID1lbw0Yzw - Used the WayBack Machine YouTube downloader: https://www.waybackyt.download/ - June 12, 2014 video: UAV-Captures Airliner and UFOs by RegicideAnon: http://web.archive.org/web/20140827060121/https://youtube.com/watch?v=ShapuD290K0 - Download link: https://web.archive.org/web/20190107190546oe_... - MES local download: https://1drv.ms/v/s!As32ynv0LoaIirheG432fgdwTFwXEA - Ashton Forbes calls me out LOL: https://twitter.com/JustXAshton/status/1727520818182209640 - My Duplicate Frames video got shared on the r/AirlinerAbduction2014 Reddit forum! https://www.reddit.com/r/AirlinerAbduction2014/comments/181uh0y/mh370_teleportation_video_fakery_duplicate_frames/ The timestamps of key parts of the video are listed below: - Links to videos and references: 0:00 - Ashton Forbes calls out MES... LOL: 1:55 - My earlier video shared on Reddit: 3:12 - Notes: Both videos duplicate every 5th frame: 3:28 - "Satellite" Footage moves every 5th frame: 4:09 - Mouse duplicates every 5th frame: 5:41 - "Thermal" footage duplicates every 5th frame: 6:09 - 45th second orb rotates the wrong way: 6:44 - 47th second orb rotates correctly: 8:07 - Checking the orb rotation one more time: 10:11 - Let me know if you have information on the duplicate 5th frames: 11:00 . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=frWD3cJ4L_A