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Polar Coordinates: Example 9: Cardioid: Part 4
In this video I over Part 4 of Example 9 on Polar Coordinates and this time revisit the slope formula I derived in Part 1 to show that it can be solved in a simpler way. The curve we are given is the polar curve r = 1 + sinϴ, when we derive the formula for the slope of a tangent line to that curve it is important to note that the way we go about solving it early on can greatly affect the “appearance” of the final answer. This is because when working with trigonometric functions we need to understand that there are many different trig identities we can use, and also use to simplify the final result. In this part I show that by simply replacing r with 1 + sinϴ in the parametric equations for x and y obtained from Part 1, we can get a simpler “looking” final result. This result is in fact the same in terms of value as in Part 1, and I prove that by re-arranging the result using trig identities. This is a very useful video in showing how we can save time by simplifying the equations at the start of any calculation which deals with trigonometry, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvQO014ItCWPtaSNeg
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-4
Related Videos:
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 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: https://youtu.be/usSors49Gdw
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Trigonometric Identity: cos(2x) = 1 - 2sin^2(x): http://youtu.be/XGk2CpbEl8I .
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Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvQO014ItCWPtaSNeg
View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-polar-coordinates-example-9-cardioid-part-4
Related Videos:
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 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: https://youtu.be/usSors49Gdw
Trigonometric Identity: sin(2x) = 2sin(x)cos(x): http://youtu.be/IaZFDmVtyyU
Trigonometric Identity: cos(2x) = 1 - 2sin^2(x): http://youtu.be/XGk2CpbEl8I .
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MES-Livestream-12-Andrew-Kaufman-Virology
Dr. Andrew Kaufman MD joins the show to discuss all things virology, genomic sequencing, terrain theory, and the flaws of germ theory!
November 25, 2023 (SATURDAY) at 1 PM PST / 4 PM EST / 10 PM CAT
Dr. Andrew Kaufman's links:
- YouTube @AndrewKaufmanMD: https://www.youtube.com/@AndrewKaufmanMD
- Rumble: https://rumble.com/c/c-1128483
- BitChute: https://www.bitchute.com/channel/1cY3CGBlMOZS/
- X: https://twitter.com/AndrewKaufmanMD
- Website: https://andrewkaufmanmd.com
- Other websites:
- True Medicine University: https://truemedicineuniversity.com/
- True Medicine Library: https://truemedicinelibrary.com/
- Terrain: https://terrainthefilm.com/
- True Healing Conference: https://truehealingconference.com/
- COVID-19 Myths: https://covid-19-myths.com/
Stream notes and playlist:
- Stream notes and links: https://peakd.com/hive-128780/@mes/livestream-andrew-kaufman
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams .
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VIDEO
✈
✈️-911truth-part-26-9-11-wtc-vehicle
Images compiled by: https://www.youtube.com/@xdesmond/videos (I will update the description later)
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THE D
the-dot-product-is-equal-to-zero-for
In this video I go further into the dot product and this time show that two vectors are perpendicular if their dot product is equal to zero. Since a ⋅ b = |a| |b| cos θ, then when the angle θ = π/2 radians or 90 degrees, then cosine π/2 = 0 and thus the dot product is equal to 0. This is a great way to verify if any 2 vectors are perpendicular, as which I also illustrate with an example.
The timestamps of key parts of the video are listed below:
- Perpendicular Vectors: 0:00
- Example 4: 2:05
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: The Dot Product: https://youtu.be/9uqtIk5iHys
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-dot-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GbHgvpTY1mx61nTNO-Msl8
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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GIMP
gimp-photoshop-compressing-images
In this video I go over the basics in compressing images with the powerful and free GIMP Photoshop editing software. Basically you can change the quality or compression level of any PNG, JPG, GIF, or other image formats simply from the Export As... dialog box. Compressing images is create for emails or uploading to social media sites where there are size limitations. It is also useful to simply save space on your computer hard drive!
You can download GIMP from http://gimp.org
Related Videos:
GIMP Photoshop Tutorial: http://youtu.be/dSYjD4ov6ao
Edit Multiple Layers in GIMP Photoshop: http://youtu.be/ifQOah2IA7A
GIMP Photoshop Tutorial - Adding a Color Border to Text and Objects: http://youtu.be/fTyLewIVB-8
GIMP: Rounding Text Edges with the Gaussian Blurr Function: http://youtu.be/lEAO6Ajr1AY
GIF Animations with GIMP 2.8 - A very simple step-by-step tutorial: http://youtu.be/vg8IFbHsvng
Whiten Teeth with GIMP 2.8 Photoshop - Simple Tutorial: http://youtu.be/2ENln3t6J94
GIMP Tutorial: Curve Text and Objects with Cage Transform: http://youtu.be/frZj7DmObhY .
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EXERC
Exercise-4-Velocity-Water-Wave
In this video I go over the water wave velocity equation and approximate it when the waves are deep and when the waves are shallow. For deep waves, the hyperbolic tan or tanh(x) term in the water wave velocity equation approaches zero, which greatly simplifies the equation. For shallow waves, we can use the Maclaurin series approximation for tanh(x) and show that 3rd order or higher terms approach zero for shallow waves. I also calculate the error of this shallow wave speed approximation by using the alternating series estimation theorem.
Timestamps:
- Exercise 4: Water waves speed: 0:00
- Solution to (a): Deep water wave speed approximation: 1:43
- Approximation using hyperbolic tanh(x) = 1: 3:38
- Deep wave speed approximation formula: 5:29
- Solution to (b): Shallow water wave speed approximation: 6:04
- Maclaurin series approximation for tanh(x): 7:05
- Determining derivatives of tanh(x) at a = 0: 8:44
- Writing out our Maclaurin series approximation of tanh(x): 17:18
- 3rd order terms approach zero when water is shallow: 20:07
- Shallow water speed approximation: 21:43
- Shallow water speed approximation formula: 23:22
- Solution to (c): Alternating Series Estimation Theorem for the error: 24:25
- Estimation for tanh(x) approximation: 26:53
- tanh(x) remainder approximation if L is greater than 10d: 30:00
- Estimating accuracy of shallow water wave speed: 32:33
- Error is less than 0.0132gL: 34:02
Full video, notes, and playlists:
- Full video and playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0F76sIU8xm09oqBTq1mlry3
- HIVE notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-applications-of-taylor-polynomials
- Infinite Sequences and Series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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EQUAT
equation-of-a-sphere
In this video I go over the equation of a sphere by utilizing the distance formula in 3D I solved earlier. A sphere is by definition just the set of all points whose distance from a particular point (the center) is equal to a constant r or radius. I go over the equation of the sphere for a center at an arbitrary point in space and also when the center is at the origin.
The timestamps of key parts of the video are listed below:
- Example 5: 0:00
- Equation of a Sphere 3:07
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: 3D Coordinate Systems: https://youtu.be/xJ-qPJFf2gE
- Video notes: https://peakd.com/hive-128780/@mes/vector-space-and-geometry-3d-coordinate-systems
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GiAJeLMzhOsrMliibfce5m
Related videos:
Vectors and Geometry of Space video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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APPLI
applications-of-integrals-discovery-6
In this video I go over question 3 on the Discovery Project: Rotating on a Slant video series. This time I derive the general formula for the volume of a shape generated by rotating a curve about a slanted line. I use the derivation I made earlier in Question 1 for the area of the region between the curve and the slanted line to solve for the volume. The volume equation I derive is very similar to that for the area but involves squaring the radius of revolution. To understand this question in detail, make sure to watch the first questions of this video series!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104360&authkey=!ABktqgP4-ovLXSE&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-discovery-project-rotating-on-a-slant-question-3
Related Videos:
Discovery Project: Rotating on a Slant: Question 3: https://youtu.be/zwodt1OsFjE
Discovery Project: Rotating on a Slant: Question 1: https://youtu.be/dXlhpDOBDe0
Discovery Project: Patterns in Integrals: Question 1: 1/((x+a)(x+b)): http://youtu.be/uQUu0XFMw8I
Discovery Project: Patterns in Integrals: Question 2: sin(ax)cos(bx): http://youtu.be/O0p1DGMOcfM
Discovery Project: Patterns in Integrals: Question 3: x^n * ln(x): http://youtu.be/PA9-Me1ko10
Discovery Project: Patterns in Integrals: Question 4: x^n * e^6: http://youtu.be/XgE75Pa0n-c
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
Integrals and Volumes: http://youtu.be/-evdvkDwBuQ .
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MES L
MES-Livestream-30-Toasted-Cars-Mystery-Planes-911-Revisionist
9/11 Revisionist joins the show again, this time to discuss the 1400 toasted and warped cars, as well as the several mysterious planes flying overhead during all the events of 9/11.
March 30, 2024 SATURDAY at 1 PM PST / 3 PM CST / 4 PM EST / 10 PM CAT
9/11 Revisionist Links:
- Substack: https://substack.com/@911revision
- X: https://x.com/911Revisionist
- Telegram: https://t.me/Sept11_Deprogramming
- Odysee:https://odysee.com/@911revisited:7
- Facebook: https://www.facebook.com/groups/879905060007964
- Rumble: https://rumble.com/c/c-2588430
- Email: revisionof911@gmail.com
Stream notes and playlist:
- Stream notes and links: https://peakd.com/hive-113182/@mes/livestream-30-toasted-cars-and-mystery-planes-911-revisionist
- MES Livestreams: https://www.youtube.com/playlist?list=PLai3U8-WIK0FqwyUa_ICwTlqO0S6Y3kAn
- All Livestreams: https://www.youtube.com/@mes/streams .
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VIDEO
MH370
mh370-teleportation-video-fakery-clouds
In this video I go further into the Malaysian Airlines Flight MH370 teleportation video fakery, and this time go over the discovery of the clouds stock images background used for the "satellite" plane footage. The clouds stock footage was found by Reddit user DI370DPX3709DDYB2I6L and the person that took the photos was Jonas De Ro while he was visiting Japan on January 25, 2012. The alleged "satellite" footage, which was actually just a 2D to 3D conversion by YouTube's then experimental feature, had clouds that match exactly to those taken by Jonas. Not just a few clouds, but the entire sky background! Kim Dotcom accepted the debunk and will pay both Jonas and DI370DPX3709DDYB2I6L a payment, although not the original $100,000+ bounty since they didn't claim to be the hoaxers themselves. Even disinfo agent Ashton Forbes accepted the debunk and has now shifted his goal to becoming an electrical engineer LOL This alternate reality game was quite the joy ride!
Links shown in the video are listed below:
- MES Links: https://mes.fm/links
- Cloud stock footage found: https://t.me/meslinks/21840
- Video 1: https://www.reddit.com/r/AirlinerAbduction2014/comments/18dkpwb/video_of_entire_sky_matching_11_with_stock_footage/
- Video 2: https://twitter.com/TJPofTexas/status/1733037105020879295
- Cloud photo taker Jonas De Ro speaks out: https://twitter.com/JonasDeRo/status/1733055672747741412
- Video explanation: https://www.youtube.com/watch?v=o5BNiduJwnM
- RAW cloud images: https://drive.google.com/file/d/1JT0KOI1yJEtZVzdQtVBHWzyKujFDlBrb/view
- MES local download: https://1drv.ms/f/s!As32ynv0LoaIir0USutwZB-igTBO8w
- Kim Dotcom accepts debunk and promises to pay Jonas De Ro and the original Redditor a payment (but not the original $100,000 since they weren't the original hoaxers): https://twitter.com/KimDotcom/status/1733198949522293158
- Ashton Forbes accepts debunk but will continue investigating MH370: https://twitter.com/JustXAshton/status/1733214296463544660
- Ashton's next goal is becoming an electrical engineer LOL ?https://twitter.com/JustXAshton/status/1733221117819486361
- Ashton Forbes is a debunker now LOL ?https://twitter.com/JustXAshton/status/1733306006535348245
- GIMP Photoshop file: https://1drv.ms/u/s!As32ynv0LoaIir09m_bG1m4N1LxIgw
- 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/
The timestamps of the video are shown below:
- Links to cover: 0:00
- MES Link: 1:36
- Reddit user DI370DPX3709DDYB2I6L discovers cloud images: 1:57
- Entire sky matches stock footage: 2:28
- Jonas De Ro took the photos in Japan: 4:49
- Kim Dotcom accepts debunk: 5:58
- Ashton Forbes accepts debunk: 7:10
- Ashton's next goal is to become an electrical engineer LOL: 9:11
- MES photoshop matching "satellite" footage with cloud stock footage: 10:24
- Live correcting the stock clouds images: 13:30
- Link to MES MH370 playlist: 16:50
Related Videos:
MES MH370 video playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EJGgDKXr-wW8z1jd7pZ069 .
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https://www.youtube.com/watch?v=gja-PGvv8fE
Transaction
Created
4 months ago
Content Type
Language
video/mp4
English