In this video I go over another related rates application and solve an example that involves a ladder sliding down a wall.
Download the notes in my video: https://www.dropbox.com/s/1d72ooghavkg05v/465%20-%20Related%20Rates%20-%20Sliding%20Ladder%20Example.docx
Related Videos:
Related Rates: Introduction + Balloon Example: http://youtu.be/oYU51dBqWo0
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Related Rates Examples: Part 1: http://youtu.be/xLcUkjORXFY
Similar Triangles - Part 1: http://youtu.be/gXcQEKVcesc
Related Rates Examples - Part 2: http://youtu.be/jDGQr5dSvnc
Similar Triangles - Part 2: http://youtu.be/XFgudym55CU
Derivative Rules: Proof of Chain Rule: http://youtu.be/tYDDpKzP-VU
Derivative of y = x^n: Power Rule Part 1: n is positive integer: http://youtu.be/-Yv85MZNYgU .
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https://www.youtube.com/watch?v=m7qZDl_82Wo
In this video I go over Problem 1 which asks us to determine the 15th derivative at x = 0 for the function sin(x^3). Instead of manually solving the derivatives one by one, we can instead use the Maclaurin series for sin(x), replace x with x^3, and then solve for the 15th derivative for the corresponding series coefficient.
The timestamps of key parts of the video are listed below:
- Problem 1: 15th Derivative of sin(x^3) at x = 0: 0:00
- Maclaurin Series for sin(x): 0:40
- Derivatives as Series Coefficients: 3:30
- Calculation Check: 5:06
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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In this video I go over the famous Book Stacking Problem, and show that it is possible to stack books that extend infinitely far away from the table! To do this you have to stack such that the first book extends 1/2 from the second book which extends 1/4 from the third which extends 1/6 from the 4th, and so one. Then the center of mass of the stack of books can be determined and shown to be still above the table, which means the books won't tip over. Lastly, I show that the series of distances 1/2 + 1/4 + 1/6 + ... etc. is a divergent Harmonic series, which means that the distance keeps extending out to infinity as we add more books. Try this yourself and let me know how many books, or playing cards, you can stack up!
The timestamps of key parts of the video are listed below:
- Problem 12: Book Stacking Problem: 0:00
- Solution: Book extending completely off the table: 1:57
- Center of mass of the stack of books: 7:20
- Center of mass doesn't extend past the table: 17:02
- Books can extend infinitely far via the divergent Harmonic series: 18:42
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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https://www.youtube.com/watch?v=_2IAh41R1sg
In #PizzaGate Part 23 I go over a brief overview of the pedophilia activism through what was known as the “Childlove Movement”. In my previous videos in which I covered the Wikileaks released FBI document showing the various logos that pedophiles use to identify themselves and communicate their preferences. In that document the FBI referenced several times a Wikipedia article titled “ChildLove movement” which currently is no longer available, but luckily it was archived. In this video I go over the article which looks at various pedo activism organizations and their push to lower, or even abolish, the age of consent, legalize C.P., and argue that children can “consent” to relationships with adults. Also, many prominent figures within these organizations were later convicted of abuse and/or possession of C.P.
In this video I also take a quick look at the way the mainstream media reports on pedophilia through some quick “site:” Google searches. It is clear that many big news outlets, those that appear in the first page of Google, cover less about news regarding pedophilia, and much more on opinion pieces that are empathic to pedophiles. In essence, the MSM is normalizing pedophilia as something we can openly tolerate in our society, while reporting very little on the negative consequences or criminal cases involving pedophilia. In contrast, I show how sites such as Infowars are the complete opposite of these other media outlets, and instead actually report on news involving pedo and tracking rings. The contrast is night and day.
Also in this video I provide some quick updates on the alleged elite Dutch Banker whistleblower Ronald Bernard, French Presidential candidate Emmanuel Macro’s strange relationship with his wife, and Bill Nye’s completely bizarre and cringy video from his Netflix series “Bill Nye Saves the World”…. Actually don’t watch that Bill Nye video if you want to save some brain cells… #DontSayIdidntWarnYou
And as usual, I discuss even more YouTube demonetization…. So we have to support each other without relying on company’s fleeting ad revenue.
Stay Tuned for #PizzaGate Part 24…
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvBJmQ_UUovt5fH6Cw
View video notes on the Hive blockchain: https://peakd.com/pizzagate/@mes/video-notes-pizzagate-part-23-pedophilia-activism-and-normalization-ronald-bernard-macron-bill-nye-more
Related Videos:
View full #Pizzagate series: https://peakd.com/pg/@mes/videos
#PizzaGate Part 20: BLogo & LBLogo Origins + Alex Jones Apology + Dr. Phil Red Pill + Trudeau Foundation + MORE: https://peakd.com/pizzagate/@mes/video-notes-pizzagate-part-20-blogo-and-lblogo-origins-alex-jones-apology-dr-phil-red-pill-trudeau-foundation-more
#PizzaGate Part 21: GLogo Origins + YouTube Censorship + Craig Sawyer + April 7th NYC Protest: https://peakd.com/pizzagate/@mes/video-notes-pizzagate-part-21-glogo-origins-youtube-censorship-craig-sawyer-april-7th-nyc-protest
#PizzaGate Part 22: CLogo Origins + Google Censorship + Haiti UN Trafficking + MORE Censorship: https://peakd.com/pizzagate/@mes/video-notes-pizzagate-part-22-clogo-origins-google-censorship-haiti-un-trafficking-more-censorship
#911Truth video series: https://peakd.com/truth/@mes/911
#Occult video series: https://mes.fm/occult-playlist .
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In #MESExperiments 16 I demonstrate one of the most fascinating demonstrations ever conducted, and which even baffled my mind when I first tried it out. A gyroscope can even rise while precessing at the tip of a needle! Yes, a needle… The gyroscope is literally dangling in midair with nothing to hold on to but the tiny tip of the needle. I’ve included a zoomed in box during the gyro rising to show a close up of the stem and needle. This is some truly breath-taking stuff!
The progression of the gyro experiment and numerical results are listed below:
- Initial Gyro Angle: 47°
- Rising Time: 0:40 - 0:04 = 36 seconds.
- Sleep Time: 0:58 - 0:40 = 18 seconds.
- Time to Fall: 1:02 - 0:04 = 58 seconds.
- Total Spin Time: 2:45 - 0:04 = 2:41 = 161 seconds.
- Note: Very interesting loud noise coming from the gyro at the 20 seconds mark during rising.
Note that the gyroscope weighed 100.29 grams and the needle is less than 0.5 mm thin.
The full results are shown in the corresponding Hive post: https://peakd.com/mesexperiments/@mes/mesexperiments-16-gyroscopes-can-even-rise-on-the-tip-of-a-thin-needle-wow
Stay Tuned for #MESExperiments 17…
Related Videos:
#MESExperiments Video Series: https://peakd.com/mesexperiments/@mes/list
DRAFT #MESExperiments Video Series: https://mes.fm/experiments-draft
#AntiGravity Video Series: https://peakd.com/antigravity/@mes/series
#FreeEnergy Video Series: https://mes.fm/freeenergy-playlist .
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In this video I go over the 5 specific properties of the Dot Product as well as their proofs.
The timestamps of key parts of the video are listed below:
- Properties of the Dot Product: 0:00
- Proof of Property 1: 1:53
- Proof of Property 2: 3:02
- Proof of Property 3: 5:10
- Proof of Property 4: 8:26
- Proof of Property 5: 13:04
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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https://www.youtube.com/watch?v=_WjqOhJdDGU
In this video I construct an infinite series of right triangles rotated about a single point and show that the central angle diverges to infinity as the number of triangles approach infinity. To show this, I first construct a table determining the base lengths of each triangle using the Pythagorean Theorem to obtain a formula for the n-th triangle base. From this we can obtain the angle as a formula involving the inverse tangent trigonometric function. Applying the Limit Comparison Test with a diverge p-series, I show, using L'Hospital's Rule, that the angle series diverges, hence the angle approaches infinity as the number of triangles approach infinity. This means that the series of triangles makes infinitely many turns around the central point.
The timestamps of key parts of the video are listed below:
- Problem 22: Spiraling Triangles: 0:00
- Solution: Repeating Pythagorean Theorem: 1:16
- Formula for n-th Triangle: 5:16
- Limit Comparison Test: 8:57
- Comparing with a Divergent p-series: 10:21
- Applying the Limit Comparison Test with our original series: 14:36
- Recap on tan(x): 18:59
- Applying L'Hospital's Rule: 20:56
- The angle of the triangles diverges to infinity: 22:30
- Recap on the derivative of arctan(x): 23:11
This video was taken from my earlier video listed below:
- Infinite Sequences and Series: Problems Plus: https://youtu.be/zjdkQIIdTbg
- HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-problems-plus
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FQ96Egr5R7fZGeDTIUKz8P
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EXHAJ3vRg0T_kKEyPah1Lz .
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In this video I go over the orthogonality or perpendicular theorem for cross products and prove that it is indeed true. The cross product of two non-zero vectors produces a vector that is orthogonal or perpendicular to the two vectors. I prove this by showing that the dot product of the cross product with either vector that produces it is equal to 0, hence they are perpendicular as per my earlier video on the Dot Product.
Also in this video I go over the Right-Hand Rule convention for the cross product. This rule is such that the cross product produces a vector in the direction of your right-hand thumb while your fingers curl in the direction from the starting vector a to the ending vector b.
The timestamps of key parts of the video are listed below:
- Cross Product Orthogonality Proof: 0:00
- Right Hand Rule: 6:01
This video was taken from my earlier video listed below:
- Vectors and the Geometry of Space: The Cross Product: https://youtu.be/k8GRt95i-Gc
- Video notes: https://peakd.com/hive-128780/@mes/vectors-and-the-geometry-of-space-the-cross-product
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FuRJ8rg-YVQvfPoPOwhuRW
Related Videos:
Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=wdYSNvT2nsg
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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https://www.youtube.com/watch?v=49qZEuhNhbI