In this video I go over the proof of the integral of the trigonometric function cos^2(x) and show that it is equal to 1/2*(x + sin(x)cos(x)) + C. In evaluating this integral I show that it is easier to evaluate if we can get rid of the square power, which is possible when using the half angle trig identity: cos^2(x) = 1/2*(1 + cos(2x).
In #PizzaGate Part 6 I look further into the Madeleine McCann reported missing child case, and this time take a close look at yet another witness statement that the mainstream media purposely fail to write about. The witness is a professional child services and social worker with over 25 years of experience, Yvonne Warren Martin, who happened to be on holiday vacation in Portugal during Madeleine’s reported disappearance. Madeleine was reported missing on May 3, 2007, but Yvonne Martin heard about this in the news on the day after, May 4th, and which she decided to travel to the apartment where Gerry and Kate McCann were staying. She met up with the McCanns, who were accompanied by their close family friend David Payne, at around 9:30 AM. Yvonne tried to console Kate McCann, who was clearly distraught and in tears.
Yvonne offered to help the McCanns in any way she could by offering her expertise and knowledge. She also wanted to speak with Kate alone to get a better idea of the situation because, from her experience, child cases are almost always the result of other family members or family friends being involved. But Kate was advised by her friend David Payne to stop talking to Yvonne and was told it was better she be quite and not say anything. Yvonne found this extremely strange and wondered why the McCanns would not want to speak about possible ways in uncovering the mystery of Madeleine. Also of note is that Yvonne found David Payne very familiar but could not spot where she may have seen him. Nonetheless, her encounter with the McCanns caused her to believe that they may have been involved in Madeleines disappearance. She also suspected David Payne to be involved as well, and wanted the police to investigate whether he may be a pedophile. This comes as quite a revelation given the statements made by Katherina and Savio Gaspar, see #PizzaGate Part 5, which also suggest that David Payne may be a pedophile.
Yvonne’s encounter with the McCanns was reported by the former chief Portuguese police investigator Goncalo Amaral in his book “Maddie: Truth of the Lie”, by Kate McCann in her book titled “Madeleine”, by David Payne during his witness testimony, and by countless other citizen journalists online. But as expected, the only place that the Yvonne testimony was not written about is the mainstream media, including Wikipedia. This is yet another example of the mainstream media appearing to not be about the truth, but rather push pre-existing agendas and narratives they either they, or others more powerful, have.
Stay tuned for #PizzaGate Part 7…
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuE6sWqT1sdCGB05cA
View Video Notes on Steemit: https://steemit.com/pizzagate/@mes/video-notes-pizzagate-part-6-mccann-case-y
...
https://www.youtube.com/watch?v=Vgv5WYb0PbU
In this video I go over another example on the logistic differential equation for modeling population growth, and this time use Euler's Method to estimate the solution to the logistic equation. The Euler's method is an iterative procedure to model the solution by using the data from each previous point and applying the derivative, through the differential equation, to model each next point. I also develop an Excel sheet that applies the Euler's method for multiple step sizes, in which case the smaller the step size the more accurate the calculations; and this Excel file is free to download below.
Download the notes in my video:
PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIhtRhLVje9tyauUQO9w
Excel File: https://1drv.ms/x/s!As32ynv0LoaIhtRmBKSoLoX7z4Dehw
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-population-growth-logistic-equation-example-3
Related Videos:
Differential Equations: Population Growth: Logistic Equation: Example 2: https://youtu.be/vvL1STfPRkY
Differential Equations: Population Growth: Logistic Equation: Example 1: https://youtu.be/FMFTLa8URDg
Differential Equations: Population Growth: Logistic Equation: https://youtu.be/yE8aoY8Bks4
Differential Equations: Population Growth: Proportionality Constant: https://youtu.be/y4cJX0rcXqw
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94
Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA
Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM .
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https://www.youtube.com/watch?v=33XlP5vlVsM
In #MESExperiments 11 I go over several gyro rising experiments comparing different gyros to various initial spin speeds in order to understand how the rate of rising is affected by initial spin speeds. I compare 3 different gyroscopes and 2 different initial spin speed types: full speed and a delayed start. The 3 gyroscopes include a small plastic gyro (29.10 grams), a UFO light-up plastic/metallic gyro (134.39 g), and a metallic precision gyro (150.68 g). For each gyro I have placed the experiments side-by-side to better compare their behavior. The delayed start time for the small gyro is 30 seconds, for the UFO gyro it is 1 minute, and for the precision gyro it is 3 minutes. All the experiments had angles very close to 45 degrees from the vertical but it should be noted that even a 1 degree difference can have a drastic impact on the rising rate or even the ability to rise.
The findings show that the small gyro and the UFO gyro rose faster when delayed indicating that slower spin rate helped increase rising rate. But the opposite happened with the precision gyro in that the faster spin speed with no delay rose faster. These are are very interesting findings and require further investigation. It is also important to note that the weight of the gyro spinning mass and non-spinning mass are key components in the gyro's magical ability to rise; and which can even allow the gyro to generate torque over-unity in lifting relatively heavy weight as demonstrated in my game-changing #AntiGravity Part 6 video, https://mes.fm/antigravity-playlist.
Note that the video thumbnail has the full speed rising time shown in the above vertical gyros while the bottom are the initial starting positions of the delayed start gyros.
The full results of each experiment are shown in the accompanying Hive article and Excel File:
View video notes on the Hive blockchain: https://peakd.com/mesexperiments/@mes/mesexperiments-11-increasing-gyroscope-spin-speed-doesn-t-necessarily-increase-rising-rate
Excel File: https://1drv.ms/x/s!As32ynv0LoaIh-53X75dowZjPNboJA
Note that the rising rate increases for the small and UFO gyro but decreases for the precision gyro. Also interesting is the rising rate for the precision gyro is several times smaller than the other gyros. Furthermore the full speed gyros were in the "sleep" or vertical position for longer and as well as taking longer to fully fall down. This may be due to the minimal bearing friction in the vertical position.
Note that further, more detailed experiments are required to quantitatively measure the spin speeds as well as the relative weights of the spinning vs non-spinning mass. Also in the works is that I'm trying to obtain a gyro wheel with no outer casing at all to get a better understanding of how the gyro behaves with no non-spinning mass. I will also be looking to get a battery powered gyro wheel with variable and uniform spin speed control to further understand the magic of gyros; if you are able to make one or know of a place that sells it please get in contact with me at contact@mes.fm.
It is also worth noting that the according to the website I purchased the 150.68 g precision gyroscope from, the weight of the spinning brass disk including the rotating shaft is 112 g. Thus the ratio of the spinning mass to the total weight is 112/150.68 = 0.7433 = 74.33 %. I believe weighing the spinning rotors of the small toy gyro and UFO gyro and comparing the relative spinning mass ratio with the precision gyro may reveal further important information regarding the rising rates; which I will look to dissemble soon.
Stay Tuned for #MESExperiments 12…
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 prove Cauchy's Mean Value Theorem, which is basically a general version of the Ordinary Mean Value Theorem, and is important because it is used in the proof of L'Hospital's Rule.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIibZxlzYxpauPOfLeBA?e=lZ04N9
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/cauchys-mean-value-theorem-proof
Related Videos:
Mean Value Theorem - A Simple Proof: http://youtu.be/x-2MiiG2E38
Rolle's Theorem: http://youtu.be/GYha-rqCaxY
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Derivative of Power Functions Part 1 - x^n where n is a positive integer: http://youtu.be/-Yv85MZNYgU .
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In this video I use the calculus methods for curve sketching that I showed in my earlier videos and solve a very useful real life example on optimization by trying to maximize the area of a rectangle.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiagi8s_YWPRrMdzIaw?e=0WkivR
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/optimization-examples-part-2-minimizing-manufacturing-costs
Related Videos:
Optimization Examples - Part 1 - Maximizing Area of a Rectangle: http://youtu.be/OO4Hmd9wntc
Local and Absolute Max/Min and Critical Points/Numbers: http://youtu.be/aOvwQaEFbjw
First Derivative Test Introduction and Examples: http://youtu.be/60UMYG7Ppeg
Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg
Derivative of y = x^n: Power Rule Part 1: n is positive integer: http//youtu.be/-Yv85MZNYgU
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .
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In this experiment, I continue further with a Gyroscope’s amazing ability to precess upwards on rotating surfaces (or low friction surfaces) and this time show that it can rise upwards even at very steep angles. This time I am using a Super Precision Gyroscope (see link below) and starting at a super steep angle of about 60 degrees from the vertical. I had initially thought it was not possible for the gyroscope to rise fully upwards from such a steep angle, but the magical gyroscope continues to baffle everything I thought was possible!
Starting from an initial angle from the vertical of about 60 degrees, the gyroscope precesses upwards in about 3 and half minutes to about 42 degrees, and ultimately perfectly vertical in 7 minutes.
The gyroscope then maintains a stable vertical position for about a minute before it starts wobbling off course. Then in roughly a minute longer, the gyroscope precesses downwards until about 60 degrees from the vertical. A minute later the gyroscope eventually precesses at GREATER than 90 degrees from the vertical (or a negative angle below the horizontal) until it strikes one of the base supports thus falling over. Looks like I will have to perform a second test in which I raise the support higher to see just how long the gyroscope can precess below the horizontal angle. The gyroscope precesses for a total of about 10 minutes moving both upwards and then downwards; truly amazing stuff!
Later in the video I place the gyroscope on its side on show how just lightly touching it causes it to behave in bizarre and truly remarkable ways! The Super Precision Gyroscope spun for a total of 17 and half minutes. Another BOMBSHELL discovery about gyroscopes, which I will demonstrate in future experiments, is that the gyroscope NEVER loses spin speed as a result of its precession, or even manually twisting it. In other words, the gyroscope’s ability to move, interact, and impart forces upon *some* changes to its orientation DOES NOT SLOW DOWN or use the “energy” of the spinning gyroscope. Now this brings into question, WHERE is this “energy” coming from?? If not from the gyroscope itself, then maybe Bruce DePalma, founder of the N-Machine #FreeEnergy Machine before his untimely almost certain assassination, is right in that the gyroscope is acting like an “antenna” to the energy field all around us…. #Aether
MES Note: I say *some* changes to its orientation because, as will further be explained in detail, as the Earth Rotates the gravity field moves but the gyroscope or spinning tops in general aren’t affected by this change in the forces (in this case a moving gravity field) acting upon its orientation; i.e. #InceptionIsReal
Anyways, let me know what you think is behind this amazing property of the gyroscope to magically rise as it precesses. I am of the view that rotation, or even all forms of motion itself, interacts with Gravity in a similar way that rotation of electric fields and magnetic fields interact with each other. This is some truly fascinating concepts to ponder!
Stay Tuned for #MESExperiments Number 3!
Super Precision Gyroscope: https://www.amazon.com/Gyroscope-com-Super-Precision-Gyroscope/dp/B00J3UTRZW
View full experiment results on the Hive blockchain: https://peakd.com/mesexperiments/@mes/mesexperiments-2-super-precision-gyroscope-precesses-upwards-even-at-super-steep-angle
Related Videos:
#MESExperiments video series: https://peakd.com/mesexperiments/@mes/list
DRAFT #MESExperiments Video Series: https://mes.fm/experiments-draft
#MESScience video series: https://mes.fm/science-playlist
#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 an example on Euler's Method for numerically approximating solutions to a differential equation and this time look at the initial-value problem: y' = x + y with y(0) = 1. Initially I use the step size of 0.1 to roughly approximate the solution at x = 0.1, 0.2, ..., 1.0. But to get more accurate approximations we can decrease the step size even further. As shown in this video, when we decrease the step size further and further the solution approaches closer and closer to the exact value. This is a very useful video to understand Euler's method in detail, as well as how to develop spreadsheets to calculate it, so make sure to watch this video!
Download the notes in my video:
Notes: https://1drv.ms/b/s!As32ynv0LoaIhsQlsgrDZEb68Fl1LQ
Excel Notes: https://1drv.ms/x/s!As32ynv0LoaIhsQnSuqAQ7rhC3PsFg
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-euler-s-method-example-1
Related Videos:
Differential Equations: Euler's Method: https://youtu.be/VlwVl-3oPDM
Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Direction Fields: Example 1: https://youtu.be/mtbMQQZeMoQ
Differential Equations: Direction Fields: https://youtu.be/zWv1y8Xp1ac
Differential Equations: General Overview: https://youtu.be/jit59tIY4UI
Differential Equations: Spring Motion: Example 1: https://youtu.be/Twu30EJ93Wg
Differential Equations: Motion of a Spring: https://youtu.be/mk2TiR5dwVs
Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA .
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...
https://www.youtube.com/watch?v=L_l5DLZsZLQ
In this video I have uploaded a short clip of Fox News and the mainstream media in general blaming Osama bin Laden in minutes to even seconds after the second WTC impact on 9/11. Looking back at it all now, it is quite eye-opening the level of propaganda of fear and hatred that was driven by the MSM to ultimately rally people for war, aka mass ritualistic genocide. This, of course, parallels the same propaganda used during the COVID-19 psychological operation... The person speaking initially in the video is Dr. Morgan Reynolds and his website is https://nomoregames.net.
The timestamps of key parts of the video are listed below:
- Fox News Anchor Solves 9/11 in Under 45 Seconds!: 0:00
- MSM Pushes Osama bin Laden nonstop: 0:53
- OBL convicted by MSM in 30 minutes: 1:02
This video was taken from the following video listed below:
- 9/11 Observable Evidence (MES Dubbed): Still Working On It...
- 9/11 Observable Evidence (Original): https://youtu.be/8Xw-00NbEE8
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh
Related Videos:
- #911Truth video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EzqTamtIXtgX8QudQSxuxh and https://peakd.com/truth/@mes/911 .
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In this video I go over part b) of Question 4 of the Applied Project: How Fast Does a Tank Drain? This example continues from my last video, which was part a), and uses the differential equation developed in that video for a spherical water tank, to evaluate the time it takes for the tank to completely drain out of water. Although I don't solve the equation of the water height explicitly, it is still good enough to determine it explicitly as a function of time because it still allows us to evaluate specific heights at specific times. Also in the video I do a lot of calculations by hand as opposed to simply using a calculator, so make sure to watch this video if you want to also see a good exercise in algebra and calculations by hand!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhs1KxO8BeFj6I5yykw
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applied-project-how-fast-does-a-tank-drain-question-4-part-b
Related Videos:
Applied Project: How Fast Does a Tank Drain? Question 4: Part a): https://youtu.be/OyREUg6uCqc
Applied Project: How Fast Does a Tank Drain? Question 4: Introduction: https://youtu.be/9J4QOCi1VbE
Applied Project: How Fast Does a Tank Drain? Question 4: Introduction: https://youtu.be/9J4QOCi1VbE
Applied Project: How Fast Does a Tank Drain? Question 2: https://youtu.be/QtR1QuSNoyk
Applied Project: How Fast Does a Tank Drain? Question 1: https://youtu.be/KhsbeI9QPls
Applied Project: How Rainbows are Formed and the Order of it's Colors : http://youtu.be/Q3Euh4K93_c
Applied Project: How Double Rainbows are formed - Calculus of Rainbows Part 2 : http://youtu.be/bKfyV_YKLR4
Applied Project: The Shape of a Can - The Science behind Can Manufacturing : http://youtu.be/pfpd8RJi9jw
Applied Project: Where Should a Pilot Start Descent?: http://youtu.be/DI4WMqrYB4Q
Applied Project: Building a Better Roller Coaster: http://youtu.be/QjtaMIlKYxQ
Applied Project: Where to Sit at the Movies: http://youtu.be/oEkFJuCE-4A
Addition and Subtraction by Hand - An in-depth look: http://youtu.be/Tkb7xU-lFWU
Multiplication by Hand - In depth look at the wonderful world of multiplication: http://youtu.be/bUKGh5R_0Sw
Long Division by Hand - An in depth look: http://youtu.be/giBZg5Vqryo
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .
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https://www.youtube.com/watch?v=v1-HF67u2Xw