In this video I go over a quick proof of the trigonometric identities tan(x + y) and tan(x – y). The identity is simple to derive because we can use the identities which I derived in my earlier videos for sin(x +/- y) and cos(x +/- y), as well as the fact that the tangent function, tan, is just equal to the ratio of sine over cosine. Although deriving the set of identities for tan(x +/- y) is pretty simple, I show how even that process can be simplified further by utilizing the use of the notations “+/-“ and “-/+”. This allows for the solving of two identities or sets of identities at the same time! I will be utilizing this set of trig identities in my later videos so make sure to watch this video!
In this video I show a simple proof that you can sort n distinct objects in n! ways. This is very useful and important to understand especially if you are interested in statistics or even poker.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIibxXE_25YrR9cknp-w?e=XtVe42
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/factorials-sorting-n-distinct-objects-proof
Related Videos:
Factorials - i.e. 4! = 4*3*2*1 = 24: http://youtu.be/SWnrhDOLQgA .
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In this video I discuss the equation of a circle and show how to graph it. I also prove that the distance from any point on the circle from the center of the circle is just the radius of the circle. The circle and its equation are used in many applications so make sure you have a thorough understanding of it!
Download the notes in my video: https://www.dropbox.com/s/ik28bt7n7t9k9mv/87%20-%20Equation%20of%20a%20Circle.pdf
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/equation-of-a-circle-and-its-proof
Related Videos:
Simple Proof of the Pythagorean Theorem: http://youtu.be/yt-EJlbJQp8
Transformation of Functions Part 1: Vertical and Horizontal Shifts: http://youtu.be/CBZd19GFOTE
Transformations of Functions Part 2: Horizontal Stretching and Reflecting: http://youtu.be/8sUgreHjTt8
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 .
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In this video I make use of the extremely powerful mathematical search engine and computational database of Wolfram Alpha and basically show how it can provide you with all the steps in solving for the integral of a function, even very very complex ones.
Download the notes in my video: https://www.dropbox.com/s/yskcnw2uogyksir/164%20-%20Step-by-Step%20Integrals%20Wolfram%20Alpha.pdf
Related Videos:
Graphing with the Google Search Part 1: http://youtu.be/1k3QDg2sB4o
Graphing with the Google Search Part 2: Multiple Curves and Wolfram Alpha Comparison: http://youtu.be/jBThO3o1K3Y
Google Graphing Calculator Part 3: 3D or Multi-Variable Graphing! AMAZING!: http://youtu.be/zQtcDvYxmGY
Using Google Search as a Calculator: http://youtu.be/RxCqjklGw9A .
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https://www.youtube.com/watch?v=jTcZZkloVWY
In this video i go over a quick introduction to 3D Quadric Surfaces and recap on their 2D counterparts, Conic Sections. A quadric surface is the 3D graph of a second-degree equation in three variables x, y, and z. I illustrate the most general equation as well as two standard forms that be obtained by rotation and translation (and lots of algebra via completing the square). Quadric surfaces have 2D counterparts in conic sections, which I have listed below.
Ellipsoid vs Ellipse
Paraboloid vs parabola
Hyperboloid vs hyperbola
I also go over a recap on the equations and graphs of conic sections.
GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec
Time stamps:
- Quadric Surfaces have second-degree equations: 0:00
- General equation: 0:15
- Two Standard Form equations: 1:33
- Recap on conic sections: 3:08
Full video below:
- Cylinders and Quadric Surfaces: https://youtu.be/k4EyLr4uOUA
- HIVE video notes: https://peakd.com/hive-128780/@mes/cylinders-and-quadric-surfaces
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0EfmYwT81SebJnU1Ny8Fc5u
- Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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In this video I go over a brief introduction and history lesson on the BMI or the Body Mass Index. This is the most widely used index for obesity so it is important to understand the history of the BMI and it's usage.
Basically the BMI is a measure of relative mass based on an individual's mass and height and has units of kg/m^2. The BMI Formula is: BMI = mass/height^2. This equation was discovered by Adolphe Quetelet to be a better relationship between mass and height as opposed to a direct proportion of mass and height.
Learn more by watching this video as well as calculating your own BMI by using our BMI Calculator at http://BMICalculator.cc
References:
"Body mass index". Wikipedia http://wikipedia.org/wiki/Body_mass_index
Eknoyan, Garabed (2007) "Adolphe Quetelet (1796 -- 1874) -- the average man and indices of obesity". Nephrol dial Transplant. Volume 23: pages 47-51. Download the PDF: mes.ph/notes/541o1
Keys, A; Fidanza, F; Karvonen, M; Kimura, N; Taylor, H. (1972). "Indices of Relative Weight and Obesity". Journal of Chronic Diseases. Volume 25, Page 329-343. Download the PDF: mes.ph/notes/541o2
Download the notes in my video:
PDF Notes:http://1drv.ms/1iYny2M
Excel File: http://1drv.ms/1nT7T5x
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Food and Nutrition: What are Calories? and How much in Carbs, Fat, Protein, and Alcohol?: http://youtu.be/RaKutEJc64g
Grade Calculator: gc.mes.fm (Update): https://youtu.be/KjAfCz-8e4w
GPA Calculator: finalexamcalculator.com/gpa: http://youtu.be/wEwOjGJmiDU
Percentage Calculator: PercentCalculator.com (Update): https://youtu.be/wxbwPBve4sQ
Mortgage Calculator Tutorial: mc.mes.fm: http://youtu.be/IZkpH9bWgPU
Reconsideration Requests in Google and Site Policy Violations: http://youtu.be/J2omP3cEO2w .
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https://www.youtube.com/watch?v=4kuCuBjoXmE
In this video I go over an example on how to go about determining the hydrostatic force on a dam by applying the basic principles of integration. As explained in my last video, water applies increasing pressure with depth and thus to calculate the total force due to the water pressure, we would have to look at a small sub-interval of the dam, determine an approximation for the force, and then take the limit of an infinite number of small sub-intervals. Thus as always we can write this limit as an integral and from there determine the amount of hydrostatic force on the dam. This is a very useful and important example to better understand how to apply integrals to real world physics and engineering problems, so make sure to watch this video!
Download the notes in my video: https://onedrive.live.com/redir?resid=88862EF47BCAF6CD!104483&authkey=!ALQbBTRdl0hhIko&ithint=file%2cpdf
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/applications-of-integrals-hydrostatic-pressure-and-force-example-1-force-on-a-dam
Related Videos:
Applications of Integrals: Hydrostatic Pressure and Force: https://youtu.be/fesMt6vmXIo
Applications of Integrals: Surface Area: https://youtu.be/JkDPmAD37qk
Applications of Integrals: Arc Length Function: https://youtu.be/MWKK3qLvSwU
Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg
Simplified Filter Criteria: A Dam Filter Example: http://youtu.be/yGEeYAb4Olw
Soil Mechanics 101 - Phase Relations: http://youtu.be/DtKheQcL2BU
Types of Tailings Embankments: Upstream, Downstream and Centerline Construction Methods: http://youtu.be/1wm1XR6z-QE
Buoyancy - What is Archimedes' Principle and it's Proof: http://youtu.be/mXzccaH2KNI
Area Under a Curve: Introduction to Integral Calculus: http://youtu.be/JbEbhv8ybmE
The Definite Integral and Riemann Sums: Introduction : http://youtu.be/vhMP5SKbQjU .
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iPho
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https://www.youtube.com/watch?v=Gr5H4icS4CQ
The Syrian Civil War has been in the news for many years, and the rhetoric has just now escalated to a really global reach. In this video I take a look at the current state of the city of Aleppo, Syria, which is under the most armed conflict. In doing so, I present the various narratives of the situation brought forward by the United Nations, the Western mainstream media, Russian and Syrian, as well as independent journalists and news outlets. It is clear that the views presented are split into two narratives:
1. The UN and Western mainstream media present the Russia-backed Syrian Government as the aggressors while present the opposition forces as revolutionaries.
2. The Syrian Government, Russia, as well as independent journalists and media present the Syrian government doing its best to fight off against terrorists that look to overthrow the democratically elected government of Syria.
While I present both narratives objectively, it is clear to me that the second narrative is most aligned with the truth. Also, I go over the claims made by the UN of war crimes by the Syrian government, but it turns out those claims are nothing more than unnamed witnesses and sources. These are serious claims which deserve serious evidence, rather than presented as facts in which the Western established media pushes, almost in a coordinated fashion. This is very similar to the Washington Post article about the CIA stating that Russia "hacked" the United States election, which I covered in my earlier video and I concluded that it was simply propaganda.
A good quote to illustrate these competing narratives is "The first casualty, when war comes, is truth" by United States politician Hiram Johnson, who died eerily on the day the US dropped an atomic bomb on Hiroshima.
Stay tuned for Part 2...
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht1CatlHs5ru1mvOKQ
View Video Notes on Steemit: https://steemit.com/war/@mes/syrian-civil-war-part-1-aleppo-media-narrative-as-of-december-2016
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How to Spot Fake News: "Russia Hacked the U.S. Election": https://youtu.be/93sh_hQBO-0
#PizzaGate Part 2: https://youtu.be/PXO64aActSg
#PizzaGate Part 1: https://youtu.be/mdluzbv4MYA
Politics: Electoral College vs. Popular Vote + Money in Politics: https://youtu.be/2z1MS5ZiC-A
USA FBI Crime Statistics: Arrests by Race in 2015: https://youtu.be/AZyp6lTMC4Q"
Climate Change: Consensus of Scientists? Cook et al (2013) Review: Part 1: https://youtu.be/9NQpPx07gjo .
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...
https://www.youtube.com/watch?v=UGGFXsp9PME
Did you accidentally download the Babylon Toolbar when downloading another program and now you are having trouble getting rid of it?? Well this tutorial is a must see because it not only shows how to get your default Firefox browser settings back but it also shows how to completely remove Babylon from all of the inner workings of Firefox!
Related Videos:
Completely Remove Babylon Toolbar/Search/Settings from Google Chrome!!: http://youtu.be/3JenkmYXBWc
Completely Remove Babylon Toolbar/Search/Settings from Internet Explorer!!: http://youtu.be/5EBoBvr3vmw
Search Any Website Easily with URL Keyword Search for Mozilla FireFox and Google Chrome!: http://youtu.be/XSDHhbnIjhs .
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https://www.youtube.com/watch?v=lUcOy3fojr0
In this video I quickly go over how to verify if our 3D to 2D projection is correct, which I do so by adding sight lines in GeoGebra. These "sight lines" are just lines drawn connecting the coordinates of the camera and the projected points on the screen. If these sight lines intersect our clipped points along the 3D line, then it means our projection is indeed correct. This is because the clipped points are simply projected along a straight line from the camera to the screen. In the amazing GeoGebra 3D graphing calculator, we can quickly create sight lines by using the line segment function: https://www.geogebra.org/calculator/twezjbu5
The timestamps of key parts of the video are listed below:
- Question 3: Verifying the Projection with Sight Lines: 0:00
- Solution: 0:18
- Adding sight lines with GeoGebra: 1:31
This video was taken from my earlier video listed below:
- Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ
- HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective
- Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK
Related Videos:
Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .
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https://www.youtube.com/watch?v=27eRZ2DYCzE