In this video I go over an example on Ellipses that looks at the amazing reflective property of ellipses! This property is such that the angle between a line drawn from one focus to a point on the ellipse is equal to the angle from that same point to the other focus. This means that emitting light or sound from one focus gets reflected onto the other focus! This is an amazing property of ellipses and is used in many real world applications such as Lithotripsy to treat kidney stones, and in Whispering Galleries. I will go over these applications in a later video so stay tuned! In proving this property, I use the formula I derived from my earlier video on the angle between two intersecting lines in terms of the slopes of the lines. Using that formula twice, one for each angle, and determining the slope of the tangent line at the point on the ellipse, I show how the tan value of both angles are equivalent, and thus the angles themselves. Although this is a very tedious and detailed example, the methodical steps I go through provide a great understanding of the algebra and equation manipulating behind the derivation, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvlZADcp8Lq3bF-tUw View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-conic-sections-ellipses-example-3-amazing-reflective-property Related Videos: Conic Sections: Ellipses: Example 2: Vertical Ellipse: https://youtu.be/cK0z2ZMC1fU Conic Sections: Ellipses: Example 1: https://youtu.be/m9FXGv3kMkk Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_M Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE Angle Between Two Lines: Formula in terms of Slopes: https://youtu.be/O8M4ZErxE-M . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our 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 Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile ... https://www.youtube.com/watch?v=H5IPfg3HSRU

In this video I explore why the shape of cans that you see in the supermarket are the way they are and use calculus to determine what ratios of can height to can radius are used in real life. This is an applied project question in my calculus text book and I thought it was really interesting and worth doing a math easy on it! Enjoy! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiaVwg0FLYrhmuJLiUA?e=acxCHW View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/applied-project-shape-of-a-can-science-behind-can-manufacturing Related Videos: Area of a Regular Hexagon - Simple Proof and other Properties: http://youtu.be/RAReWAs_dEY Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 Derivative of y = x^n - Part 2: General Power Rule: http://youtu.be/Ibvu33oh49o Local and Absolute Max/Min and Critical Points/Numbers: http://youtu.be/aOvwQaEFbjw . ------------------------------------------------------ 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

In this video I have uploaded the 6th song titled "Osama" of the music album 1109 by Keor Meteor. This song outlines the role that CIA agent and patsy Osama bin Laden as a perennial "boogeyman" which the US can blame for anything and everything. Legendary radio broadcaster William "Bill" Cooper was the first to see through this farce, and Vice President Dick Cheney said the truth for the first time in his life. After Osama's (alleged) death, all criminal charges were dropped regarding 9/11 (of which he obviously had nothing to do with it) thus making him never formally charged and certainly not convicted even by mainstream standards. The original album and more links are listed below: - Original Album: https://keormeteor1.bandcamp.com/album/1109 - Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FUd8p-bzqCVSDd6gOcHcDr - Keor was inspired by my 9/11 Truth series: https://t.me/meslinks/22610 Timestamps and footage used are listed below: - William "Bill" Cooper 9/11 prediction: https://youtu.be/qPW_W_z6ovw: 0:00 - Vice President says Osama bin Laden was not involved in 9/11: 0:47 - US Government dismisses all charges against Osama after his death: 1:36 Related Videos: - #911Truth video series: https://www.youtube.com/playlist?list=PLai3U8-WIK0EzqTamtIXtgX8QudQSxuxh - Uncensored playlist: https://peakd.com/truth/@mes/911 - 9/11 Observable Evidence video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0G_HHWt33moIqEeUBP3cgCh . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes 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

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 . ------------------------------------------------------ Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes 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=gqe8gnRF8Ew