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LBRY Claims • rotating-a-vector-proof

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@mes
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16 Dec 2023 21:58:34 UTC
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Rotating a Vector: Proof
In this video I derive the formula for rotating a vector by any specific angle. In the derivation, I utilize the cosine and sine angle addition identities which I had proved in my earlier videos. The concept of rotating vectors is very important in mathematics and physics, so make sure you fully grasp it!

This video was taken from my earlier video listed below:

- Complex Numbers as Rotation Matrices: https://youtu.be/Mgp2vrQeLEw
- Video notes: https://peakd.com/hive-128780/@mes/complex-numbers-as-rotation-matrices
- Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0E6x0dZEAx77Kqv7LLxYdbx

Related Videos:

Vectors and the Geometry of Space Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ .

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shifted-conics-example-2-horizontal
lbry://@mes/shifted-conics-example-2-horizontal
In this video I go over further into conic sections and this time go over a quick example on shifting a horizontal parabola, i.e. one that opens horizontally. The example involves graphing the parabola x = 1 – y^2 and while it is pretty straight forward to graph this equation, I follow the same methodology used in my earlier videos on shifted conic sections. This is to better illustrate how we can shift conic sections by simply replacing the x and y values with (x – h) and (y – k). Thus the formula x = -y^2 with the origin as the vertex gets shifted to (x – 1) = -y^2 and with vertex (1, 0). This is a very useful video in illustrating the steps in shifting a parabola, even though the parabola formula itself is pretty simple, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIh5gm4K-nyJof2EePHQ View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/shifted-conics-example-2-horizontal-parabola-notes Related Videos: Shifted Conics: Example 1: Parabola: https://youtu.be/VqxlOUqzvGY Shifted Conics: Hyperbolas: https://youtu.be/Evz6duQ2-U8 Shifted Conics: Parabolas: https://youtu.be/UlrAkAW3T8Y Shifted Conics: Ellipses (and Circles): https://youtu.be/ZqtUfaQbj7U Conic Sections: Hyperbola: Definition and Formula: https://youtu.be/UBIHovXNV9U Conic Sections: Parabolas: Definition and Formula: https://youtu.be/kCJjXuuIqbE Conic Sections: Ellipses: Definition and Derivation of Formula (Including Circles): https://youtu.be/9dETsJ2tz_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: 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
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DERIV
derivatives-of-hyperbolic-trigonometry
lbry://@mes/derivatives-of-hyperbolic-trigonometry
In this video I go over the derivative of hyperbolic secant or sech(x) and show that it is equal to -sech(x)tanh(x). Download the notes in my video: https://www.dropbox.com/s/ouy3zvgiq11u8sq/442%20-%20Derivative%20Hyperbolic%20Functions%20Proof%20-%20sech%28x%29.pdf Related Videos: Derivatives of Hyperbolic Trigonometry: csch(x): http://youtu.be/K2mqMP-gVTw Derivatives of Hyperbolic Trigonometry: tanh(x): http://youtu.be/BAPcdco7zBk Derivatives of Hyperbolic Trigonometry: cosh(x): http://youtu.be/4AGkxTGxASQ Derivatives of Hyperbolic Trigonometry: sinh(x): http://youtu.be/9QpIDqYg52c Hyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1: http://youtu.be/Y6iYC4VEAi0 Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc Derivative of Hyperbolic functions - y = sinh(x), tanh(x), cosh(x): http://youtu.be/tdlbLP5pzis Derivative of Inverse Hyperbolic Functions: inverse sinh(x), cosh(x), tanh(x): http://youtu.be/ubYbYbJOsNs 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 . ------------------------------------------------------ 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-apps ... https://www.youtube.com/watch?v=ozsEwXpHXZs
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geometry-of-a-tetrahedron-question-3-3d
lbry://@mes/geometry-of-a-tetrahedron-question-3-3d
In this video I go over Question 3 of the Discovery Project: Geometry of a Tetrahedron. This question uses the results from Question 1, in which I calculated the areas of the 4 triangular faces. Using those results, I show that the area squared of the opposite triangular face is equal to the sum of the squares of the 3 areas adjacent to the opposite vertex. In other words, we have a three-dimensional version of the Pythagorean Theorem: D^2 = A^2 + B^2 + C^2 This video was taken from my earlier video listed below: - Discovery Project: The Geometry of a Tetrahedron: https://youtu.be/yRws7Jk2iHU - Video notes: https://peakd.com/hive-128780/@mes/discovery-project-geometry-of-a-tetrahedron - Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0GoEi9wxl8nTFcfw1ay-_1T . ------------------------------------------------------ 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=kkKOsLoF3tA
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problems-plus-26-partial-sum-of-harmonic
lbry://@mes/problems-plus-26-partial-sum-of-harmonic
In this video I go over a very unique problem on showing that the n-th partial sum of the harmonic series is NOT an integer. The harmonic series is the sum of the terms 1/i where i is a positive integer. To show that the partial sum is not an integer, we require some truly outside-of-the-box thinking, which fortunately for us is made easier with the given hint. To prove this, we first assume that the partial sum IS an integer and then observe what happens to 2 similar equations. The first is the multiplication of (the product of all odd integers less than or equal to n) * (the largest power of 2 that is less than or equal to n) * (partial sum). The second equation is the same as the first but with the assumption that the partial sum is an integer. After going over some very unique mathematical reasoning, I show that the left side of the equation is always odd while the right side is always even. This is a contradiction and thus the partial sum can not be an integer! Pretty epic brain twister! The timestamps of key parts of the video are listed below: - Problem 26: Partial Sum of Harmonic Series is NOT an Integer: 0:00 - Solution: 2:27 - Right side of hint equation is even: 4:16 - Left side of hint equation is odd: 7:23 - Checking when r is less than k: 13:41 - Checking when r = k: 16:56 - Summary: Partial Sum of Harmonic Series is NOT an integer: 20:45 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=AknFzsQ1dZU
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parametric-calculus-arc-length-example-2
lbry://@mes/parametric-calculus-arc-length-example-2
In this video I go over another example on determining the arc length of a parametric curve, and this time revisit the unit circle but instead deal with a slightly different set of parametric equations, namely x = sin(2t) and y = cos(2t) for the interval where t is between 0 and 2*pi. The interesting thing about this curve is that the point traced on the curve completes two full cycles or revolutions of the circle. This means that using the arc length formula measures double the parametric curve, or twice circumference of the circle, namely 4*pi. This is a very important example because it illustrates the need to always be careful about selecting the interval of the parametric curve to ensure that the curve is only traced once, otherwise the arc length will be longer than expected, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuRWpZqN2T-EmOnrQQ View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-calculus-arc-length-example-2-unit-circle Related Videos: Parametric Calculus: Arc Length: Example 1: Unit Circle: https://youtu.be/leyln2bRCpk Parametric Calculus: Arc Length Part 1: https://youtu.be/AWvJDK-m6wQ Parametric Calculus: Areas: https://youtu.be/XdplYV61xlM Parametric Calculus: Tangents: https://youtu.be/deQwD2o0Sas Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Applications of Integrals: Arc Length Proof: https://youtu.be/2rb4H_rmgxg Parametric Curves: Example 2: Unit Circle: https://youtu.be/SBkzZDlqTTE Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: http://youtu.be/o-fAx_96lgw Parametric Curves: Example 3: Unit Circle: https://youtu.be/VpiJdEviBbk . ------------------------------------------------------ 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-apps ... https://www.youtube.com/watch?v=X-iElfvx34c
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lbry://@mes/5-pin-bowling-scoring-and-free
I recently played 5 pin bowling for the first time ever and I really enjoyed it and thought it would be fun doing a video tutorial on it's unique scoring system. I also made a Microsoft Excel 5 Pin Bowling Scores Calculator and you can download that in the link below! Download the notes in my video: PDF Document: https://www.dropbox.com/s/vvjl8mu90av2q82/251%20-%205%20Pin%20Bowling%20Scores.pdf Excel Calculator: https://www.dropbox.com/s/f2x5d36nusxlrny/251%20-%205%20Pin%20Bowling%20Calculator.xlsx Related Videos: Bowling Scoring System: 10 Pin Bowling: http://youtu.be/EsMocP3Gx-g . ------------------------------------------------------ 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-apps ... https://www.youtube.com/watch?v=ezXX5RlHRXk
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derivatives-application-electrical
lbry://@mes/derivatives-application-electrical
In this video I go over another derivatives application and show how the electrical current can be defined using the definition of the derivative. The electrical current is the rate of change of the electrical charge with time which makes it applicable to write it as a derivative because the derivative can also be interpreted as a rate of change. Download the notes in my video: https://www.dropbox.com/s/qyuy4jdgv6lwec8/393%20-%20Derivatives%20Application%20Example%20-%20Current.pdf Related Videos: Derivatives Application: Linear Density: http://youtu.be/2-GjlsX3yOc Derivative Application: Deriving the Velocity from the Distance Function: http://youtu.be/3oT83konhlU Interpretation of the Derivative as a Rate of Change: http://youtu.be/3nu6U-p6Ctg Definition of Derivative Simple Explanation: http://youtu.be/0rjGMpM06Eg . ------------------------------------------------------ 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-apps ... https://www.youtube.com/watch?v=JOiWE3JSAuQ
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true-false-quiz-question-1-series-may-or
lbry://@mes/true-false-quiz-question-1-series-may-or
In this video I go over the first question of the True-False Quiz from my Calculus Book on infinite sequence and series, and show a series may or may not converge if the limit of the terms go to zero. Thus Question 1 is false. An example is the Harmonic series is a divergent p-series whose limit of the terms approach zero but the sum diverges to infinite. Note that the reverse is actually true, that is, if a series is convergent then the limit of the terms must approach zero. Timestamps: - Question 1: 0:00 - Solution: False: 0:42 - Note: Harmonic series is a divergent p-series: 1:47 This video was taken from my earlier video listed below: - Infinite Sequences and Series: Review and True-False Quiz: https://youtu.be/F0dsQLdXXpI - HIVE video notes: https://peakd.com/hive-128780/@mes/infinite-sequences-and-series-review-and-true-false-quiz - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FCqXVJv1r7eJvrvphfkr6L Related Videos: Infinite Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ 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=i1i7Q_r3UnA
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DIFFE
differential-equations-orthogonal
lbry://@mes/differential-equations-orthogonal
In this video I go over a recap on orthogonal trajectories as well as an example on how to go about solving for a family of orthogonal trajectories to the parabolas x = k*y^2, where k is a constant. The first step is to write the parabolas equation as a differential equation and solve for the derivative. Then, as proved in my earlier video, if a curve is perpendicular or orthogonal to another, then the slopes of the tangent line must be a negative reciprocal to the tangent line of the other curves. Thus from this fact we can obtain a second differential equation, which luckily is a separable equation, and can be solved resulting in a family of ellipses. This is a very useful example on the steps involved in determining the orthogonal trajectories, which are actually used a lot in physics and engineering applications such as electricity and fluid-dynamics! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhssPKzJnQRYh0guekA View Video Notes on Steemit: https://steemit.com/mathematics/@mes/differential-equations-orthogonal-trajectories-example-1 Related Videos: Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94 Differential Equations: Euler's Method: Example 2: https://youtu.be/-4qb_mniDR0 Differential Equations: Euler's Method: Example 1: https://youtu.be/L_l5DLZsZLQ 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 Orthogonal Trajectories - A Brief Introduction: http://youtu.be/b4GpN01EiAc Negative Reciprocals and Perpendicular Lines: http://youtu.be/Ue7FmrfmuX4 . ------------------------------------------------------ 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://mor ... https://www.youtube.com/watch?v=WE5Zltu-9cI
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