In this video I go over another model for modeling population growth, and this time look at an example of a model that accounts for seasonal growth. Sometimes the growth rate is affected seasonally, such as the availability of food during summer vs. winter, etc., so it is important to account for this periodic variability in the differential equation model. To do this, it is often modeled through using a time dependent factor, usually in the form of a trigonometric function because of their periodic wave-like behavior. In this video I derive the solution to such a seasonal-growth model, but in my next video I will look at analyzing the behavior of the solution with different values for the constants used in the model, so stay tuned for that video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhtoYJ-wyX1wSSS235g View Video Notes on Steemit: https://steemit.com/mathematics/@mes/population-growth-other-models-seasonal-growth-example-1-part-a Related Videos: Population Growth Other Models Gompertz Example 1: Part 2: https://youtu.be/MEMyYm6YWSU Population Growth: Other Models: Example 3: Extinction: https://youtu.be/Pa6UTdh2r9M Population Growth: Other Models: Harvesting: Example 2: https://youtu.be/jNAYTNhpZzk Population Growth: Other Models: Harvesting: Example 1 Part 2: https://youtu.be/l1n6WUOxYCs Population Growth: Other Models: Harvesting: Example 1 Part 1: https://youtu.be/ZLQEJwViIw0 Population Growth: Introduction to Other Models: https://youtu.be/-l5Anv9VA3M Differential Equations: Population Growth: https://youtu.be/Td8C_cTEGkA Differential Equations: Logistic Equation: Analytic Solution: https://youtu.be/BlvLWTSYDDk 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 Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0 Logarithms and their Properties - An Introduction: http://youtu.be/AZ6KKym19gI Trigonometry Identities: sin(-x) = - sin(x) and cos(-x) = cos(x): http://youtu.be/tD5EA2SXyFQ . ------------------------------------------------------ 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 Twitte ... https://www.youtube.com/watch?v=yl9GQWXpE0A

In this video I go over an example on determining the distance between two parallel planes. The first step is to find a point on one of the planes and then next is to simply apply the distance formula between a point to a plane that I derived in my earlier video. I also double check the distance by calculating it using the amazing GeoGebra 3D graphing calculator, which you can play around with here: https://www.geogebra.org/calculator/zmwhau8b The timestamps of key parts of the video are listed below: - Example 9: Distance Between Parallel Planes: 0:00 - Applying the Distance Formula from a Point to a Plane: 1:57 - Calculating Distance with GeoGebra 3D Graphing Calculator: 6:35 This video was taken from my earlier video listed below: - Equations of Lines and Planes: https://youtu.be/qWQz6qPhXR8 - Video notes: https://peakd.com/hive-128780/@mes/equations-of-lines-and-planes - Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FO3u0IupqllNNkZTsffpIV Related videos: Vectors and the Geometry of Space video series: 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=9B8bUqX5YHg

In #MESExperiments 22 I have repeated Experiment 21 by making sure the casing does not rotate as the gyroscopes rise thus confirming that some gyroscopes can in fact rise much quicker when extra weight is added. The earlier Experiment 21 involved comparing a gyroscope with no added weight with that of a 30% by-weight added putty gyro test, in which the added weight gyro rose by almost 3 times faster. Since the gyro spin speed was very fast, the casing of the non-added weight gyro was rotating rapidly during rising while the added weight gyro did not experience casing rotation. After criticism that the casing rotation may causing the slower rising rate of the non-added weight gyro test, I have repeated the experiment by adding a small 5% by-weight putty to ensure the gyro casing does not rotate. Thus in this video, I compare the same gyro without casing rotation for a 5% by-weight added putty with that of a 30% putty; and as expected the heavier added weight gyro test rose 2X faster. The original unedited experiments are shown in the links below: - No weight added test (Experiment 21): https://youtu.be/GUFSjbiLFw4 - Light weight added test: https://youtu.be/HgBnqnBZCUI - Heavy weight added test: https://youtu.be/agBSVjmE-nM Experiment 21 with the casing rotation can be view here: https://peakd.com/mesexperiments/@mes/mesexperiments-21-added-weight-can-make-a-gyroscope-rise-faster-magic The toy gyroscope weighs 100.63 g, the light putty weight weighs 5.44 g, and the heavy putty weight weights 29.67 g. The full experiment results, weight measurements, and screenshots of the experiment progression can be viewed on Hive: https://peakd.com/mesexperiments/@mes/mesexperiments-22-added-weight-can-make-a-gyroscope-rise-faster-no-casing-rotation Stay Tuned for #MESExperiments 23… Related Videos: ?#MESExperiments 21: Added Weight Can Make a Gyroscope Rise Faster #Magic: https://peakd.com/mesexperiments/@mes/mesexperiments-21-added-weight-can-make-a-gyroscope-rise-faster-magic ?#MESExperiments 11: Increasing Gyroscope Spin Speed Doesn't Necessarily Increase Rising Rate: https://peakd.com/mesexperiments/@mes/mesexperiments-11-increasing-gyroscope-spin-speed-doesn-t-necessarily-increase-rising-rate ?#MESScience 1: How Does a Powerball Gyroscope Work? + Gyros Are Inverted Pendulums: https://peakd.com/messcience/@mes/messcience-1-how-does-a-powerball-gyroscope-work-gyros-are-inverted-pendulums ☝#AntiGravity Part 6: Objects in Rotation Defy ‘Mainstream’ Physics + MES Duality Concept: https://peakd.com/antigravity/@mes/antigravity-part-6-video-1-objects-in-rotation-defy-mainstream-physics-mes-duality-concept #MESExperiments Video Series: https://peakd.com/mesexperiments/@mes/list DRAFT #MESExperiments Video Series: https://mes.fm/experiments-draft #MESScience Video Series: https://peakd.com/science/@mes/tutorials #AntiGravity Video Series: https://peakd.com/antigravity/@mes/series #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist . ------------------------------------------------------ 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 go over Part 6 of the Laboratory Project titled Running Circles Around Circles, and this time plot out varying types of Epicycloids. I use the same methods as in Parts 2 to 4 for which I plotted out Hypocycloids. In all the cases I assume that the outer circle has a radius b = 1, and then vary the fixed circle radius ‘a’ by considering it as a positive integer, a fraction, and an irrational number. The epicycloid shapes vary from multiple-leaf clovers, to Cardioids, to crazy spiral shapes. Also, as with hypocycloids, when the fixed circle radius, a, is an irrational number, as the range of the angle increases, the curves becomes more and more solid, and thus eventually appearing as a solid washer. This is a very cool video on once again using the amazing Desmos calculator, as well as for understanding the behavior of cool parametric curves, such as the epicycloid, so make sure to watch this video! Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuIZHtzQvHTuqvFlpA View Video Notes on Steemit: https://steemit.com/mathematics/@mes/running-circles-around-circles-part-6-graphing-epicycloids Related Videos: Running Circles Around Circles: Part 5: Epicycloid Proof: https://youtu.be/vPxcRlzC8dk Laboratory Project: Running Circles Around Circles: Part 4: https://youtu.be/sypHRx10RXM Laboratory Project: Running Circles Around Circles: Part 3: https://youtu.be/uCdvK29T5Z0 Laboratory Project: Running Circles Around Circles: Part 2: https://youtu.be/-hCw2HJF0YQ Laboratory Project: Running Circles Around Circles: Part 1: https://youtu.be/MiCqDNQN7_E Parametric Curves: Superellipses: https://youtu.be/JqkjQjtenPQ Parametric Curves: Example 11: Conchoids of Nicomedes: https://youtu.be/Ir1tVdwGWec Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk Parametric Curves: Example 6: Graphing Devices: https://youtu.be/cwpEasc9mhQ Parametric Curves: Example 5: Lissajous Figure: https://youtu.be/0OT1OnnAQ9I Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw . ------------------------------------------------------ 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 Calculato ... https://www.youtube.com/watch?v=vJAAJsrzrwk