Population Growth: Other Models: Harvesting: Example 2
In this video I continue further into the series on other models for population growth as opposed to the basic logistic and exponential models. This time I look again at the modification of the logistic equation by adding a negative constant to it, which in terms of a fish population represents the harvesting or collecting of fish at a constant rate. This time I look at varying the values of the constant and graphing the resulting direction fields to see where the equilibrium solutions occur as well as determining at which c-values that no equilibrium solutions occur. When no equilibrium arises, this means that the fish population keeps decreasing until it completely dies offs, which indicates that overfishing took place. This is a very important video on using differential equations to model and affect decisions that fishers and fishing industries must make, so make sure to watch this video!
In this video I go over the vector equation of a line segment instead of the entire line. I first start off with an example involving parametric equations and noting that setting the parameter t = 0 gets the first point on the line, while setting it to t = 1 gets the second point. From this fact, we can start off with our usual vector equation of a line and then describe it using our desired starting and ending vector, which point to the 2 positions of a line we want. Then we can just impose the interval of the parameter t to be from 0 to 1 to get our desired line segment!
The timestamps of key parts of the video are listed below:
- Parametric Equations of a Line Segment Example: 0:00
- General Vector Equation of a Line Segment: 5:32
- Summary of Equation of a Line Segment: 11:58
- Note on t = 0 and t = 1: 12:40
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 .
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https://www.youtube.com/watch?v=WG8C-5aonjY
UPDATE: I just realized I made a typo at the 3:26 mark of the video. I added an extra θ by accident. Can you spot it??
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In this video I go over part 3 of the Laboratory Project titled Running Circles Around Circles. In this part I continue to play around with the parametric equations for a cycloid and this time look at how the curves look when we make the 'a' constant a fraction. Graphs of several values of a are plotted which show just how cool the parametric curves can get. Some of the curves include a star shape, and even an apple or heart shape! This is a great video on graphing using the Desmos calculator, so make sure to watch this video (and try out their calculator)!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuFsxqoYlL4N4vPFyQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/running-circles-around-circles-part-3-amazing-hypocycloids
Related Videos:
Laboratory Project: Running Circles Around Circles: Part 1: https://youtu.be/MiCqDNQN7_E
Laboratory Project: Running Circles Around Circles: Part 2: https://youtu.be/-hCw2HJF0YQ
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 .
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https://www.youtube.com/watch?v=uCdvK29T5Z0
In my earlier video I showed calculated by hand 111,111,111 x 111,111,111 and showed that it is equal to 12345678987654321 but I solved that using basic hand multiplication techniques and the calculation was very tedious. But in this video I show how you can calculate any multiplication that involves only the number 1 in just a few seconds! This video is a must see and you can definitely show off you calculation skills to friends!
Download the notes in my video: https://www.dropbox.com/s/pkeakwcccu3i3m3/394%20-%20Multiplying%20by%201s%20-%20Easy%20Method.pdf
Related Videos:
111,111,111 x 111,111,111 = 12345678987654321 - Hand Calculation: http://youtu.be/N1g-fe7ZxfA
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 .
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https://www.youtube.com/watch?v=XUF6HaiKzMY
In this video I go over differentials notation when dealing with linear approximations. That is, to write linear approximations using the differentials dy and dx. This notation system (also known as Leibniz notation) is very useful because it makes writing linear approximations very simple and straight forward.
Download the notes in my video: http://sdrv.ms/1bXtBkQ
Related Videos:
Linear Approximation: Introduction: http://youtu.be/nepXMVPFmkc
Linear Approximation: Example on Square Roots: http://youtu.be/mLFa8QfH8qE
Equation of a Line - A Simple Explanation: http://youtu.be/a3ntO-xNN5M
Tangent and Secant Lines: http://youtu.be/9E6fBySBsYw
Equation of Tangent Lines - Examples: http://youtu.be/VqIhcWmCx_Q .
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https://www.youtube.com/watch?v=NBXH3P_qekU
In this video I sketch a hyperboloid of two sheets, which is a quadric surface with horizontal traces being hyperbolas while vertical traces are comprised of both hyperbolas and ellipses. There are no vertical traces in the xz-plane thus the quadric surface is split into two sheets, hence the name: Hyperboloid of Two Sheets.
GeoGebra 3D graphing calculator: https://www.geogebra.org/3d/tabys4ec
Time stamps:
- Example 7: Hyperboloid of Two Sheets: 0:00
- Solution: Re-arranging equation into standard form: 0:17
- Comparing equation with hyperboloid of two sheets from Table 1: 1:56
- Traces in xy and yz-planes are hyperbolas: 2:09
- Traces in y = k planes are ellipses: 3:41
- No traces in the xz-plane: 5:57
- Re-writing y = k traces equation: 6:44
- Sketching the graph using traces: 7:48
- Graphing in GeoGebra: 10:55
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 my brother Mark aka MFA goes over another NBA basketball video and this time explores the infamous Hack-a-Shaq strategy. This strategy involves intentionally fouling a poor free throw shooter and is named after historically bad free throw shooter Shaquille O'Neal. To analyze if this is a good strategy or not, MFA calculates the league average for points per possession in the 2021-2022 NBA season and found it to be 1.146 points / possession. This translates to a free throw percentage of 57.3%. This means that intentionally fouling a player that shoots below 57.3% benefits your team but above this % it hurts your team. For example, Stephen Curry shoots 92.3% from the free throw line, so you should definitely avoid fouling Steph!
Note that additional factors need to be considered when employing the Hack-a-Shaq strategy, such as getting into the Bonus too early or new NBA rules that penalize intentionally fouling opponents at the final 2 minutes of each quarter. Also note that the "Bonus" is when a team goes above 4 fouls in a quarter, thus resulting in 2 free throws even in non-shooting motions.
The timestamps of the video are shown below:
0:00 - History of the Hack-a-Shaq
0:27 - Intentionally Fouling an Opponent
0:39 - 2021-2022 NBA Season
0:59 - Don't Foul Steph Curry!
1:38 - What % Free Throw Shooter Should be Intentionally Fouled?
2:05 - Conclusion
Download Video Notes: https://1drv.ms/b/s!As32ynv0LoaIidJaHnh5CfQWGPSb2A?e=5ctXi6
Related Videos:
View the full NBA Basketball video playlist: https://www.youtube.com/playlist?list=PL43B7E7AE41C847FA
NBA Three Pointers vs Two Pointers: Which is Better? https://peakd.com/hive-128780/@mes/nba-three-pointers-vs-two-pointers .
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https://www.youtube.com/watch?v=Zq_aDORR880
In this video, Mark aka MFA, goes over the definition of 20/20 vision as well as going through some examples on different types of vision based on using the widely used Snellen Chart. The Snellen Chart was created by the Dutch ophthalmologist Herman Snellen in 1862 and has been used worldwide since.
Basically having 20/20 vision means that at 20 feet, you can see as well as a nominal, or predefined normal person's vision at 20 feet. Where normal vision is defined as being able to see 2 lines separated by 1.75mm apart from 20 feet. A person with 20/30 vision means that you can see from 20 feet the same as a normal person from 20 feet.
Download the notes in my video: http://1drv.ms/1M0GJck
View Video Notes on Steemit: https://steemit.com/science/@mes/what-is-20-20-vision
Related Videos:
Difference Between Expresso and Coffee: http://youtu.be/0zcRNLfOMIg
Food and Nutrition: What are Calories? and How much in Carbs, Fat, Protein, and Alcohol?: http://youtu.be/RaKutEJc64g
Does Coffee and Tea Count Towards Water Intake?: http://youtu.be/WMVpJatcktg
Water from Food and 8 Cups of Water Myth: http://youtu.be/uvxU09XmQNU
Complete Proteins - Vegetarian Diet and Myths about Plant Proteins: http://youtu.be/LHzzutoupY0 .
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https://www.youtube.com/watch?v=31kYnnIjugQ
In this video I explain a very useful topic in Water Mechanics which is used throughout much of engineering, Buoyancy. In around 200-300 BC Archimedes formulated and showed that any object in a fluid has a buoyant force that tries to keep up floating upwards and that force was equal to the weight of the displaced volume of fluid due to the object. This is known as Archimedes' Principle and I show an easy to follow proof and example of how to use it through force equilibrium or free body diagrams.
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIiedLs6aY3HDy5irrWA?e=u384MS
View video notes on the Hive blockchain: https://peakd.com/hive-128780/@mes/buoyancy-archimedes-principle-proof
Related Videos:
Soil Mechanics 101 - Phase Relations: http://youtu.be/DtKheQcL2BU
Types of Tailings Embankments: Upstream, Downstream and Centerline Construction Methods: http://youtu.be/1wm1XR6z-QE
Simplified Filter Criteria: A Dam Filter Example: http://youtu.be/yGEeYAb4Olw .
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In this video I continue on to part 2 of example 1 on the predator-prey systems using the Lotka-Volterra equations which I derived in my earlier videos. In part 2 I go over parts d) and e) of the example. These parts involved looking closely at a specific phase trajectory and then from that predict the population curves for both wolves and rabbits. The data from the Hudson Bay Companies fur trading business of hares and lynxes over a 90 year period was used to compare how well the Lotka-Volterra models compare with real-world applications. In turns out that the HBC data generally does in fact follow the model developed in this example. This is a very interesting video on showing how real-life applications can be represented and modeled through mathematics, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht03MC9m9w54TJAO2g
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/predator-prey-systems-example-1-part-2
Related Videos:
Predator-Prey Systems: Example 1: Part 1: https://youtu.be/dkQYqI4FXxA
Differential Equations: Predator-Prey Systems: https://youtu.be/b3NCjsZhQdQ
Linear Differential Equations: https://youtu.be/T3MliJDBaxc
Differential Equations: Exponential Growth and Decay: https://youtu.be/DZtDUIZuxcg
Differential Equations: Separable Equations: https://youtu.be/pBV-xT9ty94
Power Functions and their Properties Part 1 - A Simple Explanation: http://youtu.be/2MKko4ZkSf0
Differential Equations: Electric Circuit: Introduction: https://youtu.be/E6vij-RzQ-o
Differential Equations: Separable Equations: Example 4: https://youtu.be/75CyQpqbYV .
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https://www.youtube.com/watch?v=Jvpl1qpBLa8