Pen and Paper Science
Pen and Paper Science
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Why I haven't uploaded...
⭐️ COUPON CODE: PENANDPAPERSCIENCE2
👉Link: www.udemy.com/course/statistics-for-data-scientists/?referralCode=F0802B4DC85BBA1CCD55
Where have I been? Well, I've been busy creating a complete course on Statistics! It recently launched on Udemy. The course treats most of the topic within Statistics that you need to build a solid foundation. We focus on cultivating an intuitive understanding by simulating artificial scenarios using Python code.
⭐️ YOUR free math and science tutor: www.ai-tutor.io
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-- discord.gg/mrdvf6VK6k
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👍 Thanks for watching!
#course #statistics #coupon
Переглядів: 248

Відео

Rotation Matrix: Example Exercise - Step-by-Step!
Переглядів 7617 місяців тому
👉 In this video we use the Rotation Matrix to see how a square is described in a rotated coordinate axis. This is a follow-up on the video where we derive the rotation matrix step-by-step. ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the comment section below or join the Discord Server! discord.gg/...
Frictional Energy: How Far Does It Slide? Step-by-Step solution! 🚀
Переглядів 19411 місяців тому
👉 An object slides down an inclined plane without friction. Upon reaching the bottom it slides across a surface with non-zero friction coefficient. The question asked is how far will the object slide given its mass and height above the ground it started. We will solve this exercise by using conservation of energy. ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questio...
Solving THIS Numeric Puzzle Step-by-Step! 🤓
Переглядів 5811 місяців тому
👉 The sum of three consecutive odd numbers is 75. Can YOU find the smallest number? In this video we translate this sentence to a mathematical formulation that we can solve to find the solution to this puzzle. ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the comment section below or join the Discor...
How To Solve This Different Type Of Integrals, Step-by-Step! 😱
Переглядів 16711 місяців тому
👉 Integrals of the form f(x)*f'(x)dx can be solved by using a very simple trick. In this video, however, we first solve such an integral by using substitution Step-by-Step. Afterwards we check our result with what we could have obtained much easier. ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the ...
How to Solve This Geometry Puzzle Step-by-Step. 🤯
Переглядів 14511 місяців тому
👉 How to solve such geometry puzzles, step-by-step approach. Given two concentric circles with radius R1 and R2, and a tangent line to the inner circle, touching the outer circle. Can you find the expression for C in terms of R1 and R2? ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the comment secti...
Working With Nested Functions - A Puzzle 🧩
Переглядів 85Рік тому
👉 In this video we learn about how to work with nested functions, and how you cannot simply swap them around. In particular, f(g(x)) is not always equal to g(f(x)). ⭐️ YOUR free math and science tutor: www.ai-tutor.io 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the comment section below or join the Discord Server! discord.gg/mrdvf6VK6k 🎥 Subscribe: ...
Can YOU Solve This Puzzle? Using AI for Math.
Переглядів 81Рік тому
⭐️ Try for Free: www.ai-tutor.io 📚 In this video we try to solve the following puzzle: "For which three consecutive numbers is their sum equal to their product?". In the end, we will use AI to help us along the way. One of the most important things to do is to translate a problem into mathematical language. ⏱ Timestamps: 00:00 start 00:30 Translate to mathematics 02:13 Mathematical Statement to...
AI Solves Math: How To Solve A Set Of Equations Step-By-Step.
Переглядів 256Рік тому
⭐️ Try for Free: www.ai-tutor.io 📚 In this video we solve a set of two linear equations using the help of an AI-tutor. This is AI technology that helps you with homework and other math and science problems. ⏱ Timestamps: 00:00 start 01:57 Using the first equation 02:23 Substitution step 03:55 y = -1 04:29 x = 1 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me kn...
AI solves Trigonometry Equation Step-by-Step. AI Homework Assistant. 🤯
Переглядів 350Рік тому
⭐️ Try for Free: www.ai-tutor.io 📚 In this video we use AI technology to help us solve the trigonometry equation sin(2x) - cos(x) = 0. These equations can be very difficult to solve, but thanks to our trusty AI-tutor we get hints that help us on our way. ⏱ Timestamps: 00:00 start 00:48 First Hint 02:20 Factorisation 04:30 First subproblem 05:13 Second subproblem 06:30 FINAL SOLUTION 🙋‍♀️ If you...
AI Solves Integral step-by-step. AI homework assistant.
Переглядів 6 тис.Рік тому
⭐️ AI-TUTOR: www.ai-tutor.io 📚 In this video we use AI technology to help us solve an integral. The AI-tutor doesn't just give us the solution, but instead guides us with questions. 🙋‍♀️ If you have any questions, remarks, or suggestions for future topics, let me know in the comment section below or join the Discord Server! discord.gg/mrdvf6VK6k 🎥 Subscribe: ua-cam.com/users/timok 👍 Thanks for ...
Can You Solve This Puzzle?
Переглядів 356Рік тому
⭐️ OTHER PUZZLES: Geometry Puzzle: ua-cam.com/video/n4DWG8zNGks/v-deo.html Trigonometry Puzzle: ua-cam.com/users/shortsoC5WnzVm1WA Derivatives Puzzle: ua-cam.com/video/M-rrMGFmZ_w/v-deo.html Geometry Puzzle 2: ua-cam.com/video/IC-xJIGSuSc/v-deo.html 📚 Can you solve this Geometry Puzzle where you need to find that line that cuts BOTH rectangles in half? 🙋‍♀️ If you have any questions, remarks, o...
Step-by-Step Calculation of the Taylor Expansion: sqrt(1+x)
Переглядів 4,8 тис.Рік тому
📚 How to calculate the Taylor Expansion of sqrt(1 x). This is what we will do in this video, step-by-step. We will compute the first 4 terms in the series. ⏱ Timestamps: 00:00 Intro 00:19 General Formula 00:49 First Term 01:36 Second Term 02:18 Third Term 02:53 Fourth Term ⭐️ Related content: Taylor Expansion of e^x: ua-cam.com/video/ZcvxlNKKY_Q/v-deo.html Taylor Expansion Explaining Each Term:...
Hydraulic Principle : Hydrostatics Exercise (Step-by-Step)
Переглядів 171Рік тому
☝️In this video we are solving an exercise on Hydrostatics, in particular the Hydraulic Principle. We compute how much leverage we can achieve. In this way we learn about physics by doing exercises step by step :) ⏱ Timestamps: 0:00 Intro 00:14 Set-up 01:20 Step 1: Pressure in point 1 02:30 Step 2: Force in point 2 03:48 Step 3: RESULT 04:24 General Principle 05:02 Outro ⭐️ Related content: Hyd...
Calculate Permutations Of Atoms: Combination 3
Переглядів 198Рік тому
👉 NEW VIDEO on the ARROW OF TIME: ua-cam.com/video/lW7HT6IxI_o/v-deo.html ⭐️ In this video we are computing the number of permutations of placing different coloured atoms on a grid. It is a nice exercise on how to calculate permutations, without having to learn the formula by heart. ⏱ Timestamps: 0:00 Intro 01:16 No Mixed Atoms 02:27 One Atom Of Mixture 06:23 Two Mixed Atoms 15:07 Three Mixed A...
Real Life Derivatives Problem - Maximum Volume!
Переглядів 714Рік тому
Real Life Derivatives Problem - Maximum Volume!
Taylor Expansion Of cos(x): How To Calculate!
Переглядів 358Рік тому
Taylor Expansion Of cos(x): How To Calculate!
The Draining Tank Exercise - Hydrostatics Step-by-Step
Переглядів 431Рік тому
The Draining Tank Exercise - Hydrostatics Step-by-Step
How To Calculate The Taylor Expansion of e^x?
Переглядів 526Рік тому
How To Calculate The Taylor Expansion of e^x?
How To Invert This Special Matrix?
Переглядів 729Рік тому
How To Invert This Special Matrix?
Understanding Every Symbol - Taylor Expansion
Переглядів 228Рік тому
Understanding Every Symbol - Taylor Expansion
How to do Integration By Parts - REVIEW SESSION
Переглядів 180Рік тому
How to do Integration By Parts - REVIEW SESSION
Function Analysis - REVIEW SESSION
Переглядів 71Рік тому
Function Analysis - REVIEW SESSION
How To Calculate Derivatives - REVIEW session
Переглядів 200Рік тому
How To Calculate Derivatives - REVIEW session
How To Solve Systems Of Equations - REVIEW session
Переглядів 85Рік тому
How To Solve Systems Of Equations - REVIEW session
How to Solve Polynomials - REVIEW session
Переглядів 90Рік тому
How to Solve Polynomials - REVIEW session
Matrix Algebra Review Session #backtobasics
Переглядів 398Рік тому
Matrix Algebra Review Session #backtobasics
An Alternative Look At Pressure!
Переглядів 117Рік тому
An Alternative Look At Pressure!
The Sigmoid Function Derivative - Step-by-step
Переглядів 1,4 тис.Рік тому
The Sigmoid Function Derivative - Step-by-step
A Surprising Application Of Bernoullis Law
Переглядів 228Рік тому
A Surprising Application Of Bernoullis Law

КОМЕНТАРІ

  • @MrRichie444
    @MrRichie444 День тому

    1 is equal to -1, just that -1 is moving in the opposite direction

    • @PenandPaperScience
      @PenandPaperScience День тому

      What you're saying is correct: the magnitude (or absolute value) of -1 and 1 are equal: namely 1.

  • @lillii9119
    @lillii9119 День тому

    Either define √x as +√x OR -√x Or √x is undefined for negative and complex input

  • @deshsharma2277
    @deshsharma2277 2 дні тому

    *Forget any big numbers, I guarantee no humans will even come close to fully comprehending (actually picturing in the brain) this number.* *3↑↑↑3 (or 3^^^^3 which is* *_3^(7,625,597,484,987)._* *To give you some perspective, there are only about 1.3 x 10^50 atoms in this world. That's a 13 followed by 50 zeros (1,300,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000).* *Now, let's try this: the number of molecules in all the oceans is approximately 4.7 x 10^46 (give or take several orders of magnitude).* *Can you picture a number with 46 or 48 zeros? If you succeeded, now try to picture a number that has over 3 trillion digits: *3^(7,625,597,484,987)*

  • @joelakowei1757
    @joelakowei1757 6 днів тому

    Utter Oblivion

  • @TravelWalksVibes-jh5xh
    @TravelWalksVibes-jh5xh 7 днів тому

    Hope u ll be back soon with more videos.Keep it up

    • @PenandPaperScience
      @PenandPaperScience 7 днів тому

      Thanks! What kind of video would you watch, on what topic? :)

  • @lovegro3649
    @lovegro3649 8 днів тому

    Wow, this was an amazing explanation! thank you

    • @PenandPaperScience
      @PenandPaperScience 8 днів тому

      You're very welcome! It's always a pleasure to read a comment like this one, thanks! (:

  • @JosefNovak-ge9sn
    @JosefNovak-ge9sn 9 днів тому

    you are amazing in mathematic. SUper.

  • @Anamika-gm8re
    @Anamika-gm8re 10 днів тому

    Now am totally Satisfied 🙇

    • @PenandPaperScience
      @PenandPaperScience 10 днів тому

      Haha :D You're the first one to comment on this video. Computing a 4x4 determinant is not for the faint of heart!

  • @Kek_lucifer
    @Kek_lucifer 17 днів тому

    Keep it up Hope u ll be back soon with more videos

  • @xxxhristopher
    @xxxhristopher 18 днів тому

    This was wonderful 🤧

  • @TeamUnpro
    @TeamUnpro 19 днів тому

    its insane how efficient this is, its no wonder libraries like LG uses matrices

  • @savitatawade2403
    @savitatawade2403 Місяць тому

    wait a minute, cant we derive a general formula for this? i infact seem to notice that if *a>b, then a^b<b^a* for some reason, but im not able to prove this maybe you can help

  • @jungminlee-ot5zq
    @jungminlee-ot5zq Місяць тому

    ㅈㅈㅈㅊㅈㅈㅈㅈㅈㅈㅈㅈㅉㅈㅈㅈㅈㅈ .

  • @nikhilbontha1621
    @nikhilbontha1621 Місяць тому

    Simple: 2022 - 2024 = -2. 2022 will be a factor of Graham's number of years ago within eight months.

  • @nikhilbontha1621
    @nikhilbontha1621 Місяць тому

    _3(3) is an unnecessarily large factor of Graham's number.

  • @nikhilbontha1621
    @nikhilbontha1621 Місяць тому

    Infinity is not a real number, so it'sn't allowed.

  • @user-qe5zm2yq7e
    @user-qe5zm2yq7e Місяць тому

    Thanks man 👍

  • @Fuel_for_SuccessG
    @Fuel_for_SuccessG Місяць тому

    I just can’t seem to understand nothing

    • @PenandPaperScience
      @PenandPaperScience Місяць тому

      Can you pinpoint the point where you seem to get lost? That's the first step :)

  • @Jenny-kq9jv
    @Jenny-kq9jv 2 місяці тому

    Hi, I love the video, but I have one question: when I change the x and y values of a function to xcos(b)-ysin(b) and xsin(b)+ycos(b) on Desmos graphing calculator , where b is the degree we want to rotate the function by, the function actually rotates in a clockwise direction instead of anticlockwise like shown in the diagram in the video, and I’m very confused about why?

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      You raise an excellent point. The difference has to do with your point of view: In this video I show how to derive the rotation matrix if you want to rotate a vector within a fixed coordinate system (x-y). But: if you use this same matrix and apply it to your x and y axes, you are basically rotating your coordinate axis, and not the vector. Now imagine the following: rotating your coordinate axes clockwise over an angle b, then what that equivalently does is rotating any vector (or function) inside that coordinate system *counter clockwise* over the same angle. Does that make sense? :)

  • @MichaelDarrow-tr1mn
    @MichaelDarrow-tr1mn 2 місяці тому

    Can you calculate the chance for 8 cards to include exactly two pairs

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      Sure, that's possible! In fact, you can do so with the exact same reasoning, and it's an excellent exercise to see whether you understand how it works :)

  • @Omaryyo
    @Omaryyo 2 місяці тому

    What if we start with 1000^1001/1001^1000?

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      Then, it gets a bit more complicated since you cannot simplify. But, you should have a go :D

  • @sreser111
    @sreser111 2 місяці тому

    that's funny i was in bed and listening to the videos and never had herd this one before. My first thought was Grahams number when you started and asked us. of course i had no idea the title of this vid. So yea not all people think of small numbers.

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      Yeah, that's a good point :D Though, I think you are one of the few ;)

  • @BCSFM-ku2fr
    @BCSFM-ku2fr 2 місяці тому

    loved ittttt

  • @jasonzhang7725
    @jasonzhang7725 2 місяці тому

    THANK YOU VERY MUCH!!!!

  •  2 місяці тому

    remember: the event that occurs First goes to the Right side of the bar e.g. P(A|B) B happened first P(B|A) A happened first Start by defining what is A and what is B

  • @realdragon
    @realdragon 2 місяці тому

    Great video

  • @mr.stranger3417
    @mr.stranger3417 2 місяці тому

    Thank you so much for your efforts sir 💞🌈🍀 so helpful for us 😀

  • @slifer4963
    @slifer4963 2 місяці тому

    Hey there, in the first exercise, do you know why [x' y"] is written in a 2x1 matrix instead of a 1x2 matrix? Like : | a | | b | instead of [a b]

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      I'm not entirely sure, but it *has* to be written as a 2x1 matrix for the matrix multiplication to be valid. If you want to get the new vector R_new = Matrix * R_old. Does that answer your question?

  • @liquidportal9082
    @liquidportal9082 2 місяці тому

    By far the best derivation for rotational matrices on UA-cam. Excellent work.

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      Thank you for the kind words! I'm glad I could help :))

  • @leandrogcosta
    @leandrogcosta 2 місяці тому

    Very good!

  • @MuhammadSadiq-gz8go
    @MuhammadSadiq-gz8go 3 місяці тому

    I am very lucky to found this video what a good explanation

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      Again, thanks for commenting! I am very happy I could help :)

  • @MuhammadSadiq-gz8go
    @MuhammadSadiq-gz8go 3 місяці тому

    really good explanation of vectors

  • @jacksonmadison9994
    @jacksonmadison9994 3 місяці тому

    What’s the difference between fundamental matrix and matrix exponential ?

    • @PenandPaperScience
      @PenandPaperScience 2 місяці тому

      What do you mean with fundamental matrix? The matrix exponential is different because it might not be evident to know what it means to have a matrix in the exponent.

  • @coffeeklepto1067
    @coffeeklepto1067 3 місяці тому

    Thanks for the assist with this. Great visuals and procedures. Much appreciated!!

  • @TheXxxprotogirlxxx
    @TheXxxprotogirlxxx 3 місяці тому

    really good video!

  • @waltermadao4300
    @waltermadao4300 3 місяці тому

    Thanks for the in-depth explanation 👍

  • @ameliedzinka
    @ameliedzinka 3 місяці тому

    Finally, a normal explanation. Because everybody starts with a vector rotated from 0 angle.

  • @TheLuminousOne
    @TheLuminousOne 3 місяці тому

    i heard the Oíler equation's very slippery to deal with

  • @Fouriersuir
    @Fouriersuir 3 місяці тому

    Isn’t there a faster way for the second question? Since we are modelling the pendulum as just a normal sine function (there’s no energy loss in this scenario) well we know that the period (time for 1 oscillation ) is just 2 pi / b Where b is the coefficient of t inside sin, eg sin(bt) Since our model is a sin ( sqrt(g/L) * t ) Well our b is sqrt(g/L) So period = 2pi/b = 2 pi * sqrt(L/g) No calculus needed HOWEVER, It’s a good problem nonetheless as it teaches u to think through the problem which is useful for more general cases where u cannot model the pendulum with a simple sine function. In real life, obviously as the pendulum swings, it loses energy and has a lesser displacement over time Using calculus can help find the time for 1 oscillation within this more complex functions One of them that I can think of my head is e^(-t) * sin(t)

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      That is a clever way to tackle problem 2 yes. I like how you can get there without any computations :D Well done!

  • @Nithin-tu7ob
    @Nithin-tu7ob 3 місяці тому

    make this epic video popular

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      Haha this is a very obscure video, almost no views :D You can always share it with people you think will like it as well ;)

  • @MOXTHEGAMER
    @MOXTHEGAMER 3 місяці тому

    This is a wonderful video. I tried using my textbook to learn this, but this video made it so easy to understand. Absolutely love this video.

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      Wow, thanks for the kind words! I motivates me to make more videos :))

  • @user-xm8qc9yp5j
    @user-xm8qc9yp5j 3 місяці тому

    Tan 90 degree - 1 is the greatest number

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      That's infinity - 1, which is still infinity, strictly not a number :D But good try ;)

  • @louisinfini274
    @louisinfini274 3 місяці тому

    woaw! u just saved my semester

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      I'm super glad to hear that! What are you studying? :)

  • @gamingxpromax
    @gamingxpromax 3 місяці тому

    tree of grahams number tetrated to tree of grahams number

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      Mind blowing :D But, does your number have a practical use? :)

  • @JaydenCloudwalker
    @JaydenCloudwalker 3 місяці тому

    Shouldn't l(t) = α*cos(sqrt(g/L)t)?

  • @povdata
    @povdata 3 місяці тому

    Best explanation in the Internet!

  • @user-sy9dx5zp9d
    @user-sy9dx5zp9d 3 місяці тому

    3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    • @PenandPaperScience
      @PenandPaperScience 3 місяці тому

      The number should have a concrete use, to be a solution of a tangible problem of some sort. But good try ;)

  • @user-sy9dx5zp9d
    @user-sy9dx5zp9d 3 місяці тому

    10^(1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000!)

  • @bushraayman2587
    @bushraayman2587 4 місяці тому

    Thank you.

  • @santoshgujar5237
    @santoshgujar5237 4 місяці тому

    ✨Thank you, Sir, 🙏✨