Mathematics

what would it be then?

Hello all. Am on first steps to make a solar thermal water pump for drip irrigation purposes. Assume 60% efficiency of solar thermal irradiation (600W/m2. Assume average daylight temperature 25C. Assume average night temperature 15C. Or, make those parameters real, entered in the formula. Area of sun exposure as parameter, say =1 m2 (Tank lid) Capacity of reservoir as parameter, say = 1 m3 Volume of air, =Va. Volume of water =Vw. For a desired pumping height, what would be the flow in 24 hours ? [Plus whatever am missing] In the hermetic reservoir, the solar heat expands the air pushing the water up during the day, and suctioning water …

3x+1 if odd x/2 if even So why not create a sieve of multiples of 2, 4, and 8? When x equals a logarithm of 2, 4, or 8 then x/2 repeated equals 2. 2*2*2*2… 4*4*4*4… 8*8*8*8… These 3 logarithms of 2, 4, and 8 encompass all the numbers that reduce to 2 when repeatedly divided by 2. What am I missing? Did I break the rules of the pattern? I am trying real hard not to factor semiPrimes. I did not research the problem yet. I am only working with 3x+1. I realize that this is more complex with larger numbers. I am just stating a simple example.

I have been researching Quantum Algebra for a few days. I have a few questions about it in hopes that people can help me on here. 1. How do quantum groups differ from classical groups in mathematics? 2. Can you explain the concept of Hopf algebras and their significance in quantum algebra?

6 balls are drawn from a total of 49 balls randomly. Order does not matter, as long as 6 balls are matched, first prize is won, what is the probability of winning the first prize? Another question is horse racing. For certain three matches, which may have 10 to 14 horses in total, different horses may have different conditions and abilities so the winning odds of each horse may not be as simple as 1/10 or 1/14. You choose three horses from each of the three matches so you are choosing 9 horses in total, if all 9 horses in three matches finish for the 1st, 2nd and 3rd place, order isn't counted, i.e. ABC, ACB, BAC, BCA, CAB, CBA don't matter.), then you win the jackpo…

Sales tax Pyramid Scheme Ok say I buy something for$100 + $6.00 sales tax. Then the person I bought from buys something for $100 + $6.00 sales tax. And so on and so forth for n, the number of money transactions. Does that mean that on $100 the government just make $6.00 * n. And after $100 / $6 times the government is making more money than the original $100? So the act of saying $100 is worth so much in gold, actually makes more than the value of the gold? And then transfer of money is promoted because it generates more value? And you thought bitcoin was a scam.

In a mechanical memory system, such as a tape recorder or gramophone, the input movements of sound waves are constrained by the mechanism to motions back and forth along a single line. A separate mechanism(s) adds motion along a different line to stretch the needle marks far enough that they don't overlap at frequencies within the design range. The question is, how can the speed and direction of the added movement(s) be calculated from the recording needle track? With a needle bouncing perpendicular to the length of a recording tape, if the tape moves in a straight line past the moving needle there are only two directions to choose from. Can we tell if the tape …

I am not going to specify my age here. But I am ahead of my time. I finally understand most of calculus and now want to get into some other complicated stuff. The only problem is that I have a short attention span. I need something I can read and something that keeps it interesting to understand matrixes or linear algebra. Can anyone help me?

Hi there, When it comes to disputes, the more you engage in arguing/conflict the more complicated the argument becomes for a third party to try and resolve. The sooner you take your conflict to your manager or a judge (litigation), the easier it is going to be for them to figure out what has happened and resolve things quickly. Is there away to present this idea mathematically? Preferably in simple maths... I was thinking something similar to: Conflict with two facts to resolve: C = 1/2 x 1/2. (i.e. if there is two facts then each fact is one half of a whole). Conflict with three facts to resolve: C = 1/3 x 1/3 x 1/3. (i.e. if there are three…

Large Language Models (LLMs) like GPT-4 and its predecessors are, as far as I know, built upon a foundation of mathematical and computational concepts, some of which were established long ago. I've been asked to do a short presentation about LLMs and I'm thinking of including a timeline of mathematical concepts to give some context to the audience. Can you suggest significant discoveries that could be included? There is likely no exact answer and I would value your opinion. For a short list I have these as a starting point: -Probability Theory -Foundations of Calculus -Vectors and Matrices (Linear Algebra) -Neural Networks -Information Theory (entropy) …

I know this is a bit crazy, but I do feel like I'm onto something. I just don't know how to do the complicated math for it. I'm not the sharpest tool in the shed. This has to be a theory of some kind. So, we all know about Sacred Geometry (google images to sum it up) hopefully, this adds to the effect if you can think in 3D. If you could have a root equation that explained everything, I feel it's this. The Key for Everything, the Crown of Thorns feedback appreciated

Okay, I know that the definite integral is used in finding the "AREA UNDER A CURVE" And there is also maxwell's electromagnetism equation I think. I know that there is a lot of examples, but how did they all find out how and why to use them? Sorry, I meant indefinite

Hello guys. You know about the "find a shape that can roll over any surface" thingy? Well, I have found a way to do that sketch on your paper! You see, all you have to do is find the radius of every time it majorly changes and evenly distribute it in EVEN numbers! Let me give you a visual presentation: As you see, we calculate the radius every time it significantly changes. Unfortunately, this is not a practical method, so we will have to sort of, draw the curve on the road. Let me give you another example As you see, the circle is the easiest to do, as its radius is never-changing therefore the surface is never-changing. Lets look at something …

here is my algebraic equation that not even symbolab solver could solve. The equation says that the x root of x equals 100. So what does x equal? Just a brain stumper for ya'll

Is i - i 0? how do we know that epi*i=0? what would a sigma notation with an upper limit of i look like? Is my "take this with a grain of salt" topic dead?

I am not the best at trigonometry. And I need help solving inverse trig functions. Can someone help me? You can also head over to take this with a grain of salt. I need help over there

I have this personal counting system to help understand complex numbers and I want you to help me improve it. remember, this is not actual math, And I just made it to make sense of complex numbers. Here is what it is. they are called rational integers (don't get mad) So, for short, R-Integers, are just like actual numbers, but they are also complex numbers. They just work a bit differently from real numbers. So first, the way to write them is with a line under the number. So, r-1 would be 1. They are the same as normal numbers but multiplication is different. What you do is when you multiply them, you keep the first number the same, but the numbers after that, they are co…

Imagine that you are given a smooth space of unknown geometry. What kind of constructions would you use to figure out the number of dimensions of this space?

11 12 54 69 72. those numbers have nothing to do with each other. But why did I put them on screen? I came up with an idea in my mind. What if we could take a random set of numbers, rearange them from lowest to highest. And find a sort of "Rate" at which they are changing. I am not speaking "Rate" In a literal sense. I just wonder if there could be a connection between those numbers. Idk why I though of this. I am going insane. But please help me with this

I can't tell if this is false or already exists, but I have come up with a proof for the Pythagorean theorem. Let me show you: If you can't figure out what this means. I will tell you. First, you draw a right triangle, and then another so it makes a square. Than you draw two triangles, which direct in the same position as the hypotenuse. Than the two triangles are equal to A and B. If you can't figure out what I said, Idk what to say. Take a harder look at the triangle. You can also prove this proof with einsteins proof.

Everyone knows how to find the area under a curve (I am joking) but I don't know how to find the area UNDER a curve. Chatgpt (After hours of arguing) told me that you have to define an upper limit, do the integral of that. with the same bounds, you find the area under a curve and you subtract them. I can't tell if this is true or not. Can you help me? And the reason I am doing this is to turn a curve into a ratio (under to over)

I am not IN college, but I am watching college classes online on YouTube. (MIT ones, to be exact). They brought up linear differential equations. I don't even know how to solve any I come across. I know algebra and calculus but I know nothing about whatever that is. Can someone help me?

Okay, Here is a number theory concept i thought about Lets say you have two imaginary colors, and you have to calculate the number of mixtures between those (The reason it is imaginary is because to many mixtures makes it brown) You have two colors. So how many mixtures do they have possibly? Well one! So what about three? Well three! But when you get to four, that is when it gets hard. So if it keeps going on forever, what numbers do you get?

If a product that costs me $100 to make and I want to make 25% profit on it so I sell it for $125, later on, the cost of raw materials and production decreases by 20% but I still want to sell it for $125, in that case, what is the % of profit? In other words, I want to keep the final selling price unchanged, but the actual cost of the product decreases, how to calculate the profit %? Of course, $100 is just a number for illustration. I have many different numbers for real. Is there a general formula for that? Then I can apply more quickly.

I took the first 23 numbers of the fibonacci sequence and turned them into a lcm. Here it is: 1.43734E23