Mathematics

Every second, a green marble has a chance to appear. You are not told what the probability of this occurring is - instead, you are given a number which is equal to the average number of seconds it takes for a green marble to appear (let's call it 'mean time to happen'). Now let's say you want there to be a chance of a red marble appearing instead of a green one. In order to make this happen, you must define a separate 'mean time to happen' for the red marbles. But you do not want to change the overall chance of any marble to appear; the combined probability of a red or green marble appearing must be the same as the previous probability of a green one appearing. …

I know that the area of an ellipse is 1403761773.43497 and its circumference is 145485.418131498. Is there any way to calculate from those numbers that the semi-major axis is 26534.9039306654?

I started to study about diff eq for this summer class. And I already have trouble with it. The professor lecture is also probably too fast and I couldn't get anything to my brain. Is there any site exclusively for this matter? Please tell me.

Me and a few friends at school the other day were wondering if pi and phi were somehow connected, After a while i managed to throw out [math]\phi^{(\displaystyle\frac{\pi + \phi}{2})}= \pi[/math] which manages to roughly approximate [math]\pi[/math]. I then found if you did [math]\phi^{(\displaystyle\frac{\pi + \phi}{x})}= \pi[/math] with [math]x = 2.000811416[/math], the equation exactly reached [math]\pi[/math]. But [math]x = 2.000811416[/math] seems too random to me, is there any connection between [math]\pi and \phi[/math] that would produce [math]x = 2.000811416[/math]? On the slight chance you understood what i said, do you know where [math]x = …

The Australian philosopher colin leslie dean points out Godels theorem is invalid because it uses invalid axioms ie axiom of reducibility it is the biggest fraud in mathematical history everything dean has shown was known at the time godel did his proof but no one meantioned any of it http://gamahucherpress.yellowgum.com/books/philosophy/GODEL5.pdf look godel used the 2nd ed of PM he says note he says he is going to use AR but Russell following wittgenstien took it out of the 2nd ed due to it being invalid godel would have know that russell and wittgenstien new godel used it but said nothing ramsey points out AR is invalid before godel did his …

Hi all. I am new here. What actually are two dimensional objects? Do they really exist in material world?

Hello! I am stuck with a relatively simple task. I am doing some coding and need a certain kind of motion to apply to an object. The motion graph should look something like in the picture. It may look like sqrt(x) at first but this isn't the case, I am wondering if there is some function that actually reaches a slope of 0 relatively quickly (or a VERY tiny slope) ? Thanks!

Numerus “Numerans Numeratus” Let all abstract numbers be defined exactly as concrete numbers. Concrete number: A numerical quantity with a corresponding unit. Let the corresponding unit exist as an abstract dimension notated with the use of (_). Let the length and width of all dimensional units remain abstract and undeclared. Let the dimensional unit be equal in quantity to the numerical quantity it corresponds to. Let all numerical quantities inhabit their corresponding abstract dimensional units. Let zero be assigned a single dimensional unit. Classic Isomorphic 0 = …

So, given enough time, a monkey typing random words on a keyboard will eventually type out Hamlet word for word. Let us calculate the expected time it would take the monkey to do that. In my intuitive (but limited) understand of probability, I think we only need to know: 1) The number of letters in Hamlet (or characters if you want it to include spacing, punctuation etc., but excluding capitalization) 2) The average time it takes someone to type one letter, or in other words, words per minute. We must be given some leeway here because we must agree upon whether the monkey is frantically mashing the button with its fingers (not whole hands, because then the probabi…

Hi everyone! Stupid question in the topic. Obviously, radius is perpendicular to a tangent at a point of intersection, but can it be said that radius is perpendicular to the circle itself? Does such statement even make sense?

Square Through Squares Copyrighted©PiyushGoel

Accuracy up to how many decimals...........? 32 + 42 = 52 9 + 16 = 25 1.(3/4)2 + (4/4)2 = (5/4)2 0.752 + 12 = 1.252 0.5625 + 1 = 1.5625 2.(3/5)2 + (4/5)2 = (5/5)2 0.62 + 0.82 = 12 0.36 + 0.64 = 1 O.K. Fellas, let’s notice a difference here. 3.(3/3)^2 +(4/3)^2 = (5/3)^2 1^2 + 1.3^2 = 1.6^2 1 + 1.69 = 2.56 Difference => 2.69 – 2.56 = 0.13 Accuracy =>0.13/2.69=.048 4.(3/3)^2 +(4/3)^2 = (5/3)^2 1^2 + 1.33^2 = 1.66^2 1 + 1.7689 = 2.7556 Difference => 2.7689 – 2.7556 = 0.133 Accuracy => 0.133/2.7689 = 0.00…

So I was confused if I should post this to math or to brain teasers, if I posted in the wrong spot I apologize, I got this probability question and I couldn't figure out the answer could some help me with the needed formula to solve it. The question is: given a binary string that contains 11 digits what is the probability that there is exactly four 1s in the number. I can solve half of it, I know that 11 digits means 2^11 or 2048 total numbers, but I can't figure out how to find out how many contain exactly four 1s through a formula.

How to get ,The Area of Trapezium from Triangle Lot of mathematicians have proved Pythagoras theorem in their own ways. If you google it you will indeed found hundred of ways. Meanwhile I was also sure that maybe one day I could find something new out of this incredible Pythagoras theorem and Recently I got something which I would like to share with you. To Prove: Deriving the equation of area of trapezium using Arcs Proof: There is a triangle ABC with sides a b and c as shown in the figure. Now, Copyrighted©PiyushGoel

Hi all, this is my first post here and I wanted to run something by people who are more knowledgeable than I. In the past couple days I've decided that I need to teach myself more advanced mathmatics as it is of great importance to my studies in physics, astronomy and biology. In school we never went past algebra 1 and geometry and that has proven to be a hindrance. So I decided to brush up on the basic math that I learned in school and then move on to more advanced maths. I decided to make up a bunch of problems to solve while waiting for my books to arrive and I ran into my old nemesis, finding square roots of large numbers. I was taught prime factorization, which didn'…

When I first came accross the mystery of Buffon’s needle, it was presented as a mystery because, apparently, nobody could understand why it would result in the value of pi or what the problem of scattered needles had to do with a circle. You might actually do the experiment and find that the results really did statistically converge to pi as the sample size grew larger or you might find the mathematical solution would indeed result in a probability that is exactly equal to pi. You might notice that there is a cosine of the angle between the needle and the lines on the table involved. You might even be able to construct a circle to describe how the cosine functio…

Could anyone walk me through on this equation and what proves its validity?

How would one use a quadratic formula with time as a variable? For example, what the intersections between two circular functions would be when T=0 compared to T=5 if the radius of the functions increases over time? Also, is there a general equivalent of the quadratic formula for circles? I would like to basically have a simple equation that gives me the coordinates of an intersection (x, y, z) for a given value of x, y, and time. After that, the derivative of an intersecting function is going to be treated as an axis for a change in slope of the other function over time (the slope will 'reverse' over the perpendicular line to the other function's derivat…

The space that we are used to is 3D and we construct it (the model) by ensuring that the 3 planes (x=0:y=0:z=0) are orthogonal to each other. How do we move on from there if we want to build a model with 4 such planes ,all presumably orthogonal to each other in the same way? To my untrained eye it seems that the new( 4th) plane will have "nowhere to go" ie ,if it is orthogonal to the x=0 plane then it feels like it should be identical to the y=0 or the z=o plane which already occupy those areas("area" is a poor choice of word ,but I hope the meaning is clear) How do we "shoehorn " this extra plane into the model when it f…

Zero Element Equivalency Can this be considered a field? Can this be considered a solution for division by zero? Can this sufficiently create varying amounts of zero? Allow that there exists an integer zero element ( -0 ). 0 =/= (-0) |0| = |-0| 0 |=| (-0) Where |=| is defined as “Zero Element Equivalency”, where any two unique or similar additive identities are considered equal because they share the same absolute value and cardinality but may or may not possess different multiplicative properties. Allow that : 0: possess the additive identity property and possess the multiplicative property of zero. …

X^0 is 1. such as 10^0 =1, since 10/10 =1, and 10^1/10^1 = 10^(1-1) = 10^0. How about 0^0.

If I have some function like y = kx/(1+x) How do I take the derivative of dln(y)/dln(x) ln is natural log... Can someone do like a step by step kind of a thing...

What is the Infinitesimal sign?

I have a system of 1st order odes given by $$ \dot{x_1}(t) = \alpha_1 f_1(x_1,t) + \beta_1 u(t) \\ \dot{x_2}(t) = \alpha_2 f_2(x_2,t) + \beta_2 u(t) $$ They are constrained by an algebraic equation $$ x_1(t) + x_2(t) = k $$ where $\left( \alpha_1,\alpha_2, \beta_1,\beta_2 , k \right) \in \mathbb{R}$ are known constants (i.e. parameters). $f_1(t)$ and $f_2(t)$ are both unknown. Starting from a rich set of input-output **noise-free** data available from simulating a complex proxy system, what would be the best procedure to identify (even a subset of repeatable/characteristic properties) the unknown **_possibly time-varying_** functions $f_1…

Using equation with mathcad 15 I can't to output table and plot. What is wrong in my mathcad code? drop2.rar