Mathematics

Scenario: Let us suppose we have a stationary Target T being orbited in a perfect circle by an Attacker A. The circle has the radius of R in meters. T has a weapon that can track A at a set rate, T1 measured in radians per second. Given those conditions, I want to find the minimum velocity (V) in meters per second at which A can move around the circle of the fixed radius (R) and still exceed the value of T1. Let us also suppose there are no outside influences to consider. So here's how I worked this. First, we know the circumference of a circle is [math] 2\pi R [/math] We can then write a formula based on the velocity that determines how long it tak…

Hi guys, I'm currently trying to do statistics to compare the variance of results in two different methods. However, my results are in totally different units. So I think I need a way of scaling my data so that statistical analysis can take place. The two methods are very different ways of measuring something, and the units cannot be converted to match. Is there a way of scaling, or perhaps a method concerning ratio? The data sets are BOTH dependant variables and here are a few of the equivalent data points: 183 - 7.8 173 - 7.7 173 - 7.7 175 - 7.6 166 - 7.4 174 - 7.4 Any help would be GREATLY appreciated! Thanks A x

I know it is a no solution problem, but I was taking a look at it through the use of a limit and wanted to see whether this approach was valid. Given that [math]\lim_{n\rightarrow \infty }\frac{x+1}{x}[/math]. We can apply this to 1^x = 2, which can be turned into [math]log_{1}(2) = x[/math]. [math]x = \frac{log(2)}{log(1)}[/math] Now, this is undefined. Therefore, we can take the limit by applying the above together. [math]x = \lim_{n\rightarrow \infty }\frac{log(2)}{log(\frac{n+1}{n})}[/math] [math]x = \infty[/math] Is this math wrong? I am assuming some of it is, though checked wolfram: http://www.wolframalpha.com/input/?i=limit+of+x+approac…

Hi folks. I am a student and i have to do an essay about a topic that intrigues me. I read the quote " The Unreasonable Effectiveness of Mathematics in the Natural Sciences" ( of E.Wigner) on the book "Is God a mathmatician" of Mario Livio, and that hit me. Maths in fact can seem useless or a mere tool of applied sciences, but in reality, often it has anticipated some evolutions of physical theories and every branch of it has been applied in some way. One example could be the knot theory that, from the theory of mathematics it has been applied to the study of DNA (for whom interested: http://www.tiem.utk.edu/~gross/bioed/webmodules/DNAknot.html). What do you think? Do…

I just wanted to learn some hyperbolic geometry by myself. And I found this YouTube channel which has many lectures on many different math topics: https://www.youtube.com/user/njwildberger Has anyone tried his lectures before? Is he any good?

Hi there, this is my first time posting so forgive any indiscretions on my part. I was wondering what the name of the attached geometric curve is? It was produced by a population of bots in a exploration simulation I am running using neural nets. To me it looks like a dimpled limaçon, but with two inner loops instead of one. If the curve has a name, or a defining formula, I would greatly appreciate it.

Ten samples are taken and an average reading of 6.1 resulted. The IQR was 0.6. Does this mean the sample readings were pretty close in range about the mean?

infinity^0=infinity^(1-1)=infinity/infinity equals any positive number.

It finite difference method is unstable?

Hello. Do you know the Monty Hall problem? It states: "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?". The contestant should switch to the other door. Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their choice have only a 1/3 chance. After doing some research I found that there is a formul…

What unit of measure was used when the distance from the pole to the equator was being measured to later define the metre ?

If we assume that (-1) (-1)=-1 and (-2)(-2)=-4 but know that (0) (0)=0 Then (1+-1) (1+-1) must equal 1-1-1-1 =-3 and not the sum of (0) (0) which it should equal 0 unless we have assumed otherwise but have not. Likewise (-1+2) (-1+2) =(-1)(-1) must equal -1+-2+-2+4=-7 and not the product of (-1+2) (-1+2)=(-1)(-1) which should equal -1, which is inconsistent and does not equal -7 if we assume that (-1)(-1)=-1. But if we assume that (-1)(-1)= 1 then (1+-2)(1+-2) should equal 1+-2+-2+4=1 likewise (1+-1)(1+-1)=(0) (0)=1-1-1+1=0 which it does

The answer is yes! infinity*0= infinity (1-1)=infinity-infinity, which equals any number. because infinity-infinity-3 is absorbed in infinity like a blackhole. and still equals infinity-infinity, likewise infinity-infinity-5 equals the same thing.

Hello everyone In order to write a paper on the differences in epidemiology of pandemic influenza A(H1N1)pdm09 during that pandemic, between Europe and Africa, I need to understand a concept in a German article I'm using: "Der Altersmedian der Einzelfälle liegt bei 16 Jahren (IQR 10;28)." Which means as much as: "The age median of the individual cases is 16 years old (IQR 10;28)." Now, I know that IQR means inter-quartil-range, but can someone explain the meaning of this range 10;28 in this specific context? Would it just mean that Q1 = 10 and Q3 = 28? Thanks. F.

hello everyone I need help in this exercise. my attempts: i)resolved. ii) (t)=(1/n)=inf{s \in T: s>t}=1/(n-1) (t)=sup{s \in T: s<t}=1/(n+1) (t)= (t)-t = 1/(n-1) - 1/n =1/n(n-1). my answer for (ii) is right !! Thanks.

Isn't there a law that refers to the question of equations and how they are read, as far as forwards and then in reverse? In the simple 1+1+1=3, the ones can only add up to three, no debate. In the reverse order, three can be one plus one plus one, or a near infinite variations of numbers that add up to 3. This seems to have something to do with the 2nd law of thermodynamics, and why reality can only function forward in time. Thanks....

Hello! Suppose so you, mathematician, have such task: find whether point P (xp,yp) (2d) or (xp,yp,zp) (3d) is in triangle defined by vertexes A,B,C. Please show me your algorithms. The more optimized algorithm, the better *) Here is common stage needed for all below algorithms: (please note that this can be already calculated once at triangle initialization stage) min = Min( a, Min( b, c ) ); max = Max( a, Max( b, c ) ); if( ( p.x >= min.x ) && ( p.x <= max.x ) && ( p.y >= min.y ) && ( p.y <= max.y ) && ( p.z >= min.z ) && ( p.z <= max.z ) ) { [...more detailed check h…

Hello, Would someone be able to help explain the meaning of a term in a formula? The one in question is the deep learning weight adjustment formula from DeepNeuralNetworks. And here it is. So this shows the the iterative adjustment for the weights. Or is it the adjustment to the change applied to weights (as indicated by the delta)? But the main part I am unclear about is this. C is the cost function but what does this term mean?

Some people will draw a horizontal line through their Z's so they don't get confused with the number 2. Indeed, it is very easy for someone who is writing fast to write their Z's and their 2's identically. The only difference between the letter Z and the number 2 is that a 2 is supposed to have a loop at its top, wile a Z is supposed have a sharp zig-zag. So, when you're trying to write fast, some people - simply out of muscle memory - will draw a horizontal line through thier Z so it looks completely different form a two. But for some reason, Z is the only letter like that! There are plenty of other letters that can look like numbers, or even other letters, if…

Stupid question, would a constant composed of all the primes 23571113... be an irrational number? I've been thinking it would be, but wanted to double check.

Yes If we let 3^0 then; (3^0)^infinity=3^(0*infinity)=3^((1-1)*infinity))=3^(infinity-infinity)(3^infinity)/(3^infinity)=infinity/infinity) <br><br> which equals any positive number.

When solving for 0^0 the question remains what number when multiplyed by 0^1 equals 0. The answer is any number. Just as 1^0 is the number when multyplied by the base 1 equals 1^1, the answer is only 1.<br><br> Or more conscisely what does 0^(1-1)=0^0 equal. The answer is (0^1)/(0^1)=(0/0)=0^0 which is not 1. The teaching in schools all across the world that 0^0=1 is a conspiracy.

I've recently stumbled on some people claiming that some mathematical equations can produce random results. To me this seemed quite strange. Essentially, to my understanding mathematical equations are always by definition deterministic and this results in the possibility to make predictions in terms of science. Granted, my understanding often needs revising and I enjoy doing that upon encountering solid arguments. That means I am learning and my mind is evolving. It seems to me that if science is to use mathematics to approximate the behaviour of the Universe and if that modelling is successful, that in turn indicates that the Universe is entirely deterministic. …

Problem Description: Being a some constant, further assume that we are in a factor ring (basically all operations modulo some sumber p). Note, that the division below is a multiplication by the modular inverse. You always have to start with x=9. Consider the following recursive formula: Code: new_x = (x²-1)² / (4*x*(x²+a*x+1)) How often do you have to perform this operation to get a specific x (basically getting the new_x and feeding it back into the formula to get another new_x, and so on)? Note: You can start multiple such chains beginning at x=9, and add the resulting x values using the addition algorithm from http://en.wikipedia.org/wiki/Montgomery_curve (Montgomer…

So, I found something very simple, but I found it very interesting. Going on with my method of multiplying the function by its inverse and taking the modified derivative, here is what I found: Let's say you have a function f(x). [math]g(x) = f(x)f^{-1}(x)[/math] Where [math]f(x) = d_{i}x+d_{e}[/math], where d_i and d_e are constants. Now, apply the modified derivative to the function g(x). [math]g(x)' = \lim_{h\rightarrow 0}\frac{g(x+d_{i}h)-g(d_{e}x)}{h}[/math] Then, have the derivative and the original function equal to each other, except replace the derivative variable with y. [math]f(x) = g'(y)[/math] And, when simplified, the resul…