Mathematics

There are two parallel plates, upper plate is static and bottom plate is porous and in motion. At the same time there are types of motion in bottom plate. Plate is oscillating with velocity Uo*e^(iwt) and also moving forward along X-Axis with constant velocity Co. Due to motion in plate Newtonian and Imcompressible fluid is injected with velocity Wo<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247, 247); ">Velocity field is given<br style="font-family: verdana, geneva, lucida, 'lucida grande', arial, helvetica, sans-serif; font-size: 13px; background-color: rgb(247, 247,…

I invented a number system in 2008 and I've never shared it with the public I thought I might as well...I had my reasons at the time for inventing it, and i think it may be useful...although i invented it, it's features are really natural features of our universe itself, and are therefore much less arbitrary than any number system i've encountered before,,,,,The number system is used as follows,,,,,a equilateral triangle is disected into combinatory permutations of it's sides,,,,there being 3 sides of a triangle there are 7 and only 7 representable permutations, no more, no less, consisting of 3 instances of one side represented, 3 instances of 2 sides represented, and t…

I just noticed this. Any reason why (x+2)x+2/(x+1)x+1 – (x+1)x+1/xx → e as x → ∞? Does it actually do this? I checked it in Excel but can't get past x = 141.

Hi, next year i'll start my bachelor's degree on mathematics, but i want to study something about it while i'm idle. I've found this: http://webdocs.registrar.fas.harvard.edu/courses/Mathematics.html And this: http://www.ufpe.br/proacad/images/cursos_ufpe/matematica_bacharelado_perfil_4904.pdf They're Syllabi from some mathematics courses, one of them is from the university near me, the other is from Harvard. Can someone suggest a study way? Where should I start and which books I should get? Thanks in advance.

first off this is not home work, and second i hope i put this in the correct area if not i am sorry so i have an alloy i made that is made up of coin silver (90%Ag and 10%Cu) and Tin now i should have recorded the amounts of each i put in when i made it but i didnt so now i would like to know is there any way to mathematically figure out how much coin silver and how much tin is in the sample? i just want to know how much "coin silver" and how much tin is in the sample i dont need how much copper, silver and tin. (i hope that makes sense) so the density of coin silver is 10.339g/cm3 (calculated by multiplying the density of silver and copper by the percentage …

I want to ask that how one can solve a problem having two different sets of data, which are equally probable to happen? Can there be any iterative method that can solve that confusion? The problem is similar to the cases in courts. But my question is that how can one use the probability and its laws in solving that case? I saw something like the Markov Chain on the Numb3rs but is it possible? How can one use it? Can someone use psychology with probability? Thank you in advance!

(1)Polygonal Epicycloid (2)Polygonal Epitrochoid

Let a,b, and c be positive real numbers. Prove that [math]\sqrt{\frac {a}{a+b}}+ \sqrt{\frac {b}{b+c}}+ \sqrt{\frac {c}{c+a}} \leq 2\sqrt{1+\frac {abc}{(a+b)(b+c)(c+a)}}[/math] I've tried squaring both sides, and that eventually lead me to nothing. Then I tried taking the common denominator of the left side, but I got nothing either... There has to be some trick involved that I'm not seeing... Anyone has any suggestions or input, that will be great!

Interpolate them.

During preparations for a mathematical contest I might take part in, I've come across an interesting problem: Let [math] n \in \mathbb{N}[/math] and [math]a, b \in \mathbb{Z}[/math] be integers such that the set [math]\mathbb{Z} \setminus \{ ax^n+by^n, x, y \in \mathbb{Z} \}[/math] is finite. Prove that n = 1. The "official" solution is the ugliest thing I've ever seen, and so incomprehensible that even my professors didn't understand it. My gut was/is telling me that there was a simpler solution, so I've been trying to find one. I've gotten to the point where all I have to do is prove that the set [math]\mathbb{Z} \setminus \{ x^{2k+1}+y^{2k+1}, x, y \in \mathb…

I've searched on wikipedia and wolfram mathworld, and i have a definiton on a book right in front of me: After that there are some properties. But I still can't understand it. Can you help me? Thanks in advance.

My interest in math is not only philosophical but as metaphors that may inspire me as an engineer as well.

Find the summation of: [math] \sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n} (1-\frac{1}{2}+\frac{1}{3}-...+\frac{(-1)^{n+1}}{n}) [/math] We know this is an alternating harmonic series if we look at the first part is just [math] \sum_{n=1}^{\infty}\frac{(-1)^{n-1}}{n} [/math] and multiplied to the second part which is [math] \sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{n} [/math], this is also another alternating harmonic series. So the product of these two should converge to ln(2) for each part right? But I don't know how to show how they converge... so the summation is just (ln(2))^2? Or another way I looked at it is, distributing... [math] \sum_{n=1}^{\infty} (1\fra…

Gotta click through the hyperlink in link removed to get to my explanation of Bayesian logic.

How is this represented?

what do i do here ?

I need to present rounded numbers in my software. For example, after calculating "sqrt(2)", the software could display the result as: "1.414" (it only shows the result to a 'reasonable' precision). How to mark this number as a round-off number? Is there a standard notation in mathematics? From the displayed value it should be immediately visible if the result is rounded or exact. For example, consider the following two cases: 1/8 = 0.125 (the exact value) sqrt(2) = 1.414 (rounded value) If there is no standard way to somehow mark numbers that are rounded, I was thinking to put a dash under (or over) the last digit. Or maybe printing out the last digi…

i have three months to study everything in the "heading " where should i start .. my whole life is depending on this crap .. seriously .. help ...

ok so if we say that a is a natural number (N) this (a+30)(a+50)(a+70) what can it be divided by? 2, 3, 5, 7? which one(help plz, btw soz maybe its bad math lang)

derivative (outer function ) (whole terms) * derivative (inner function) ?

getting lots of stuck from this algebraic expression ?? 1. The problem statement, all variables and given/known data (4x−1)1/2−1/3(4x−1)3/2 2. Relevant equations 3. The attempt at a solution I think the GCF is (4x−1)1/2 . So, I get (4x−1)1/2(1+(−1/3(4x−1))) = (4x−1)1/2(−4/3x+4/3) = −4/3(4x−1)1/2(x−1) However, the answer in the book is 4/3(4x−1)1/2(x−1) . I've done it several ways, and I either get a minus sign on the 4/3 , or the (x−1) becomes (x+1) . What am I missing?

Good day. I was working on my set theory home assignment when I found out that I got no useful knowledge on how to construct proofs. I all ready have tried reading about proofs and making sure I can read simple proofs (As should be the one I need to construct) but now I have understanding that I do not have any real understanding about what proof exactly is nor how it should be formally constructed. That is the reason I am here. I would like to get some tips and ideas on how to understand proof and help on working my way to create proofs. PS, I am a University 1-st year student and actually have really bad math background. Also, I have been working on elect…

1^∞ ≠ 1? What, Is this really indeterminate? 1 * 1 * ... * 1 = 1 1 * 1 = 1 = a a * 1 = 1 = a edit: I misunderstood "indeterminate"

Here is a question to think about. We assume that any element of a set with cardinality A, when represented by symbols, must have less than or equal to A symbols, which I think is a fair assumption. The real numbers have cardinality C. So any number in the set of reals, when represented by, whatever, 0's and 1's if you wish, can have at most C of these objects to represent it. The cardinality of the power set of the reals, is 2^C>C. Now, we can imagine a number who has 2^C symbols to represent it. This number is technically not in the reals, since it must be of a set with cardinality greater than the reals. But this number is what we would intuitively think of …

hello everyone i need some help am not good in mathematics so if any one can help i need books or software to help me and i will be grateful