Mathematics

I am trying to figure out how to make a function for this wave. I drew it terribly, but I think it works: So, how would I make that? I tried but I can't do it. This is not for home work, I'm just curious. If you can't understand that image, basically you have a sine wave on a sine wave. Sorry, I'm not good at explaining things.

Hello In July, I'm doing the approval exam for Medicine school. The exam is a multiple-choice-exam, which consists out of 2 parts: "knowledge and insight in sciences" and "gathering and processing information". The first part consists out of 40 questions (10 maths, 10 physics, 10 biology & 10 chemistry), with each 4 possible answers. A good answer (let's call the number of good answers [math]a[/math]) results in +1 point, a bad answer (let's call the number of bad answers [math]b[/math]) in -1/3 point (correction for guessing) and 0 points if you leave the question open (the number of questions to which no answer is given would then be [math]40-(a+b)[/math…

Hello everyone I played around with some binomials, variations etc. and I stumbled upon a problem. Let's first of all notice the following: [math]V^a_b=\frac{b!}{(b-a)!}=\binom{b}{a}\cdot a![/math] An equation which I have proven in "Variations formula", a topic of mine: [math]V^{n-m}_n\cdot(n+1)=V^{n-m+1}_{n+1}[/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=\binom{n+1}{n-m+1}(n-m+1)![/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=\binom{n+1}{n-m+1}(n-m+1)(n-m)![/math] [math]\Leftrightarrow \binom{n}{n-m}(n-m)!(n+1)=(n+1)\binom{n+1}{n-m+1}-m\binom{n+1}{n-m+1}[/math] [math]\Leftrightarrow \left(\binom{n}{n-m}-\binom{n+1}{n-m+1}…

Im doing distance between two points as its set out ---------------------------------- / 2 2 d = / (x2-x1) + (y2-y1) = and so i write the equation im doing out and follow the set rules to working it out.... x1,y1 x2,y2 ( 4 , 5 ) ( 1 , 1 ) --------------------------------------- / 2 2 d= / (1-4) + (1-5) = Now my text Book says the Answer is 5.. but i don't no how im getting 31.1.. im follow…

I have been trying to accelerate my math education, but I have found it difficult because most of the resources that I have been using haven't been to the point at all, or haven't been teaching just the concept. An example would be Khan Academy. I have been using them for a while but gave up because the videos are extremely slow for me. Are there any math books/resources out there that are to the point, maybe like a reference book, but not like a workbook? I also asked some of my teachers for some higher level books, but the same thing happened, they were slow, and had a lot of talking that was not related what so ever to the math.(I really couldn't care how high the …

Well, this is something that isn't really useful, but more fun. Well, here is the idea. The idea is there is a line of size x which then another line is placed at the other line's midpoint, or any given point for generalization, where one end of the new line is positioned at this particular coordinate. This is to repeat onto infinity. The idea is to find the distance between the end of the first line to the end of the last line that is placed in the particular fashion told about above. The distance of this is equal to the following function, given x as the length of the first line and F being the fraction at which to place the new line at on the original …

Im Using a Cas Calculator to work out the Following Equation x+11 2(x+14x) ------- = --------- 3 9 Now i no the Answer is -5 but when putting the following Equation in my Calculator i keep comimg up with 11 x= ---- 9 Just looking for a bit of Help if any one can help me at all.. thanks Matt

Sometime someone asked what zero divided by zero was. Someone answered if 0x=0, then 0/0=x. That's all fine in good, but isn't there a rule that anything divided by itself is one? So wouldn't you technically be turning nothing into one? How does that work? Can someone give a mathematical explanation on what is right? I don't get how 0/0=x, but how can that be true. Wouldn't 0/0=1, so x would equal one? But 0 does not equal one. Thanks for your thought and time.

m^2 = n^2 * 2 has no solution for integers m and n because root two is irrational. But m^2 = n^2 * 2 -1 does have solutions, the first of these being 7&5, 41&29, 239&169, 1393&985, 8119&5741. I believe that there are an infinite number of solutions, in other words for all N, there exists a solution with m and n both greater than N. Can anyone give me a proof ?

Does an algorithm exist that uses the most fundamental theorems of mathematics and creates even more theorems that build up mathematics? If not, I am thinking about pursuing a project as such. Though it might not be completely efficient to make one, I want to see if it is possible to produce one.

Hello For a research we have to do in class, I'd like to use mathematically correct notations. There is, however, one expression from which I don't know how it's written: a false equation. e.g. Fermat's big theorem: [math]\nexists (x,y,z,n) \in \mathbb{N}_0 : x^n+y^n=z^n[/math] [math]\forall(x,y,z,n)\in\mathbb{N}_0 : \left\{x^n+y^n=z^n\right\}=\emptyset[/math] [math]\forall(x,y,z,n)\in\mathbb{N}_0 : \left\{x^n+y^n=z^n\right\}=0[/math] Or just a very simple example: [math]\left\{1=0\right\}=0[/math] [math]\left\{1=0\right\}=\emptyset[/math] Is any of these notations correct? If not, which one could I use? Thanks. Function

Hello everyone For maths, we need to do a research of a mathematical subject. We chose the theorems of Fermat (both the big and small theorem). We are to make a question about this subject, a question worth investigating. (One big question and perhaps some smaller questions about that primary question) However, we can't seem to find one. Can someone help us? Thanks. Function

There are 51 machines in a factory, 204 workers work in the factory. Each day, grouping of workers is done. A group of 4 workers work on a single machine in a day. On the second day, the grouping is done again o, the condition that no 4 members who are together on the first day will be together on the second day. On the third day, those who are together on the first and second day should not be together. The question is: FOR HOW MANY DAYS IS THIS POSSIBLE ??

Hi, I have a transitive relation and wana build a complete set of pairs that reflect all (direct/indirect) relations among the pairs. Ex.: suppose I have this relation R = { (1,2), (2,3), (3,5), (5,7), (3,4) } I wana to produce this relation R oper R = { (1,2), (1,3), (1,4), (1,5), (1,7), (2,3), (2,4), (2,5), (2,7), (3,4), (3,5), (3,7), (5,7) } I tried to use the composite operator (°), but I got this R U (R ° R) = { (1,2), (2,3), (3,5), (5,7), (3,4), (1,3), (2,4), (2,5), (3,7) } which is not complete. In this case I need a loop operator until all pairs are restored. Is there an operator that I can used to reflect that? Thanks in advance. Hi, I am seeking h…

I'm a school student*; and like many other school students, I have a hard time with mathematics. I figured I'd do some extra work at home so I bought and tried out Langs "Basic Mathematics"; which is, as the title implies, basic. But I had a hard time following it from the first or second chapter so I quit. It was probably too advanced, so can anyone give me tips of literature that gives the absolute basics? I know the concepts of addition, subtraction, dividing and stuff you learn since you're a little kid, but after that things start to get blurry. I assume that the school system takes our knowledge of previously covered concepts for granted. But honestly, I forget most…

Hello everyone I was, with another topic in the back of my head (the one about the integration constant), making the following reasoning: In a right triangle, let's say that the two acute angles are [math]\alpha[/math] and [math]\beta[/math]. Then is true that [math]\alpha+\beta=\frac{\pi}{2}[/math] [math]\Leftrightarrow \alpha=\frac{\pi}{2}-\beta[/math] [math]\Leftrightarrow \tan{\alpha}=\tan{\left(\frac{\pi}{2}-\beta\right)}[/math] [math]\Leftrightarrow \frac{\sin{\alpha}}{\cos{\alpha}}=\frac{\sin{\left(\frac{\pi}{2}-\beta\right)}}{\cos{\left(\frac{\pi}{2}-\beta\right)}}[/math] [math]\Leftrightarrow \frac{\sin{\alpha}}{\cos{\alpha}}=\frac{\cos{\beta}}…

Hello In Math class, we were to sole an integration. While my teacher was explaining and resolving the exercise, I did it myself, finding [math]\int{\cdots}=-\arctan{e^{-x}}=f_1(x)[/math] Later, my teacher found [math]\int{\cdots}=\arctan{e^{x}}=f_2(x)[/math]. As she didn't find any mistake in my work, we agreed that the 'problem' MUST be that those two primitives are different from each other, from a constant. I now find that [math]f_2(x)-f_1(x)=\arctan{e^{x}}+\arctan{e^{-x}}=\frac{\pi}{2}[/math] And that this is not only true for [math]e[/math], but for every real number. Can this be proven? Thanks. Function [EDIT] I found - pure …

Hello everyone One of the example questions of the acceptance exam for Med school, is the following: (http://www.ond.vlaanderen.be/toelatingsexamen/nl/modelvragen/files/2013/modelvragen-wiskunde-2013.pdf "Vraag 7") Given: [math]\int{\frac{dx}{x}}=\ln{x}[/math] and [math]\int{\cos{x}dx}=\sin{x}[/math] Which one of the following statements is true? [math]\int{\frac{dx}{\cos{x}}}=\ln{\sin{x}}+C[/math] [math]\int{\frac{dx}{\cos{x}}}=\sin{\ln{x}}+C[/math] [math]\int{\frac{dx}{\cos{x}}}=\ln{x}+\frac{1}{\sin{x}}+C[/math] [math]\int{\frac{dx}{\cos{x}}}[/math] cannot be calculated on base of the given. The last option should be the correct one. …

Hi, Over the course of the last few weeks I've been attempting to learn about the foundations of mathematics and yet I've been unable to find out what the single most fundamental branch of mathematics is. I've read a few books that covered mathematical logic, mathematical philosophy, and elementry set theory, and yet the answer still eludes me. Could someone please point me in the right direction and tell me what the single most fundamental branch of mathematics is, and what branch of logic does the whole of mathematics stem from? Any help would be very much appreciated. Edit: Clarified question

So, I tried to determine if this is a prime number: [math]2^{257885161} - 1[/math] If this is a prime number, it will be the largest known prime, but if not then okay. Is there a quick way to tell? I tried dividing it by other numbers, yet after a long, long set of calculations I have found no factors yet(though I did this in Mathematica so it may be wrong).

Hello everyone I'd like to know which formula can express the number of unique possibilities in which a number, consistent of [math]m[/math] cyphers and [math]n[/math] different numbers. For example, a number with [math]n=3[/math] and [math]m=4[/math] can be written in 11 unique ways. [math]\left(=\frac{n!+m!}{2}-m\right)[/math] Be [math]n=3[/math] and [math]m=3[/math], then there are 6 possibilities. [math]\left( = 3!\right)[/math] Be [math]n=1[/math] and [math]m=3[/math], then there's only 1 possibility. Thanks! Function

in calculus, I learned that 1/infinity will approaches 0, but not equal to 0 like 1/0 is approaching infinity, but not equal to infinite tan 90 = sin(90)/cos(90) = 1/0 = infinite? 1/tan 90 = 1/infinite = 0? how does cot graph is valid (instead of using the "undefined" value or line up an asymptote there) just because the assumed value of 1/tan(90) = 0, while tan 90 = infinite..

Hello everyone In math class, we solved the next problem: How many numbers, composed out of 5 different digits, varying from 0 to 6, can be formed? So we concluded that the number of possibilities = [math]6\cdot 6\cdot 5\cdot 4\cdot 3[/math], excluding 0 as first digit. Conclusion: [math]N=6\cdot V^4_6[/math]. Then, suddenly, something came in my head; as we were working with variation formulas, I wanted to put the number of possibilities in a formula, solely using variation formulas; the first thing that came in my head was: [math]V^5_7-V^4_6[/math] My math teacher did some thinking and accepted my resolution (she said it was also a good solution), my …

Hello everyone Just messing around with some numbers and formulas, I got to the (pretty useless) idea to simplify [math]\lim_{x\to\infty}{\left[\frac{\log{x^a}+\log{x^b}}{\log{\left(x^a+x^b\right)}}\right]}[/math] The most simplified form I get is (after using the rule of de L'Hôpital once and just using some rules concering calculations with limits) [math]1+\lim_{x\to\infty}{\left[\frac{a\cdot x^b+b\cdot x^a}{a\cdot x^a+b\cdot x^b}\right]}[/math] Is there any way to simplify this even more? Thanks. Function

Hi Can some one help me in proving this statement. Show that in a Boolean algebra, for any a,b and c, if any a≤b, then a∨(b∧c)=b∧(a∨c). I got the answer thanks. Logic is X or X = X