Mathematics

Hey all, I have two 2D vectors, [math]\vec{s}[/math] and [math]\vec{p}[/math], both starting at [math][0, 0][/math] and ending in the points [math]S[/math] and [math]P[/math] respectively. I'm looking for a vector [math]\vec{x}[/math](starting at [math][0, 0][/math] and ending in the point [math]X[/math]) that satisfies the equation [math]|\vec{s}-\vec{x}| = z \cdot |\vec{s} - \vec{p}|[/math], and that [math]X \in \; \rightarrow SP[/math] (I hope that's the proper syntax for a ray begining in S and going through P). In layman's terms, I'm trying to "zoom in" on [math]S[/math]. Now, the obvious way to solve the problem is find the equation for the ray (or line to be pe…

Hey guys, I've never got problem with solving quadratic, logarithmic or goniometric equations, but I don't know how to solve them when they are all together. The most simple example is: [math] \textup{log}(x)+\textup{sin}(x)+x^2+x+1=0 [/math] Is there any way to solve them without "computer help"? Thanks, pq

Hi I have a function f: [math]f(x(t))=\frac{d(x(t))}{dt}+x(t)[/math] Now how would I differentiate f with respect to x

does (x+h)log(x+h) = xlog(x+h) + hlog(x+h) ?

Hi, Suppose I have two points A, and B in some N-dimensional manifold. I would like to define distance (or metric) between A and B as follows: [math]d(A,B)=min | \int_\gamma f(s) ds | [/math] along some curve [math]\gamma[/math] In my head, it seems to be possible to evaluate a line integral without precisely defining distance. (ie. we just take tiny little points along this line, and evaluate f(s) at each tiny little point). However, all equations I've seen uses something like: [math]ds=\sqrt{{dx}^2+{dy^2}}[/math] which seems like a euclidean metric. So here are my ultimate questions, 1) is it possible to evaluate such a line integral withou…

Hey all, I was wondering, if one were to define a number r, for which [math]|r|=-1[/math], would it be possible to logically deduce it's behavior in mathematical operations? I know that the very concept is unimaginable and I also know it would be useless. But if we can have square roots of negative numbers, why not numbers denoting negative length? I'd be interested to know what [math]r^r[/math] would be, for example. Cheers, Gabe

Often I speak about how it is impossible ever to know anything as a true and unassailable fact, that assumptions are required in all things (even the scientific method, which attempts to be as objective as possible, operates on the unknowable assumption that observations of the material world can inform of its workings). Invariably, I am rejoined with: "But we know 2+2=4! That is irrefutable and unassailable, and requires no assumptions." This disturbed me, because it seemed to violate my previously stated ideology, so I thought deeply on it, and I came to the conclusion that mathematical statements like that are actually tautologies -- that four is defined as the…

Let's say we define a set [math]S[/math] in the following manner. [math] 0 < S_0 < 1 [/math] [math] S_n = (1-S_{n-1})^x[/math] If we take the example [math]S_0 = \frac{1}{2}[/math] and [math]x = 3[/math] then the set apears to not converge and to follow no set pateren, is this chaos?

What are people's opinions on which are the most important theorems in mathematics? By important I mean those with the most significant consequences both in pure and applied mathematics (not just obscure results that happen to be interesting to a few individuals). I would suggest the the Pythagoras Theorem should be up there. What else?

Hi all Have a quick question... I'm writing up my year's project work, and shockingly enough it involves a handful of straight line graphs. Excel kindly provides me with a line of best fit and its corresponding equation, along with a value called R-squared. (Mine is 0.537... not too good) I know this is a measure of how good the fit is, but I'm not sure how to explain this in my write-up. I won't need detail on it, just a brief statement to the tune of "The correlation isn't very good". How should I refer to this R-squared value? I know very little about statistics. Cheers Kaeroll

I am amused to consider that I find nothing in nature that exists as a negative quantity, for example, a tree cannot have a minus quantity of leaves, if it started with 3000 leaves and now has 2000 it does not have -1000 leaves it has 2000 leaves. leaving aside 'debt' which is a man made concept/quantity, where if anywhere does negative exist in nature, such things as 'negative voltage' is merely a reversal of polarity or direction. Travelling at -3mph is actually travelling at 3 miles per hour in a different direction, negative is an opposite direction and not an opposite to positive in any true sense. In the sum 5-3=2 there is no negative quantity, there is …

Is there a name for a family of parametric curves [math] x(t) , y(t) [/math]where... [math](\frac{dx}{dt})^2+(\frac{dy}{dt})^2=1[/math]? If possible, generalized to multiple dimensions... [math](\frac{dx_1}{dt})^2+(\frac{dx_1}{dt})^2+...+(\frac{dx_n}{dt})^2=1[/math]

I have a surface Z, which is a function of the variables x1,x2,x3... etc. ie. Z(x1,x2,x3...) I have a point Z0 and a point Z1 which corresponds to some point on this surface. There is some line M that connects Z0 and Z1 on the Z surface, note that M does NOT have to be the shortest distance. However, M must be bound to the surface Z. How do I find the length of the line M on this surface? Ideally the expression would be somehow linked to the directional derivative, IE. I've been thinking of slicing the line M into tiny little components, and taking the directional directive at each point of M, the integrating with respect to.. something (maybe dx1, dx2, dx3... …

An open interval is an interval that does not include its end points. http://mathworld.wolfram.com/OpenInterval.html What I don't understand is why is it called an open interval?

Hello, I have a question about the change of radix, for example: Convert 1020304 base 10 into base 7: 1020304 / 7 = 145757 r 5 145757 / 7 = 20822 r 3 20822 / 7 = 2974 r 4 2974 / 7 = 424 r 6 424 / 7 = 60 r 4 60 / 7 = 8 r 4 8 / 7 = 1 r 1 1 / 7 = 0 r 1 => 11446435 There is a tip to divide a big number with a little number?, is posible with a simple calculator get the remainders from a divition like that?

Hey all, so, I was at this math contest last Tuesday. The contest consisted of 4 question, of which one was geometry. I had absolutely no clue on how to solve it, so I was wondering if anybody here could help me. We have a triangle [math]ABC[/math], which is not isosceles. Let [math]x[/math] be a line that bisects the angle [math]ACB[/math], [math]y[/math] be the perpendicular bisector of [math]AB[/math], [math]h_a[/math] be a line perpendicular to [math]BC[/math] and passing through [math]A[/math] and finally [math]h_b[/math] be a line perpendicular to [math]AC[/math] and passing through [math]B[/math]. Let [math]K \in x \cap y[/math], [math]P \in KC \cap h_a[/ma…

Would You mind telling me how to install plugin vbLatex for vBulletin? Could you tell... step to step. Thanhs a lot. K19:embarass:

Anybody want to try this problem? I know the answer and how to do it, I'll tell you later. Anyways... You have a random number generator, that generates the numbers 1-5 randomly (equal probability of each). You need to make a random number generator out of it that generates the numbers 1-7 randomly (equal probability of each). How do you make it out of the first generator? For example, you can take a number from the first one, and run it through the first one 5 more times, and say if you get some answers tell the generator to start over again, etc.

i know this is a reall general and broad question{and stupid/new to this world sounding}, im just wondering what kind of answers ill get. i love math, but when i ask myself this question, i seem to lack the answer.

Hey to everyone here in this forum. I'm new here and I have got a question concerning the exterior derivative and the Lie derivative. I have to show the following: (I searched for them for four hours on the net but no site is giving me a proof of it) These two I have to show for all p-form (p is between 0 and m if M is a manifold of dimension m) This is the formula for the exterior derivative which I have to show: Sorry I don't know why the picture are not shown here. Hope someone can help me!!! Any help is appreciated! If you have a book or a site where you have found one of these proofs let me know! Thanks

How is it a paradox? Is it just seems to be parsing the model of reality incorrectly? Or what?

i = [math]\sqrt{-1}[/math] i[math]^{4}[/math] = [math]\sqrt{-1}[/math][math]^{4}[/math] = 1 [math]\sqrt[4]{1}[/math] = i = 1 Therefore [math]\sqrt{-1}[/math] = 1, but that would mean that 1*1 = -1 Which is impossible. How is this? Did I make a miscalculation? Or is this really a paradox?

I keep doing the problem like the formula says but I keep getting the wrong answer The problem is m^2-3=-m 21. m^2 -3=-m m^2 +m-3=0 m^2/1 +m/1=3/1 m^2+(m/2)^2=3 m^2 +m+0.25=3 + 0.25 m^2 + m +0.25=3.25 (m+0.5)^2= square root of 3.25 m+0.5= square root of 3.25 and thats where I get stuck because when I look in the back I see im way off. Can someone explain what im doing wrong. It would be a big help.

Does anybody have any ideas on how to work out [imath]\sqrt{0.9}[/imath] without a calculator (to approx 10 d.p.)? I know there are a few methods for working out for working out square roots by hand, but i was wondering if there was a cleverer/easier way of doing it.

could this be a typo? in a question sheet? 2cosecx-1=0???