Mathematics

Hi can anyone help me sketch the shape of the graph X^X . Thank you

I think this is a pretty hard question: All the whole numbers from 1 to 2002, including the both of them, are written on a chalkboard in increasing order: 1, 2, 3... 2001, 2002. Then, the first number is erased, then the fourth number, then the seventh number, then the tenth number and so forth erasing all the numbers that occupy a place in the form 3k+1. In the new list of numbers(after the first erasing) the same procedure is applied, erasing all the numbers occupying a place with the form 3k+1. This same process is repeated until all the numbers are erased from the chalkboard. What number is erased last?

I have been wondering how this is worked out without just plugging it into the calculator, is it possible to do it on paper or does it take a long time to work out? I feel i should already know this but i have never learned it in school or in my maths course. Its obviously not a ratio as: 9^1.5=27 but 9^2= 81.

Dave I don't know where to put this post, you can delete it later. I would like to know if there are any plans to implement a drawing program into this forum (you know like MSpaint only your own), so that you could draw circles and straight lines, and have the drawing incorporated neatly into your post, rather than attaching a .jpg or a .bmp. Possibly even a graph program, so that you just enter an equation, and its graph comes up. How hard would something like that be? Just a thought... Regards

Observe: 2 = 2 2² = 2² 4 = 4 Unsquare both sides, and you get either 2 = 2 or -2 = 2 And if you square both sides again, you get 4 = 4 again So, does -2 = 2? Or am I just an idiot?

the one directed by simon singh. anybody know where to find that? for an award-winning documentary, it sure doesn't like to show its face. all i've found are written transcripts and references to the book. but i actually wanna see the thing, ya know? has anybody ever seen this?

Here is a problem which was given in a Norwegian mathematical contest: Suppose [MATH]a[/MATH], [MATH]b[/MATH] and [MATH]c[/MATH] are real numbers such that [MATH]ab + bc + ca > a + b + c > 0[/MATH]. Show that [MATH]a + b + c > 3[/MATH].

So I'm writing a history paper (but I'm a math major) so I choose to write it on Gauss, CF. My basic outline for this paper is that I'm gonna write on what he accomplished in his day - which shouldn't be too hard b/c he did so much, how that changed life in his day and lastly how it is still changing out lives today. I think I'll focus a bit on the bell curve because it has so many application today (poll for election...) and on complex numbers. I'm actually getting more and more excited about his paper the more I reasearch. SO my question is do you think i'm missing any super important issues and if you have any great sources that i could get information from. an…

I'm returning to school after 18yrs of hi-tek hell / BS - so lets be honest my in that my brain is still recovering from corporate insanity at the highest levels. I'm taking bone head algebra (pre MTH95) and doing fine --- but I really freak out when it comes to factoring large numbers - esp during tests A fine example is on the last test on square roots - I ran through a word problem getting the sq root of 6400 as the answer - and that need to be simplified - I freaked and blew it - obviously the sq root of 64 is 8 so 6400 would be 80 --- but that never made it thu my panic layer What are good methods to break large numbers down beside guessing or divine…

Evaluate: [math]\sum^{49}_{k=1} (-1)^{k} \binom {99}{2k}[/math] Figure this out without using calculator at all.

Is there any way to put a dot above something. I am going to use [math] \omega [/math] to denote angular velocity, and I want to put a dot over the omega symbol, to denote the angular acceleration. The notation [math] \frac{d\omega}{dt} [/math] is too cumbersome for what I want to do. Thank you

The area of a triangle with vertices (a,b), (c,d), and (e,f) is (sorry, I don't know how to put it into vertical bars for determinants) +/- .5 determinant of A where A is a b 1 c d 1 e f 1 and the symbol +/- indicates that the appropiate sign should be chosen to yield a positive area. How can one prove this? I think I have a method for proving it, but it seems too tedious and long to do.

I'm trying to prove that, hopefully this comes out right, [math]\sum_{r=0}^{n}{(-1)}^{r}{_n}C{_r}{(n+1)}^n = n![/math] Can anyone help? The pattern is from 1 4 9 3 5 2 1 8 27 64 7 19 37 12 18 6 1 2 1 etc.

How do I prove that lim x->a [xf(x) ] = cL, given that Lim x->a f(x) = L?

Hi, I have never really been a math type of person and am taking a intro to math course at uni. I am asked to solve an equation in the same format as the one below and indicate clearly the method used. The trouble is I have no idea how to do it [math] {6}/{y} + {8}/{y^2} = -1 [/math] I would really appreciated any help. Thanks edit: I don't know how to make fractions with latex

[math]w = \frac{K^{\frac{1}{4}}}{K^\frac{1}{2}}\frac{p}{2} \left(\frac{w}{2r}\right)^\frac{1}{2}[/math] [math]r=\frac{1}{8}[/math] and [math]w = \frac{1}{2}[/math] What is K in terms of p? The answer is [math]K=4p^4[/math] but I want to see the working out because, for some reason, I got [math]K=2p^2[/math].

Who, invented the mathematical idea of cross product, and in what year? Why did they invent it, and how did they do it? Thank you

how would i show that the values of x at which sinxe^(-sinx) has stationary points form an arithmetic sequence. I've so far worked out dy/dx=cosxe^-sinx(1-sinx)=0 so cosx.e^-sinx= and sinx=0 arcsin0=pi,2pi,3pi,4pi,etc so cospi.e^-sinpi=0 cos2pi.e^-sin2pi=1 cos3pi.e^-sin3pi=0 cos4pi.e^-sin4pi=1 therefore it is a repeating sequence and common difference 1,-1 but i don't think this is correct as again (im not sure how to solve (cosxe^-sinx(1-sinx)=0)) any ideas? thanks for any help

I've spent two hours trying to do this, but I cant figure a way out . We've just started the Gr. 12 Geometry and Discrete Mathematics and so far we've done dot product/cross product of vectors in 2,3 dimentions in cartesian and algebraic form Any help would be greately appreciated

Hi there If i had a function in the format cos(ln(x+1)) =0 how would i go about trying to solve for the solutions (roots) I can see there are three roots but i'm not sure how to solve it. ps. how do you solve secx(2sec^2x-1)=0 as ih happens i know it has no solutions, but how would i go about showing this. where can i look this stuff up thanks guys!

e^i(pi) + 1 = 0 if we modify it like so e^(i(pi)) = -1 e^(i(pi))^2 = 1 i^2(pi)^2 = ln1 = 0 so -pi^2 = 0 which is obviously wrong... so why?

since i began posting on this site, i have seen more than one thread like "what is sin, cos, ...?". so, somewhat inspired by daves two calculus lessons, decided to post the relevent parts of my trig notes. it was a one semester class, so it will probably be really basic. note: i will not cover graphing and inverse trig function. i will begin by introducing a unit of measurement of angles, because i find them much easier to work with. that unit is radian. the name will make sense after the description. we have a circle whose center is at the origin. as we all know, the circumference of a circle is [math]C=2{\pi}r[/math]. assume the radius of the circle is one. the circ…

I tried \newcommand but clearly that's been disabled. Is there some way to quickly write Einstein notation? [math]\eta_{\rho\sigma} = \Lambda^u{}_{\rho} \Lambda^v{}_{\sigma} \eta_{uv}[/math]

Im a total idiot and i can't find a pyramid or a triangular prism that was a surface area that is less than its volume by a 40 cm margin.. If you could find a triangular prism/ pryamid that has no more than 320 cm squared and at the same time has a volume of over 360 cm cubed....i would really apprieciate it thank you soo much

I have a question about something i read here. Why did they choose not to define vector division exactly? They said something about non-uniqueness, and I don't follow. To help me refresh my memory, suppose that we have two lines in an xy plane. For the sake of reality, let the plane be a real plane in real space. An equation for any line in the plane will have the following form: Ax+By+C=0 Suppose we have two lines. [math] A_1 x + B_1 y + C_1 = 0 [/math] [math] A_2 x + B_2 y + C_2 = 0 [/math] We can rewrite the equations as follows: [math] A_1 x + B_1 y = - C_1 [/math] [math] A_2 x + B_2 y = - C_2 [/math] We can rewrite this in …