Mathematics

The function [math]f:x \to , x^2 - 10x + 29 , x \in \Re , x \ge k[/math] is one-one. Find the smallest possible positive value of [math]k[/math] and the range of [math]f[/math] in this case. My understanding of "one-one" is that there can only be one value of f(x) per value of x. So I'm thinking that maybe k=5 because that is the minumum point of the function. Although I was only just introduced to the concept of "one-one" verus "one-many" so I can't be sure. Am I on the right track? Thanks.

I'm amazed by how many people fail to accept repeated proofs of .999... = 1 utilizing multiple methodologies. Don't read the body of this blog, just read the comments: http://polymathematics.typepad.com/polymath/2006/06/no_im_sorry_it_.html There are some rather intelligent people making revprez-style bombasitc arguments towards the contrary. Why? What fundamental misunderstanding compels these people?

Hi, I'm unsuccessfully looking for the proof of some sums. I'm sure they are very well known, so I wonder if some mathematician could redirect me to useful resources on the web, or just give me a hint about where to start for solving them. The first is the famous binomial. If: PP(i) = p^i * (1-p)^(s-i) * s! / ( i! * (s-i)! ) with 0<p<1, i and s positive integers, then I know the proof for: Sum(PP(i), i, 0, s) = 1 But I can't work out the proof for: Sum(i * PP(i), i, 0, s) = s*p and for: Sum((i-s*p)^2 * PP(i), i, 0 , s) = p*(1-p)*s A related problem leads to the definition of: PR(i) = Product((n*p-j)*(s-j)/((n-j)*(j+1)), j, 0…

hi every1~! I was just curious that what is the point of studying only integar solutions of a problem. One reason that comes up to my mind is that some irrational numbers have infinite numbers after decimal, so therefore it would be a problem to write an exact solution. But are there any more reasons that prevent us playing with other numbers?

I have no experience of using MATLAB but I would like to learn it (part time) in 6 weeks, probaby to a respectable standard, for something I'm doing over the summer. I am keen to learn how to use it but is this a realistic aim in 6 weeks? I will have to teach myself. Can anyone advise/comment on this? Are there any books which are good and assume no previous knowledge? (I need to make a decision in the next day or so)

Where I work I have a patron who come in and picks my brain. Usually just politics, riddles or I.Q. Test type questions. Most I chew up and spit out rather quickly and haven't had a problem until now. I admitted to him I was no mathematician but he gave me this problem stating it was only a high school problem, but it took him 2 months to figure out. I took a look at it and it seemed fairly easy but I can't seem to find the right equation or series of to solve for the unknowns. It's been a month and I've been scanning over all my old texts for similiar questions but to no avail. Any help would be greatly appreciated, even just a general point in the right directio…

So, that's the question.

From http://www.scienceforums.net/forums/showthread.php?t=20184&page=2 I'm sorry but this is wrong, the squareroot of ANY number is a +/- result, it has 2 possibilities, that the situation dictates...

Could someone please explain to me why the following is statistically falliciouse: The prosecutor's falicy The DNA profile found at the scene matches the suspects. The probability of a randomly chosen person having the same DNA profile is calculated as 1/100. So... if the suspect left the DNA at the scene of crime, the probability that the DNA from the crime scene matches the suspects DNA is 1. If some random person left the DNA at the scene of crime, the chances of the DNA matching the suspects is 1/100. Therefore, the fact that the DNA from the crime scene matches the suspect's is 100 times more probable if the suspect left the DNA at the crime scene t…

A car, a van, a truck and a bike are all travelling in the same direction on the same road, each at its own constant speed. At 10 am, the car overtakes the van; at noon, its overtakes the truck; at 2pm its overtakes the bike. At 4 pm the truck overtakes the bike and, at 6pm, the van overtakes the truck. a) Let c an T represent the speeds in km/h of the car and the truck respectively. i) Find the speeds of the van and the bike in terms of c and T ii) Show that the time when the van overtakes the bike is the same regardless of the speeds of the car and the truck

To show that the sum of two tensors is a tensor, I am taking the approach that (here for a vector, or first rank tensor) [math]V_i' = a_{ij}V_j[/math] [math]W_i' = a_{ij}W_j[/math] then summing them to get [math]V_i' + W_i'= a_{ij}V_j + a_{ij}W_j[/math] then when you sum and contract that lot you get [math]V_i' + W_i'= a_{ij}(V_j + W_j)[/math] which if I am not mistaken fulfils the criteria for a vector, showing that the sum of two vectors is a vector. Now when we get onto higher rank tensors, I am finding this a bit of a pain, since expanding and contracting that lot is tiresome. Is it a general rule that [math]V_{\alpha\beta\gamma}' + …

I didn't think these 2 questions applied to the other sub-forums so i put them in here. So Rd = [ I + (PV-NP)/n] / [(PV+NP)/2] where Rd = cost of debt I = annual interest payment PV = par (or face) value of the debenture NP = net proceeds of the issue = market price less costs n = the number of years to maturity of the debenture Eg the book gives me is... Suppose the Russ Saving Company issued an eight-year, 7 per cent debenture two years ago. The debenture is currently selling for $95.38. What is Russ Saving's cost of debt? Rd = [7 + (100-95.38)/6] / [(100+95.38)/2] = 7.95% If we assume a corporate tax…

lets say i've got this subset T of irrational numbers that i want to prove is non-denumerable... how should i go about this? i'm not seeing any way of diagonalizing without guaranteeing that the new number will still be in T. any pointers?

limit of (e^x+x)^(1/x) as x approaches 0 I remember using e^L where L=(e^x+x)^(1/x) for this 1^infinity form what do I do now?

This is a very easy problem. Prove that if you connect midpoints of sides of any triangle to form a new triangle, the ratio of the area of the new triangle to the original triangle is 1:4. Remember, proving means showing for all cases. It's easy to see this is true by equilateral triangle but that's not really proving.

Hi guys My math is rusty as heck, I haven't touched practically anything for at least 4 years. I just recieved notice that I was accepted to university, and they've invited me for a placement exam. I have to go over the basic and bit more advanced math so that i wont waste time remembering things at the exam time itself.. I've been looking for some basic algebra questions, but didn't really have a lot of luck. Anyone knows of sites that allow for algebra training? Furthermore, I'm new to the USA.. can anyone explain, briefly, what does "Math I", "Math II" and "Math III" means? What type of "difficulties" are we talking about between these? And just a las…

Why would studying precalculus be different than studying college algebra and trignometry? Why would it be different than picking up a college algebra and trigonometry book and studying them? What type of material would be covered that is different than both combined? How is it all different?

Hey, I was wondering if anyone knew or could help derive the formulas for rotations around an axis in cartesian coordinates. For example, let's say I have the point (x,y,z). I want to rotate the whole coordinate system around the x-axis. I can rotate it 90 degrees and switch the y and z axis. That one I just make the new coordinate (x,z,y). But what about rotations other than multiples of 90? Can anyone help me derive the formulas for those? Thanks

Someone please help...I'm stuck on these problems. The fenders (factor enders) of 156 are 1, 2, 3, 4, 6, 8, 9 and that 156 is a 7-fender (that is, it has seven fenders) {1},{2, 12, 52},{3,13},{4},{6, 26, 156},{78},{39} Q1 Find a 1-fender which is composite. Is the answer {1, 11, 121} Q2 Show that a number which has 0 and 9 as fenders has at least four more fenders. Q3 The smallest 10-fender is less than 700. Find it and explain why it is the smallest. Another 7-fender is 460 - its set of fenders is {0, 1, 2, 3, 4, 5, 6}, which is different from the set of fenders of 156. Q4 Find three 9-fenders less than 1000 with different sets of fenders.

heya every1~ Over the summer I plan to do some research in mathematics, but I am not sure which specific topic I should choose. I am looking for a topic that requires a lot of theoretical thinking, and can be useful in further research. Basically, my goal is to contribute something to the mathematicians of the world, whatever I can, which will be beneficial for every1~ Do you guys have any ideas in mind? What are your thoughts about this "wild" idea?

hey this is not so much a problem that i can't do, its problem that seems to have 2 answers, yet i thought laplace transforms are unique.... if i have [math] F(s) = \frac{2s-1}{(s-1)^2s^2} [/math] then if i take the inverse transform it straight from here (either by using maple, or relising that [math] \frac{2s-1}{(s-1)^2s^2} = \frac{s^2 - (s-1)^2}{(s-1)^2s^2} [/math] i get [math] f(t) = -t + te^t [/math] however if i split up F(s) to [math] F(s) = \frac{2s-1}{(s-1)^2s^2} = \frac{2}{(s-1)^2s} - \frac{1}{(s-1)^2s^2} [/math] and then take the inverse transform (either by using maple or convolution integrals), i get [math] f(t) = 2te^t-4e^t+2t…

Can you imagine a group with infinitely many identity elements? A structure like this have discovered mathematician Algirdas Javtokas, he calls it a beta group. I have read his axioms in Beta Algebra book, but still it is hard to understand how such structure can “work”. Maybe you know something more about this?

I have this diff. equation: [math]\frac{dP}{dt}=\frac{Patm}{Volume}\sqrt{\frac{(Pin^2-P^2)}{Kv})}[/math] with Patm, Volume, Kv = constant; P = Tank Outlet Pressure; Pin = Tank Inlet Pressure I would like to have a laplace function of this so I can use it easily in simulink, this way I can put many air tanks behind each other. Isn't there a way to go to a laplace form, skipping the diff. equation problem. Matlab solved the diff. equation in a way I don't like: simplify(dsolve('DP = Patm/Volume*sqrt((Pin^2-P^2)/Kv)','P(0) = Pstart','t')) like this: F=[sin((Patm*t-atan(1/(Pstart^2-Pin^2)*(-Pstart^2+Pin^2)^(1/2)*Pstart)*Kv^(1/2)*Volum................. Matlab g…

please can someone solve 2e^5t to 3 significant figures.

on dotted paper a 3 x 3 square . . . . . . . . . you can get 8 different ways of linking 2 dots diagonally at a 45 degree angle. and 2 ways of linking 3 dots diagonally on a 3 by 4 square . . . . . . . . . . . . you can link 2 in 12 different ways and link 3 in 4 different ways on a 4 by 4 you can link 2 in 18 ways , 3 in 8 and 4 in 2. assuming the verticle hieght of the square is x and the width is y. and x is the number of dots we need to link. so can anyone formulate a formula using x y and w to give me the number of diagonal combinations on N by N sqare. the formulae for verticle and hor…