Applied Mathematics

The function I need is one which calculates the number of permutations which add to "n", using "l" six sided dice. for example if i was using a single die (l=1), and i wanted to know how many ways there were to get a 4 (n=4), the function would return 1. If i were using 2 dice (l = 2) and i wanted to know how many ways there were to get a 7 (n = 7), the function would return 6 (1,6; 6,1; 5,2; 2,5;4,3; 3,4). I know it's going to be based on the old nPr function but it's more complex than that i think. I intend to incorporate it into an excel spreadsheet to demonstrate entropy and numbers of microstates.

John has just sued Company, Inc. for P dollars. Company, Inc, due to the state of the economy, cannot afford to pay the debt in one lump sum, so he has to use a payment plan. In the applicable state, judgment debts (debts from lawsuits that are not settled out of court) are subject to a 9% APR. However, here's the kicker: In every state (not just this one), Interest on judgment debts is NOT compounding! What this means is that Interest does not accrue on previously-accrued interest. The outstanding balance, as a whole, does not gain interest, like in any ordinary debt. Instead, interest accrues only on the remaining principal. So, if he has a starting balanc…

Is there an easy way to calculat the approximate altitude (maximum possible) if you know the weight of a model rocket and the engines total impulse that I can teach to 1st through 5th graders? Thanks, Paul - thinking of starting a model rocketry club for beginners through a local school.

Before I ask my question, allow me to explain how I thought of it, so that we're on the same page. I would like to reproduce a physics experiment in which a marble rolls down the concave surface of a spherical bowl and back up the opposite side. Hypothetically, the more friction the surface has, the greater the height the marble will reach on the opposite side, because its energy is devoted to translational, and not rotational, motion (I digress, sorry). I would like to test this using several materials with different friction coefficients to line the inside of the bowl--but my real question here is directed more toward my curiosity of the following geometric concept, …

Hi all, I'm looking for help with drawing some paper plans for an inflatable boat. the problem i have is working out the curves for a tube mitre joint, that can be drawn on a 2d pattern that relates to its 3d shape- is there an easy mathematical formula for drafting this? I'm really bad at explaining things so have taken a couple of pics.... the cut in this pic below is an s shape, doesn't show up well. when in 3d the cut is a perfect straight line. the only method i can think of is to use a 3d template (piece of pipe) cut to the required angle and mark out the fabric in its inflated state. Cheers Simon

If you're a contestant on Deal or No Deal, and you're down to two cases, you're given the option to switch your cases. I know that, mathematically, it is a good idea to switch the cases, due to the Monty Hall paradox; however, would your chances of getting the better case go to 1/13, or 25/26?

I have little to no interest in Sudoku what so ever! This said I was wondering if anybody could briefly explain how one could use Graph Colouring and Chromatic Numbers to solve a Sudoku puzzle? thx, daPincess

Hi all, I am a product development engineer from a small medical device company that synthesizes a polyurethane based adhesive for surgical application. I am planning a tolerance study that will essentially set specifications for the tolerance of mass amounts in the formulation. However, with the number of raw materials involved a factorial DOE would not be an efficient design. I have researched the mixing DOE and some software out there that provides statistical analysis. The programs I've been investigating are Stat-Ease and DoE Fusion by S-matrix. I guess my question to the forum is has anyone had any experience with this type of study? And has anyone …

"For hundreds of years, many people have tried to prove the Four color theorem wrong. But they have all failed miserably... Now. After countless fails. ****** comes and shows the world that he is the smartest person ever borned!!! Yes, I have made a picture that is impossible to color all the regions using at most four colors so that no two adjacent regions have the same color. Btw. Here is the picture See you guys at the nobel price show thingy." can someone beat it so we on anuther forum can make him be abit more... humble

As I am not happy with my current job, I have decided to take a competitive examination to become a state high school teacher. For one of the test you have to pass, there are 75 units to study. The day of the exam, 5 balls with 5 different numbers will be extracted from a bag. Each number corresponds to a unit and you have to choose from these 5 which one you are going to develop. It is advised to prepare around 30 units to know almost for sure you will have studied one of the 5 between which you have to choose. However, I know several people who say they studied 30 or even more units for previous official announcements and they didn’t get any of those units chose…

OK so i'm not a big mathemetician but I was reading up on number sequences the other day and of course I found a lot of stuff on fibonacci sequences. I already knew two things: a fibonacci sequence is made by adding the two previous digits to get the third and then repeating any two consecutive numbers in the sequence when divided by each other will produce an approximation to the golden ratio, and the further into the sequence you go the closer the ratio gets to the golden ratio. What I didn't know was this: You can start a fibonacci sequence with any two numbers and it will STILL tend towards the golden ratio. So I wondered whether there was a relat…

A few years ago, I took out a private student loan at loantolearn.com, and opted to pay the interest while in school. My cosigner passed away earlier this year. Now the debt is mine, all mine. I just made a huge payment on it, knocking the outstanding balance to $4580.65. The interest is 7%. Since I'm currently only paying the interest, what would my minimum monthly payments be?

Hi guys , say I have 3 random variables X1,X2 , X3 where X1 = Y1 + Y2 + e1 X2 = Y2 + Y3 + e2 X3 = Y1 + Y1 + e3 where X1,X2,X3 are normally distributed with N(0,1) and e1,e2,e3 are independent random variables (error terms) with normal distribution Do I have to include the error terms for the mean vector of X and the covariance maxtrix of X , if so how would it look like ? mean: mean(X) = [mean(X1)mean,(X2),mean(X3)]' much thanks

Hello everybody, I am working on “improvement of formulation and process parameters for a process”. For a proper planning of my experiments I need a design of experiment. I have to show the influence of 8 factors to my process. Whereas five of this factors contain 2 levels, and three factors contain 3 levels. I will have time for 15 runs maximally. Someone gave me the advice to try Plackett-Burmann, but as I have factors with 3 levels, I am not sure if it really is the right design. You can determine the influence of 11 factors in 12 runs. But as I need just 8 factors, I could combine factors 6 to 11 to three factors of 3 levels, right? Further someone …

They say the chances of dying in a plane crash are 1 in 9 million. Am I correct in thinking that these chances increase the more you fly in airplanes? If that is true then how do you calculate your chances of dying in a plane crash after every new flight you board? That is, what is the formula for calculating this? Thanks, John

hello plz help me about solving ODE or PDE via Genetic algorithm (GA) thanks

I assume this is the right board. Difficult to tell what probability maths comes under. I have a game. I start out with 26 cards. 13 of these are red. 13 of them are black. The cards are spread out face down on the floor randomly. Now I must flip over as many black cards while trying to limit the amount of red ones I flip over. Originally, I figured there is a 50 - 50 chance of getting either colour, so what I did was: Randomly select the first card to be flipped. If it was a black one, I would chose another card (only in my head this time, I would assume this other card would be red if I turned it over (seems as the last one was black). I would then igno…

L1 = L0(1 + αL(T2 − T1)) The formula to find how long will be a stainless steel rod , alpha=17.3 from initial length 700mm after delta t = 600 C Yields a senseless number. Where am I goofing?

Ok, this should be interesting, and will hopefully settle a debate between my wife and I. Let's say there's a raffle, with 10 prizes, and you can put your tickets in individual boxes for each prize (thus there will be 10 separate, non-overlapping drawings). 9 other people have already bought 10 tickets each, and as a result, each cup now has 9 tickets in it. If I buy ten tickets myself (and I'm the last person to enter), would I have a better chance of winning if I put one ticket in each cup, or if I put all 10 in one cup?

Hi, Ive heard that some reaserchers found that music (chords , notes) is actually math based - in other words: melodies that actually sounds good are following a certain patterns (of chords and notes). that idea fit's well in my opinion since not anyone who takes a guitar and starts fretting can make any "pure" melody that pleases the ear. now for my question: since music* is math based - and therfore there are finite ways to make real music, and since every song is finite** in time isn't it inevatable that in lets say 100,000 years*** from now - there wouldnt be any way to create new music that hasnt been created before? * by music i actually referei…

I'm wondering what sort of mathematics one should be looking at pursuing in undergraduate courses with a view applying them to work in paleontology. What kind of math is math is most commonly used? I believe principal component analysis and multivariate statistical techniques like that are pretty important, not that I know at at all what that means. Is there a lot of mathematical ecology, population modeling and what-not, these days? I'm ever leery of calculus.

A bead slides down the surface of a sphere. Ignoring the initial speed of the bead, define the normal force between the bead and the sphere with respect to the angle of displacement. Given Answer: N = mg(3cosL-2) , L is the angle between the bead and the vertical taken from the centre of the sphere. My answer was N = mgcosL. I don't see how the given answer could have been derived.

A roller coaster freewheels down a frictionless track from rest a height h above the ground. At the bottom the track becomes a vertical loop with diameter 2a = 16m. How high above the ground (value of h) must the roller coaster start if it is to reach the top of the vertical loop without lifting off the track? The given answer is 20m. I would have thought that the roller coaster needs to start at a height equal to, or slightly more than, the diameter of the vertical circle at the bottom. Energy at start = energy at end, therefore mgh = mg2a, and h = 2a = 16m. Please help me understand why it is not so. Thank you in advance

I have a machining problem that I am trying to solve, and it appears that math may be of assistance. Basically, I have a 12mm cylinder and a piece of 10mm brass bar stock, and I want to cut a groove in the bar that approximates the curve of the cylinder fairly closely. Unfortunately, I don't have any tools that can work with a diameter as small as 12mm, so I thought that perhaps using a larger diameter circle, 'tilted' at an angle so it intersects the bar as an ellipse, might get me close enough. (Of course, I never thought before about any formulae relating a 'tilted' circle to the defining particulars of its cross-sectional view based on the angle. Does viewin…

Please help me with this question: A man sits on a trolley, which runs without friction on horizontal rails. The mass of the trolley (with the man included) is M. The man throws horizontally a stone of mass m, in the direction of the rails. Find the subsequent speed of the trolley if: (i) The momentum imparted by the man to the stone is J; (ii) The total work done by the man is W. The answers given are (i) v = J/M and (ii) v = squareroot[2mW/M(M+m)] For the first part I got J/m and I assumed the trolley's speed did not change after the stone was thrown, which doesn't make sense to me but that's the only way I could proceed with it. For the second part I got v …