Applied Mathematics

i was wondering if someone could give me a hint for solving this equation: 3^x = 4 basic i know, but i've unfortunately had a blank.

Would someone be able to solve this equation for me: 3e^-10x = 6 i just want to see if my solution is right... thanks.

Hi all, I need a little help regarding simple optimization: There are a given number of pairs of positive numbers for e.g. [latex](a_1, b_1), (a_2, b_2)... (a_N, b_N)[/latex]. The objective is to choose a subset [latex]S[/latex] of some pairs: [latex]\max \sum_{i \in S} a_i[/latex] s.t [latex]\sum_{i \in S} b_i\le B[/latex] In other words, this problem can be thought as follows: You have some bank balance [latex]B[/latex] and there are number of different products in the market of price lets say [latex]b_i[/latex] that give some utility [latex]a_i[/latex]. Objective is to maximize utility (choose some number of products) subject to bank balance. What are s…

We conducted a trial using a RCBD in a field we didn't have much information. We realized after the end of the experiment that we were wrong on the establishment of the blocks (not perpendicular to the gradient). Can we do something to correct this experiment? Thanks for your advice and comments. Gaston

I'm working on a new statistical stochastic model, .. and I need to know what conferences I can submit at ? I'd like something related to\sponsored by IEEE ... -- thanks in advance

Hi It is well knowm by the theorem of the reminder that: [math]D(x)=d(x)q(x)+r(x)[/math] In this example: .......................If [math](2x^{119}+1)/(x^2-x+1)[/math] then figure out the reminder. Therefore I can afirm that the reminder has the form of :[math]r(x)=ax+b[/math], because [math]d(x)>r(x)[/math] and [math]d(x)=x^2-x+1[/math] And the original problem could be written as: ..................[math]2x^{119}+1=(x^2-x+1)q(x)+ax+b[/math].........(I) To this point I need two solution of:[math]d(x)=0[/math] so I can find the values of a and b. According to what I think: ...............If [math](2x^{119}+1) = D(x)[/math] and [m…

Hi All Working on my "Transport Planning Model" research I am on the phase of data collecting. I am working on a single bus route with about 22 bus stops. It is very difficult to collect data about bus arrivals and people arrivals at the bus stop(to check later which distribution they fit) for a long period. I even don't know how much data is needed for this research. Any help or advice about other approaches to this problem? Regards

Can someone please tell me the percentage of probability that the following event occurring? Furthermore, please show your work and explain how you came to the conclusion that you did. You have a bag full of 22 balls. They are identical in size, shape, color, and weight; the only difference is that 11 have the number 1 on them, and 11 have the number 2 on them. You are tasked with blindly drawing eleven of the balls, one at a time, recording the number on each of the balls you draw. Furthermore, you do not put the balls back, after you've drawn them. Instead, after the first draw, there will be 21 balls in the sack, and after that, 20, and then 19, and so on, …

Greetings, I'm working on a model, for a 2-state random variable over discrete-time domain, and I need to know what are the well-known probability models, I know Bayesian Model, and Markov Models .. what other models are there ?

I was wondering how the ancient Greeks calculated sine, cosine, etc. My guess is that they measured, and put the values in a table. Likewise, how was the first logarithms (or inverse functions in general) calculated?

A spreadsheet (e.g Libreoffice Calc) has a power function for the example scenario: annual change (%) is 3,4,5,6 for years 1 to 4 respectively. The power function is: power= ((a4/a1),1/5)-1 where a1,a2,a3,a4 correspond to the values 3,4,5,6. Can someone explain the theory behind this function please? Thanks.

When a probability question says 'what is the chances of getting at least one or at least two', how many does it mean in accordance with its stated amount..

I am using the CVX tool from Boyd for convex optimization. I need to implement the convex function [latex]\frac{1}{xy}[/latex] for positive numbers. I figured one way which is the same method used when convexifying a Geommetric Program. However for some reason it fails to do a simple case. The code in matlab is: cvx_begin variables p q r minimize( r ) p<=log(2) q<=log(3) 0<=p+q+r cvx_end [latex]\exp{r}[/latex] is [latex]\frac{1}{2*3}[/latex]. However it fails and says ??? Index exceeds matrix dimensions. Error in ==> cvxprob.eliminate at 215 temp = reshape(ndxs(temp),size(temp)); Error in ==> cvxprob.so…

A function of 10 variables in addition to that of time, have a gradient of F(x1, x11,t)! Determine the gradient properties. Away from the constrictions on this. I think that integrating F on any path is independent upon the velocity-properties. Can any one advise!

There is a drunk man standing on the number 0. The man stumbles back and forth, and he has a 50% chance of moving backward (0 to -1 ect) on each move and a 50% chance of moving forward on each move. Prove that after an infinite number of moves, the probability of the man reaching 1 is 100%.

hey guys, i am really confused on something.here is the thing: i have; i=x+(x^2-y)^(1/2) and here x is uniform distribution on (a,b) y is uniform distribution on (c,d) x and y independent and there is no information about a,b,c,d.but if you need you can assume anything like a>c. i need to find the probability density function of i but how?????? actually i dont know how to start!!

Hi there, I'm a physicist working on my PhD, trying to back out forces cancer cells generate against there environment in a controlled in vitro system. And i boilled down one of the problems that i have to a linear algebra problem, which i think is quite general. I've got a Matrix A. It is m by n with m>n (say 12000 by 10000) describing the forces in relation to the deformation x. And i got some external forces b. From that i can copmute an x that minimizes ||Ax-b||^2. Every row of A describes the forces at some position as linear combination of the deformation x. If i would now allow forces at specific index 1<=i<=m that would mean to clear the correspo…

For example, the probability of flipping heads with a two-faced coin is 1/2. Does the probability of flipping heads increase after flipping consecutive tails and vice versa?

Hey guys. As we all know that if we flip a coin, the possibility/probability of getting a tail or head is 50%. Suppose a man is flipping the coin and record the results, say , 10 times. The probability of getting all heads or tails is 0.5^10 = 9.765625x10^-4 which means that the probability is extremely small. Now, if the man has a result of 10 heads. The experimental probability of getting heads = 10/10 = 1 In that case, is there still any probability existing while we are flipping coins???

What are the advantages of normalizing a DFT with the frequency? E.g. A plot of DFT*frequency as a function of frequency.

Hi everyone, I'm a new boy. I am a retired fabricator/welder, used to most steel structure work & the mathematics thereof. Most things can be drawn - projections, geometry, onto a steel worktable & in 2D. I now need to know how the helix of a banister for a spiral staircase can be drawn, say in 60 degree parts. This means one revolution of the stair would need 6 similar arcs welded together for the banister. The length of the whole banister (per rev) is the hypotenuse of the rt angle triangle made by the horizontal of Pi x staircase diameter & the vertical rise of the (usually) 12 steps in one revolution. This hypotenuse can then simply be divided…

This is my first post on here, so I hope you guys can help! I am working on an optimisation problem concerning fitting homogeneous regular shapes (i.e. solar panels) within irregular shaped polygons (a standard house roof). I am looking to write a shape fitting algorithm. It wants to be as simple as possible to minimise computing time and of course be quick to code. I have written basic equations for standard roof shapes, but now I want to properly code something for all roof types. Clearly to be universal the polygon (roof) shape will vary, but the nested shapes (solar panels) are all identical in size, in the same orientation throughout and the shapes are in …

Hi all, This is my first post so please bear with me. I run closed recirculating fish tanks for my research, but have always struggled with maths and 'moving' equations around. Basically the scenario is this:\ I have a closed 2000 ltr system, but have no way of cooling the water. I have access to plenty of freshwater from a nearby creek which runs at outside ambient temperature. How do I work out how much colder creek water to add to the inside tank system to meet a specific temperature. I would like to generate myself a quick reference chart so I do not have to do constant calculations everyday. For example: 2000 ltr fish tank is at 20C. Creek outside is …

Hi, I wanted to know if anyone knew how to use finite difference methods to discretize the phi^4 kink antikink equation. Any help would be really appreciated

Hi everyone. I have something of a vague question to ask, so I'll try to make it as coherent as possible. I assume that with a perfectly balanced coin, for example, there really is a 50/50 chance of getting either heads or tails each time. But my question deals with situations that may have extenuating circumstances. For example, let's say you ask somebody a physics question. The possible outcomes are that they will either know the answer or not know the answer. So is it safe to say that there is a 50/50 chance that they will either know it or not know it? What if we are told that the person in question is a physicist? It may be impossible to calculate precise odd…