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    Average Percentages over 3 years

    I am just having trouble with percentages. Lets say a town has a population of 1,000,000 in 2006 1,200,000 in 2007 1,800,000 in 2008 The percentage increase from 2006-2007 is 20% 2007-2008 is 50% So, what I want to work out is the AVERAGE percentage per year. The increase...
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    Fourier Series coefficients, orthogonal?

    Homework Statement Hello. I need help with orthogonality of the fourier series coefficients. I know you can use the dirac delta function, (or the kronecker function) in the orthogonality relationship. I want to try and see the derivation using complex form rather than sines and cosines...
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    ODE phase portrait

    Homework Statement i need to create the phase diagram for the equation \ddot{x}=x^{3}-x using MATLAB Homework Equations Well i have worked out that there is a centre point at 0,0 and a saddle point at -1,0. The Attempt at a Solution i found a site on the internet which shows me...
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    Primitive Polynomials

    Homework Statement Hi, I need to show that \alpha+1=[x] is a primitive element of GF(9)= \mathbb{Z}_3[x]/<x^{2}+x+2> I have already worked out that the function in the < > is irreducible but I do not know where to go from this. Homework Equations there are 8 elements in the...
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    Proving Isomorphisms

    Homework Statement Hello, I have been asked to prove that three different matrices which are skew-symmetric with a defined operation can be shown to be isomorphic to the usual vectors in 3d space with the operation of the cross product. Homework Equations Well the operation i guess is...
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    Number Theory: Matrix Exponential

    Homework Statement If I have a matrix M, say 30 5 20 16 How do I calculate M^{1870} mod 101 using Euler's Theorem. Homework Equations I have so far worked out M ^{2} mod 101 to be 91 28 11 53 and thought I could use this as 2x935=1870 The Attempt at a Solution I...
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    Piecewise Function

    I have to make a piecewise function continuous with first and second derivatives at x=0 by finding a value for a and b. I have made the function continuous by equating the RHS and LHS limits and then solving for the variable a. The limit of the first derivatives of the LHS and RHS are the...
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    Maple; Find real solutions

    y = k^{2}-4kx+3 - \sqrt{k^2+x-1/2}=0 I need to find the range of k so that this equation has some real solutions, using Maple. I have started off by typing 'soln1:=solve(y,x);' which gives me two solutions both involving k. I just need to know how to get maple to return the range of k so...
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    Proving Cauchy Sequences

    Homework Statement Well, my problem is proving that sequences are in fact Cauchy sequences. I know all the conditions that need to be satisfied yet I cannot seem to apply it to questions. (Well, only the easy ones!) My question is, prove that X_{n} is a Cauchy sequence, given that...
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    MATLAB MATLAB vector variables

    Hello ! I was wondering if somebody could possibly help me. I am looking to create a vector of variables. [v1 v2 v3 v4 etc...] I dont want to assign the value to any of them. Then I want to multiply this vector by another, so the final answer will be: z=3v1 + 4v2 + 6v3 etc...
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    Linear and Non-Linear Regression

    Homework Statement Well I have conducted a regression analysis, and have plotted a graph of my residuals vs my input variable. I know that for a linear regression the residuals must be randomly scattered blahblah, but from this graph, it looks like it has a curve to it ? is this because I only...
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    Convergence of an infinite series

    Homework Statement Well I am analysing the convergence of the following series: \sum\frac{2n}{n^{3}+1}x^{n} from n=0 to infinity. The attempt at a solution I have begun by using the ratio test, but as i have the limit in terms of x and n, i can't tell if it is bigger than 0? So does...
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    Calulating the Mean

    Homework Statement I realise this is probably an obvious question, but if there are two groups, say group A and group B, where group A was full of old people, and group B full of children. The mean age was 67 for group A and the mean age was 5 for group B. If these two groups joined...
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    Graphs with two intervals

    In general, if f(x)=k but only for a < x < b and c < x < d how would you integrate the graph ? To find the mean for example, would you find the mean for each and add together, or is there some special thing for this case?
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    Probability Density Functions

    Statistics Jill is expecting a vist from her uncle Tom. Tom would just come whenever he felt like it, but not when he had his art class. He will either visit her in the morning, or late afternoon, between the times of 9-12am or between 3-5pm. Say X is the number of hours after 7am, what would...
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    Direct Proof

    Homework Statement Prove that 10^n leaves remainder 1 after dividing by 9. The Attempt at a Solution There is an integer K, such that 10^n = 9k + 1 Where do i go from here if I want to do it just directly?
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    Injectivity & Surjectivity

    Find whether the following function is injective and/or surjective: f(x)= (x^2-2x+2)/(2x^2+2x+2) Basically, I just need to know if it is surjective. I don't want any proof because I should work it out myself seen as it is homework haha. I have a done it a few different ways and came out with...