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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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    Elevators and Potential

    cant you do the absolute value of it as surely same power would be needed to go from 1 to 2 as 2 to 1
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    ODE phase portrait

    for any values of C?? all i am getting is what looks like a square graph translated a lot im not sure what its mean to look like thanks
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    ODE phase portrait

    i see -- ok sorry. so \frac{y^2}{2} = \frac{x^4-2x^2}{4} + C ?? i still dont really know what to do with it though forgive me!! thanks again
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    ODE phase portrait

    thanks for the reply!!! do you mean just straight forward integrate it w,r,t, x for example it would be \frac{x^4 - 2x^2}{4y} ?? then what would i do with that though?? thanks so much for your help
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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

    Haha ok just ignore me, i think i get it now anyway. many thanks for your help its much appreciated!!!
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    Primitive Polynomials

    brilliant thank you. how do i show that these elements that i have generated are the actual elements though? or is it enough just to say they are? and the fact that I havent got the same result twice from 0 to 7 means that it is primitive? thanks so much
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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

    thanks so muchhh i think i know what im doing now!! cant believe never knew that way of writing skew-symmetric matrices
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    Proving Isomorphisms

    also how can i write a skew-symmetric matrix as a linear combination of I J and K? please help thanks
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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

    thanks again. when multiplying matrices to say get M17 what order would i do the matrices in? For example does M17 = M x (M16) or M17 = (M16) x M
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    Number Theory: Matrix Exponential

    thank you everybody for your replies - much appreciated. yes i began by just squaring my way up to 1870 using the primes however i dont' really see how this uses Euler's theorem? I could square my way up easily if it was just a number, but I have never done it with a matrix and think it...
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    Number Theory: Matrix Exponential

    Okay, after researching this diagonalising I have come to the conclusion that my matrix cannot be diagonalised because all the roots of its characteristic equation are not real. is this correct? or could you point me in the right direction if it is not. thank you
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    Number Theory: Matrix Exponential

    is that just finding the inverse?
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    Buying and selling

    "a) Calculate the discount percentage relative to the initial selling price." does this not relate to the 360 dollars rather than the 200? as 200 is the buying price. Maybe I have just read it differently. Your working is correct though. your part b looks correct too
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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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    Maple Plotting With Maple

    you're using e as a vairable, you need to use exp(.....)
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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

    Okay that sort of makes sense, i have C defined in the set [-1,1] in a previous question. (if it is the same C !) but what about the 2^{n-1} where does that come in in terms of C ?
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    Proving Cauchy Sequences

    Yes I thought that was odd. But it is a follow on question so perhaps they had proved it before, I'm not sure. But I want to be able to do it just based on this. So I can't take m = n+1, that makes sense. I was just clutching at straws really, trying to use the inequality provided. So...
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    Proving Cauchy Sequences

    Hello, thanks for the reply. Here is what I have done: Take m,n>N N>0 \epsilon > 0 Take m = n+1 then |X_m-X_n| \leq 2^{1-n} \leq 2^{-n} But then i don't know where to fit epsilon into it? I actually have the answer in front of me, but it doesnt use epsilon at all, or N, which...
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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

    How do i convert '[ (2*v1)/7, -(3*v2)/7]' into (2*v1)/7 -(3*v2)/7 ?
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    MATLAB MATLAB vector variables

    thankyou, yes this is what i want I think, except if the cols of the matrix is like 7. I want it to automatically create seven things. so basically i need like: syms v1:vcols A = {v1:cols}; but i know I cannot do this!
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    MATLAB MATLAB vector variables

    Thanks for the reply. Sorry if i wasnt very clear. Basically, I want to create a vector of variables. the vector will have the same number of rows as the number of columns on a previous matrix, A. But I don't want any values assigned to the vector. So if [rows,cols]=size(A) I want to...
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