Recent content by flash

Thanks for the help guys, I've got it now :)

Hi, I'm wondering if there is an exact solution to: (2t+1)e^{-2t}=5 I've tried and have been unable to solve this for t. I can get an approximate numerical answer using the calculator but that's it. Cheers

Thanks :-)

If I take F(x)=\sqrt{1+x^2}, then the derivative is always less than one so this is a contraction mapping from R to R, right? But there is no fixed point where F(x)=x, where the contraction mapping theorem says there should be. So where have I gone wrong? Cheers

Homework Statement When considering conservation of energy and momentum in the collision between a photon and an electron (in Compton scattering for example), is it reasonable to worry about 'stationary' electrons? The Attempt at a Solution From what I can recall the derivation of the...

Excellent, thanks alot.

Hi, The problem is to determine whether or not relativistic effects are relevant for an electron accelerated to an energy of a) 100MeV and b) 100GeV. So I need to find the gamma factor of the electron in each of these cases. I have used E = \gamma m_0 c^2 and solved for gamma = 195 in the...

Homework Statement Suppose \Pi \subset \mathbb{R}^3 is a plane, and that P is a point not on \Pi . Assume that Q \in \Pi is a point on \Pi whose distance to P is minimal. Show that the vector PQ is orthogonal to \Pi . Define a differentiable vector function r(t) with r(t) \in \Pi and...

Thanks, that's what I wanted to know. Cheers

I would like to solve 2^k = \frac{n}{k} for k in terms of n, but can't seem to do it. Any help greatly appreciated!

Homework Statement The running time of quick sort can be improved in practice by taking advantage of the fast running time of insertion sort when its input is nearly sorted. When quicksort is called on a subarray with fewer than k elements, let it simply return without sorting the subarray...

Thanks. So do you mean: view the transformation associated with matrix A in a basis of {eigenvector, orthogonal to eigenvector} and find the matrix for the transformation in this basis? I'm not sure what the significance of the orthogonal vector is here.

Homework Statement Let A be a 2x2 real matrix which cannot be diagonalized by any matrix P (real or complex). Prove there is an invertible real 2x2 matrix P such that P^{-1}AP = \left( \begin{array}{cc} \lambda & 1 \\ 0 & \lambda \end{array} \right) I know how to diagonalize a matrix...

An acid solution flows at a constant rate of 6L/min into a tank which initially holds 200L of a 0.5% acid solution. The solution in the tank is kept well mixed and flows out of the tank at 8L/min. If the solution entering the tank is 20% acid then determine the volume of acid in the tank after t...

Ok, thanks. The other part of the question goes: A is a 4x3 matrix C is a 3x4 matrix such that CA = I Suppose, for some given b in R4 that Ax=b has at least one solution. Show that this solution is unique. Can I just say x = Cb which implies that there is only one solution for x? I'm thinking...