Recent content by sennyk

You should be able to use those two devices together. You modulate a signal; when the signal hits something it should echo back. Then you should be able to match the return signal. The time it takes to get your response should tell you how far away an object lies.

I believe that there are 6 or 7 answers; n = 0, 1, 512, 4913, 5832, 17576, 19683. It depends if you are counting zero or not. Proving this is another story. First, candidates for n must be equal to 'k' cubed. So we can eliminate a lot numbers with that statement. Once 'k' gets to be 54...

I want to calculate the following: \displaystyle\lim_{k\to\infty}\frac{n_k}{d_k} where, n_0 = 2 d_0 = 1 n_k = 2n_k_-_1 +d_k_-_1 d_k = n_k_-_1 + d_k_-_1 For the life of me I have no idea how to do this. By the way, the answer is supposed to be \frac{1 +...

Thank you. Thank you for the link; it is very interesting. More importantly thanks for the site that hosts the link. I apologize if it was too trivial. It just appeared to me that everyone dismissed the rectangle idea after it doesn't just work for p = 2. I found the system of equations...

I've seen Faulhaber's formula. I've read the mathworld methods at least 3 times. I'm looking for more info my specific method. I've pulled out my calculus and discrete math books, but I've seen nothing that uses my method to find the solution to the power series. Have you seen the method...

I'd appreciate any feedback that I can get. I can't find this method documented anywhere.

The other day I was thinking about the integer power sum and the general solution for each value of p. I came up with a method that will allow me to calculate the general solution. I thought that I may have stumbled upon something novel, because I couldn't find any reference to this method...

Equation of a line: y_1-y_0 = m(x_1 - x_0) Two points on the line: (0, 0) (x,y) slope: m = y' original equation: y = x^3+6x^2 +8 Start filling in the blanks.

Problem 3 is fun! There are two solutions for k. Create a model that will tell where the equations intersect. Then create a model that will tell when their slopes are the same. You should end up with two equations in terms of k and x.

Whenever I have more or fewer equations than unknowns, I use the following to obtain the least squares answer. A^T A x = A^T b, where A^T is the transpose of A.

Or you could find the angle by having a frictionless POT and using an ADC. I'm not sure a close enough to frictionless POT exists.

You need that angle. Try adding an angular rate sensor and integrating to find the angle. Then you can remove the acceleration due to gravity and integrate to find the velocity. http://www.analog.com/UploadedFiles/Data_Sheets/778386516ADXRS150_B.pdf They are about $50 on digikey. However...

It seems to me that you want to solve this DE I'm assuming that x is a function of t. \frac{d^2x}{dt^2}=1+ln(x) For the life of me, I can't remember how to solve that. I'll look it up later.

The integral of ln(x) is not 1/x. You have that backwards.

Quick question about induction. Could you prove it true for n = 1. Then prove it for n = n + 1. Then prove it for n = n - 1. Would that be enough to prove it for all integers?