Recent content by Pull and Twist

One big coincidence of thermodynamics is that automobiles are usually powered by an Otto cycle This cycle consists of an adiabatic compression (the cylinder compresses), isochoric compression (the fuel ignites, increasing the temperature in too short a time for the piston to move), adiabatic...

Thank you for verifying it for me. 🙂

Here is the problem I am dealing with... And this is how I approached it. Can anyone confirm that I did it correctly and got the right answer? Thank you.

I didn't mean to ignore it... and obviously I realized I did after the fact... then I second guessed myself. Thank you for verifying that I took the correct approach the second time around.

Here is the given problem... And I first approached it by drawing the xy footprint to get my theta and radius limits to convert to polar. Then I overlooked the original xy function and pretty much took the area of that footprint (highlighted in green.) That gave me a very nice number...

Well I'll be ****ed... didn't even spot that... and all I had to do was multiply my OT equation by (1/y^2)/(1/y^2) to get it in that same format. I can definitely solve a first-order homogeneous ODE much more efficiently then the mess I was working with.

Trying to figure out the orthogonal trajectory of x^2 + y^2=cx^3 Here's what I got... but it does not match the books answer. I don't know where I am going wrong. I think I was able to differentiate the equation correctly in order to get the inverted reciprocal slope and then I may have flubbed...

I am having trouble with the following problem; a.) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A. A=$$\left[\begin{array}{c}1 & 2 & 3 & -1 \\ 3 & 5 & 8 & -2 \\ 1 & 1 & 2 & 0 \end{array}\right]$$ So using my calculator I am able to get...

So I am having difficulty with the following problem; Determine the currents in the various branches. So I went ahead and assigned I names to the various branches and drew in flow directions to help me visualize the problem better. From there I created the following three equations...

I'm not getting the right answer... why?

How did you come to that answer though?

Find the sum of $$\sum_{n=1}^{\infty}\frac{1}{n2^{n}}$$ I tried manipulating it to match one of the Important Maclaurin Series and estimate the sum in that fashion but I cannot see to get it to match any. I was thinking of using $$\sum_{n=1}^{\infty}\frac{\left (\frac{1}{2} \right )^{n}}{n}$$...

I have never learned about the Laurent series expansion... I'm supposed to be using the Remainder Estimate for Integral Test... I am assuming that I am not using it correctly since I am not getting the same answer.

I'm working on the following problem and I have made it this far... am I on the correct path or am I doing this incorrectly?? I find series extremely confusing. Also... how do I find the error involved in the improved approximation? This is the series I am working with...

This is another problem I am having difficulty with... I set it up like I've been working the book problems, especially the sphere problems, but can't seem to get the right answer. I feel that I am calculating the radius incorrectly. I know I am supposed to us $${x}^{2}+{y}^{2}={r}^{2}$$ and...