Recent content by 12Element

The answer can be in either form ##\ -sin^{-1} \left(\frac{1-x}{2x} \right)+C= \ -2tan^{-1} \left( \frac {\sqrt{3x^2+2x-1}}{3x-1} \right)+C ##. Thanks a lot, this is really interesting, I only have a Casio calculator and whenever substituting random values in both solution does not give the...

I have a question about how to solve the following integral: ##\int \frac 1 {x\sqrt{3x^2+2x-1}}dx##, I know how to get the right answer (which agrees with WolframAlpha and the book I got the question from) through substituting ##\frac 1u## for ##x##, completing the square and finally doing a...

Thanks a lot, all is clear now.

Thanks for taking the time to answer my queries, I really appreciate it. You are right, there are quite a few typos in the text. I guess my questions would be if: $$ x^2 + x + 2 = (z-x)^2 $$ then: $$ \sqrt{x^2 + x + 2} = (z-x) $$ how did the author get: $$ \sqrt{x^2 + x + 2} = \frac {(z^2 + z...

Thanks, but my question is with regard to point 2 and 3. I am well aware about how to use the technique of point 1. Also, problem 1-3 are related to point 1.

Hi, With respect to the techniques mentioned in point 2 and 3: Can someone explain or even better, post a link for an explanation or a videos showing the use of these two techniques. Below excerpt shows problems 4 and 5 referenced in the above 2 points:

Perhaps I wasn't clear. I understand how a straw works. My question is will fluid flow encounter more energy losses in a small diameter pipe or in a larger diameter pipe. The typical answer normally given is: for the same flowrate a larger diameter pipe will be more efficient (less energy...

Hello everybody, It is normally said that fluid flow in a larger diameter pipe is easier (less energy losses) than in a smaller diameter pipe. This indeed appears to be true in relatively high flowrate applications however, I'm struggling to understand why drinking from a normal straw (small...

Thank you very much, that clarified a lot for me.

Thank for replying. What I have understood from your reply is that when the inductor is open-circuited it will have to spark (giving that no clamping method is provided), and therefore all of my assumption (which is based on the assumption that you could open-circuit an inductor without having...

Hello everybody, First of all I want to thank you all for this great forum. My question is if a superconductor inductor is charged with a certain voltage and then it is open circuited what will happen. My very basic understanding tells me that if the inductor is not a superconductor (it...