Recent content by s0ft

Ok. The actual question itself then. An open cubical container with 2.5 m x 1 m base and 2 m height, half full with water is accelerated at 4ms-2 up on a 15 degree incline along its length. Will the water spill?

Is it possible to predict whether or not water spills out of a cubical container accelerating uniformly along a specific incline? I know the expression for the angle the new water level makes with the old one(horizontal). But how do I know their point of intersection? Note : Of course the...

The table cleared it up. So, what was actually being asked was the time from Mavis's perspective. I hadn't realized that. Thank you!

The book says Stanley will measure a shorter time of 0.32s. I'll directly quote the book:

I'm sorry if I was unclear. It is : ...Mavis reads 0.4s on her timer ...

This is a conceptual problem, right out of a book. Say Mavis is moving in a spaceship at 0.6c relative to Stanley on earth. When Mavis just passes earth, both of them start their clocks. When Mavis reads 0.4s, what does Stanley read on his? Now here's the problem. I think 0.4s being proper...

Is there a single, general, solution guaranteeing method that can be applied to any first degree first order differential equations? I know there are a lot of techniques or should I say categorizations for solving these types of equations, like linear, homogeneous, Bernoulli equations...

Thanks. So I guess I will just have to accept that as a fact. No easy and 'real' way to obtain the result without resorting to other forms of Gamma function.

How does this: \int_0^\infty\frac{x^{m-1}}{1+x} dx equal \frac{\pi}{sin(m\pi)} ? It has been simply stated as a fact in a proof of the so called "Euler reflection formula" in a textbook. I have tried the usual ways, substitution, integration by parts and even series expansion of 1/1+x but I...

There are a lot of contents regarding finding vertical, horizontal and oblique asymptotes for the so called 'rational' functions online. All of these curves are given in the form y=f(x)=(g(x))/(h(x)). But as far as my search results go, there are none regarding general algebraic...

\displaystyle\int_0^\pi\dfrac{x dx}{a^2sin^2(x)+b^2cos^2(x)} I have to prove this to be equal to \dfrac{\pi^2}{2ab} but with my attempt at it this problem boils down to: \dfrac{\pi}{2ab}\bigg[\arctan\Big(\dfrac{atan(x)}{b}\Big)\bigg]_0^\pi which equals zero.

The actual problem from where this stemmed out was this btw: \int_0^\pi\dfrac{x dx}{(a^2sin^2(x)+b^2cos^2(x))^2} If it could've been solved without of all this, please tell me how.

Thanks Simon, (a^2−b^2)sin^2(x)+b^2 did help move forward but now I'm stuck at \int \dfrac{1+t^2}{(a^2t^2+b^2)^2} dt And though I may be able to continue on from here trying this and that, isn't there a shorter way?

How do I integrate: \int\dfrac{dx}{(a^2sin^2(x)+b^2cos^2(x))^2} Multiplying and dividing by sec^4(x) doesn't work, neither does substituting tan. Any pointers would be appreciated.

So, is it ok to say there is this 'mass defect' here? The 'price' to pay for creating a system is a small loss in the total energy of the system?