Recent content by Sleek

I've understood the formal definition of limits and its various applications. However, I'm trying to dive more into the history of how the concept of limits were conceived (more than what Wikipedia tends to cover), and how to formally understand and visualise infinitesimals. For example, I know...

I'd recommend reading the theory behind derivatives as rate of change, and it's geometric significance. And one more thing, be thorough with the concept of limits (not just some list of formulas), so that you can understand the "first principle" of derivatives and other elementary concepts...

I'm too a novice in case of relativity. From Wikipedia, "Second postulate (SR) - Invariance of c - The speed of light in a vacuum is a universal constant, c, which is independent of the motion of the light source." I.e., the speed of light is the same in all frame of reference regardless of...

From the question, since the Rooks are identical, I think we can assume that, in a given arrangement, even if we swap two Rooks, it wouldn't make a "new" arrangement. Your answer "1625702400" is right if all the Rooks are distinguishable. So I'll give you a small exercise, and this would be for...

Unfortunately, I have not yet studied N-R and other stuff (not yet in my syllabus). This problem is quite an interesting one. I plotted some graphs and even the one dynamicsolo suggested, which really shows the big picture. Ok, from what I see, the sine function now seems to be tilted with an...

Hello, I've read and learned the fundamentals of SR and understand it to quite a nice extent. I'm talking about the time dilation's derivation using a light clock. I've understood the derivation's concepts, i.e. the proved principle of speed of light being 'c' in all frames of reference. So...

@ehrenfest I think i get it too. Maybe 40 is the shortest. I'll look into it when I get a bit more time :). Regards, Sleek.

If the fly has to walk, then it has to cover the distance through the walls. Had it been able to fly, the answer would have been sqrt(30^2+10^2) ~ 31.6227766016838. The reason for this is, the vertical height is 12, and the fly sites 1 foot below the ceiling (11 feet). It wants to go the 1 feet...

If a function is periodic, then f(x)=f(x+p), as you said. Also notice that, f(x)=f(x+np) where n is an integer. Watch it like this. If you have an angle on the unit circle, for every 2*pi rotation, you arrive at the same point. Hence, it doesn't matter how many times you rotate, until it is an...

Yes, it is Antilog. If the base is 10, then you will find Antilogs for them in logarithmic tables. Base e can be converted into 10 if necessary (by multiplying roughly with 2.303). Regards, Sleek.

As CompuChip suggested, try the above method and post what you get. You might also want to familiarize and brush up on combinatorics. If you know how to calculate permutation and combination, it should be good, at least for now. This makes your job "slightly" easier in the above problem, and...

In C, one of the fundamental property of logarithm is used. It is, x log b = log b^x. Now, you have e^log b^x, which IS equal to b^x. Let e^(log b^x) be some number m. You'll get an equation in exponential form. Convert it into logarithmic form. What do you get? Regards, Sleek.

But have they not given the individual number of black and white marbles in each of them? Regards, Sleek.

As everyone said, you have given us insufficient information. But when you get them, try what I say. Its just a hint, but if you get it, then its good, else we're always here to give some more hints or help correct your mistakes. There are three urns and each having black and white marbles...

Another approach is, first let ABC sit. They can be ordered in 3! ways. Among A,B,C, there are 4 places from among which two can be occupied. Arrange D and E in these four places, which can be done in 4P2 ways. You can choose any method, but the second problem let's you visualize what's going...