Recent content by The legend

Homework Statement Given the equality \frac{sin^4(x)}{a} + \frac{cos^4}{b} = \frac{1}{a+b} Prove that : \frac{sin^8(x)}{a^3} + \frac{cos^8}{b^3} = \frac{1}{(a+b)^3} The Attempt at a Solution I cubed on both the sides of the 1st equation and solved a bit, reaching no where. Then I...

ok, thanks.

As i know them, black holes are dead remains of stars where the gravitational pull is so great that not even light can escape. Well, but light(electromagnetic radiation, in general) has no mass, then how does gravity effect light?

the direction finding is pretty simple. What is the direction of the component 4.7m? And the component of 1.9m is east, as you've written. So, the combination of both these directions gives you the direction of the final vector. :wink:

Correct! this is the actual answer. I gave this answer when i was first asked (except mafia was gang-leader in my sentence)...and it yet remains my favorite one :biggrin:

here's another easy one A truck-driver was turning left into a one-way street the wrong way. Halfway down, he was seen by a policeman, who made no attempt to stop him. Why?

that's pretty easy. man has hiccups...wants water to stop them. Bartender is a clever guy. :smile:

yes, it could be considered that way. :smile: so, now that the "inclined" vector is taken care of, you can just forget about it, keeping it's components. Do the same for all given vectors, and then it's just plain addition(or subtraction, in some cases) of vectors in the same direction...

Basically, if you have a vector, of say magnitude 10 units at an angle of 300 from the x axis, the component of that vector on x-axis will be 10*cos30. And the component of the same vector on y-axis will be 10*sin30. Vector components are the vectors on x and y axis, which added, give the...

mee too...but when i wake up. :-p Hey wait...it's next year for me already! :biggrin:

That website is already helping! Thanks a lot, Andre :smile:

okay. thanks a lot for the reply. :smile:

But this proof just guarantees the holding of the inequality after n>a. What the question asks is to find 'a'.

Thanks for the reply, chiro. I found the derivative for 10^n, but for the n! i used wolfram alpha and got this. http://www.wolframalpha.com/input/?i=derivative+n! There is a digamma function involved, but i don't know much of it, and couldn't carry on with the further steps you've hinted...

Homework Statement This is just a problem i came up with while doing in equations, and recently saw in a book too. Find the smallest integer n, for which n! > 10n The Attempt at a Solution The trial method (with help from the computer) yields 25 to be the answer. After a...