Recent content by RandomGuy1

I got it. Thank you so much.

This is my question: What is the largest m such that there exist v1, ... ,vm ∈ ℝn such that for all i and j, if 1 ≤ i < j ≤ m, then ≤ vi⋅vj = 0 I found a couple of solutions online. http://mathoverflow.net/questions/31436/largest-number-of-vectors-with-pairwise-negative-dot-product...

Yes, that was exactly what I was trying to say :) Sorry, I do not know how to use the definite integral symbol. But but I'm supposed to be integrating [t]2 and not [t2] as you pointed out. Won't those two be different?

Homework Statement This is from Apostol's Calculus Vol. 1. Exercise 1.15, problem 6.(c) Find all x>0 for which the integral of [t]2 dt from 0 to x = 2(x-1) Homework Equations [t] represents the greatest integer function of t. The Attempt at a Solution [/B] Integral of [t]2 dt from 0 to x...

Apologies if this is a stupid question, my basics are really weak. We have Inorganic Qualitative Analysis in our chemistry syllabus and I have somehow never been able to figure out if a substance is crystalline or amorphous. They both feel so ... powdery.

Fundamentals of Physics by Halliday, Resnick and Walker is pretty good.

You were right. That cleared a lot up. Thanks!

Here's the question: Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side d at time t = 0. Each of the particles moves with constant speed v. The particle at A always has its velocity along AB, B along BC and C along CA. At what time will the particles...

Why is Cr2+ reducing while Mn3+ oxidizing when they both have d4 configuration?

Homework Statement f(x) = [1 - tan(x)]/[1 - √2 sin(x)] for x ≠ π/4 = k/2 for x = π/4 Find the value of k if the function is continuous at x = π/4 The Attempt at a Solution This means that lim x → π/4 f(x) = k/2 I put x = (π/4 + h) and then...

Oops, sorry, it was [1 + cos∏x]/{[∏(1 - x)2} I put x = (1 - h) and as you said got lim x → 1- = a -∏ and lim x → 1+ = ∏/2 + b. Thus, I got a = 3∏ and b = 3∏/2, which happen to be the right answer. Thank you!

Homework Statement f(x) = sin ∏x/(x - 1) + a for x ≤ 1 f(x) = 2∏ for x = 1 f(x) = 1 + cos ∏x/∏(1 - x)2 for x>1 is continuous at x = 1. Find a and b Homework Equations For a lim x→0 sinx/x = 1. The Attempt at a Solution I tried...

Ah, I get your point. Energy immediately after blow is 1/2 mv2 + (mg)2/2k. It is at energy at instantaneous rest that I'm not sure. As the kinetic energy is zero, only elastic and gravitational potential energies have values. So, I get 1/2mv2 + m2g2/2k = 1/2 k[(mg/k) + h2] - mgh Solving...

Homework Statement A block of mass m is suspended through a spring of spring constant k[I/] and is in equilibrium. A sharp blow gives the block an initial downward velocity v. How far below the equilibrum position does the block come to an instantaneous rest? Homework Equations...

Oh, sorry, I meant -8m. Could you please explain the last step? Why do we equate the derivative to zero?