Recent content by goraemon

I'm studying probability and am currently stuck on this question: Let's say we have n distinct dice, each of which is fair and 6-sided. If all of these dice are rolled, what is the probability that there is at least one pair that sums up to 7? I interpreted the above as being equivalent to the...

Homework Statement Here is an exercise I came across while studying MaxFlow / MinCut and I'm rather stumped: Designate G = (V, E) as an undirected graph that has at least two vertices. Every edge e on this graph has capacity ce. Pick two arbitrary vertices from G and label them s and t...

Homework Statement We'll define a binary tree as a tree where the degree of every internal node is exactly 3. Show that the set of all binary trees is countable. Homework Equations A set is countable if it is finite or there is a one-to-one correspondence with the natural numbers. The Attempt...

Question: Suppose you have a finite state machine that accepts only strings with an equal number of zeros and ones. Show that you can then construct a finite state machine that accepts only strings of the form 0^n 1^n, i.e., an arbitrary finite number of zeros followed by the same number of...

Homework Statement Alice proposes to Bob the following game. Bob pays one dollar to play. Fifty balls marked 1, 2, . . . , 50 are placed in a big jar, stirred around, and then drawn out one by one by Zori, who is wearing a blindfold. The result is a random permutation (let's call it s) of the...

Homework Statement An ice cream shop has a special on banana splits, and Xing is taking advantage of it. He’s astounded at all the options he has in constructing his banana split: · He must choose three different flavors of ice cream to place in the asymmetric bowl the banana split is served...

OK, now I'm really confused then. Because sometimes using the surface integrals get me the correct answer but using Divergence Theorem doesn't, and vice versa. Below is a VERY similar question that I solved correctly using surface integrals...and I can't for the life of me see what is...

Homework Statement The problem is given in the attached file. Homework Equations Divergence theorem, flux / surface integral The Attempt at a Solution [/B] As you can see I got the question correct using Divergence theorem. But I wanted to make sure that I could arrive at the same answer...

Wait, so...I gather you're saying that ##\sum(-1)^{n+1}*(1-n^{1/n})=\sum(-1)^n*(n^{1/n}-1)##, so when we consider the positive term ##(n^{1/n}-1)##, it can be re-written as: ##\frac{(n^{1/n}-1)*n}{n}##, aka: ##\frac{\frac{(n^{1/n}-1)}{\frac{1}{n}}}{n}##? And from here we do a...

Homework Statement Does the following series converge or diverge? If it converges, does it converge absolutely or conditionally? \sum^{\infty}_{1}(-1)^{n+1}*(1-n^{1/n}) Homework Equations Alternating series test The Attempt at a Solution I started out by taking the limit of ##a_n...

You have sufficient information to figure out ##\theta##. Refer to a previous post that gave you all the hint you should need.

Two things wrong: 1) As another poster noted, the PE is incorrect. Note that the problem says the crate is 350 Newtons, not 350 kg. 2) Wnc is not just -50N. There's something missing there. Remember the general equation for Work and check your units.

The difference between net Force and net Torque is something you should internalize because doing so also helps you understand things like why we have separate equations for angular momentum vs. linear momentum, or translational KE vs. rotational KE.

Your calculation for ω is correct but it also appears that it's irrelevant to the angular acceleration. When the rod is perfectly horizontal with the pivot (which I assume from the question even though you didn't attach a picture), the only thing we need to figure out is the net torque at that...

If you were solving this problem via force diagrams, you COULD calculate the angle, given that the height is 5m and length of the incline is 8m (think Pythagorean theorem). But really, since you're using work / energy, you don't need to go this route. You need to factor in the friction force...