Recent content by bologna121121

I think I have the idea of what to do, but just to be sure I'll try the commutative addition one. The addition is commutative if \overline{a} + \overline{b} = \overline{b} + \overline{a} This is the same condition as x + y = y + x for all x \in \overline{a} and all y \in \overline{b}...

Homework Statement We are supposed to prove that the addition and multiplication of congruence classes for integers are associative, commutative, and distributive. Homework Equations None The Attempt at a Solution To me, it seems like this would just be trivial as all these...

Hello, In my abstract algebra class, my teacher really stresses that when you show that a set is a group by satisfying the axioms of a group (law of combination, associativity, identity element, inverse elements) these axioms MUST be proved in order. This makes some amount of sense to me...

Homework Statement Prove in general that if m does not equal n, then AB and BA cannot both be identity matrices, where A is mxn and B is nxm. Homework Equations None (that I know of at least). The Attempt at a Solution At first I thought it would be a good idea to define each...

Hello, I'll be graduating in one year with a BS in Physics and a BS in Applied Mathematics. I've done research in Astrophysics and Photovoltaics, and I'm considering pursuing a graduate degree (either MS or PhD) in Material Science Engineering. I've looked at various school websites and it...

But don't the tensions determine the resultant torque on the pulley?

Homework Statement Two masses, one of m_{1}= 3kg, the other of m_{2}=4kg, hang from opposite sides of a pulley of radius .15m. When released from rest, the heavier mass falls .34m in 4s. What is the rotational inertia of the pulley? Homework Equations Newton's second law and \tau =...

Ah...I guess that's pretty obvious. Thank you very much.

Homework Statement I have to find this integral: \int \delta (( \frac{p^{2}}{2m} + Cz ) - E ) p^{2} dp dz where E, m, and C can be considered to be constants. Homework Equations I'm semi-familiar with delta functions, i.e. i know that: \int \delta (x - a) dx = 1 and that you can usually...