Recent content by FeynmanIsCool

Hey Guys, I'm a little confused. Why would some of the P.E from the center of mass of the rod be converted to Rotational Kinetic energy? The the rod is not rotating. I see the idea that as it slips down its "rotating" about the center of mass, but is it correct to imply that in our reference...

Thanks for the reply, You're right, I found the answer quickly after a google search. Very interesting integral!

Hello everyone, I brushing up on integration techniques and I came across this problem in a book. Does anyone here know were to start? Even Wolfram blanked on it! \int_{0}^{\frac{\pi }{2}}\, \frac{1}{1+(tanx)^{\sqrt 2}} dx This integral appeared in the book before sequences and series, so...

so I also need to state: x\notin B and x\notin C ? So if I tagged those statements onto the proof after I state x\in A, then its good? Im just a little confused, by saying: \forall x\in (B\cup C), x\in B\, or\, x\in C \, or \, both \therefore \, \, \forall x\, \in\begin{Bmatrix}...

Hello, I am working through Munkres Topology (not for a class). It asks the reader to formulate and proove DeMorgans Laws. I am new to proofs, so I was wondering if this is what the book is asking. Any help would be appreciated! assume two sets \, \,\begin{Bmatrix} A-(B\cup C)\...

I got it from here, Thanks LCKurtz and Fredrik.Im making it way harder than it it. Ohh well, now I know! Thanks!

sure, wouldn't It just be: a_{0}+bx+cx^{2}+dx^{3}? edit: ahh...so that it? If the polynomial given was say: a_{0}+bx+cx^{2}+d(x+1)^{3} then it wouldnt?

This is what I mean: A simple problem that popped up with the same question was: c_{0}+c_{1}x\rightarrow (c_{0}-c_{1}, c_{1}) with T:P1→R2 This case is simple since I can find T, its just \begin{bmatrix} 1 &-1 \\ 0& 1 \end{bmatrix} I could easily find its det (test for 1-1) and RREF...

Right, and it turns out T is linear. Since the two statements hold. I'm just confused on how to show 1-1 and onto. Before in other problems, I could find T (or was given T). Now, since I don't know T, I am a little confused on how to test its "onto-ness" or "one to one-ness".

I have the tools to but I am not really sure where to start. " If ##T(p_1) = T(p_2)## can you show ##p_1 = p_2## using the usual properties of polynomials and matrices?" I know this is the test for 1-1 and " Similarly, if ##A\in M## can you find ##p\in P_3## such that ##T(p)= A##?" is...

T:P3→M2,2 Ok, I do know that its linear if: k(Tu)=T(ku) and T(u+v)=T(u)+T(v), that's simple enough. Nice, I like these definitions better than the ones I was working with.

Homework Statement Is the following transformation an isomorphism: a_0+bx+cx^{2}+dx^{3} \rightarrow \begin{bmatrix} a & b\\ c & d \end{bmatrix} Homework Equations A transformation is an isomorphism if: 1. The transformation is one-to-one 2. The transformation is onto The Attempt at a...

ahh yes, the algebraic properties of inner product spaces. Of course! Thanks edit* its -101

Homework Statement Suppose \vec{u}, \vec{v} and \vec{w} are vectors in an inner product space such that: inner product: \vec{u},\vec{v}= 2 inner product: \vec{v},\vec{w}= -6 inner product: \vec{u},\vec{w}= -3 norm(\vec{u}) = 1 norm(\vec{v}) = 2 norm(\vec{w}) = 7 Compute...

Maybe you got it confused with the simple harmonic motion eq: [FONT="Times New Roman"]\omega = \sqrt{K/M} ?