Recent content by dlevanchuk

i divided both sides by t and got y' + (2/t)*y = e^(2t)/t then i plugged in 1 for t and 0 for y. As a result I got y' = e^2

Homework Statement Consider the initial value problem t*y' + 2y = e^(2t) ; y(1) = 0: Determine the largest interval on which it is guaranteed to have a unique solution. Homework Equations The Attempt at a Solution I just need somebody to tell me if i have a logic on this one...

Ok, never mind. I got it :) Forgot about the polar coordinates..

Homework Statement The boundary of a lamina consists of the semicircles y = sqrt(1-x^2) and y = sqrt(4-x^2) together with the portion of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin Homework...

nevermind... substitution of u = 1+x^2 is easier.. :-)

Homework Statement Need to refresh my memory :-S Indefinite integral of x/(1+x^2) .. Homework Equations The Attempt at a Solution Would I use partial fractions on that bad boy?

Homework Statement I have a matrix A [1 -1 -1 -1; -1 1 -1 -1; -1 -1 1 -1; -1 -1 -1 1], its characteristic polynomial p(t) = (t + 2)(t-2)3, and given value of lambda = 2. I need to find basis for eigenspace, and determine algebraic and geometric multiplicities of labmda.Homework Equations The...

Homework Statement Consider the (2x2) symmetric matrix A = [a b; b d] Show that there are always real scalars z such that A-zI is singular [Hint: Use quadratic formula for the roots from the previous exercise ] t^2 - (a + d)t + (ad - bc) =0 Homework Equations The Attempt at a...

Gotcha. So i just have to look at the subset, and rearrange the equation, until it will look familiar (ie plane in 3d or a line in 2d..) Thanks!

Could somebody explain to me please how to figure out a geometric description of a subspace? I understand how to check wether the set of vectors is a subset, but how t ogive them a geometric description?? lets say i have a subset in R3 {x: x3 = 2x1-x2} why the G.D. is a plane with an...

could i just say that since the vectors are orthogonal, that means they are linearly independent, and that makes the matrix non singular.. sounds pretty logical to me :)

What have I done? Homework Statement (linear transformation) Let T: R2 -> R3 be a linear transformation such that T(e1) = u1 and T(e2) = u2, where u1 = [1; 0; -1] and u2 = [2; 1; 0]. Find each of the following: T([1; 1]) and T([2; -1])Homework Equations The Attempt at a Solution Here is the...

but even though its easier to believe and some results can be derived from the bohr model, doesn't make it a good idea to teach, or to represent it in the book.. Just like if astronomy teachers taught the class the geocentic model, because its easier to believe that the sun is going around the...

Everytime I pick up a general audience modern physics book, written by some phd professor, I keep bumping into the whole "electron orbiting around proton" bohr model, even though we know for nearly 100 years that bohr model is incorrect. But why do the authors (PROFESSORS) keep bringing this...

Homework Statement Let S = { u1, u2, u3} be an orthogonal set of nonzero vectors in R3. Define (3 x 3) matrix A by A = [u1, u2, u3]. Show that A is nonsingular and A'A (' is transpose) is a diagonal matrix. Calculate the diagonal matrix using the given orthogonal vectors: u1 = [1 1 1]'; u2...