Recent content by dobedobedo

Hm. Thanks for the help, but that's strange. It does produce the desired answer. In this case we've got two variables, so I think it is okay to make such an assumption. If it were the case of more variables, would such an assumption be okay if the expression were symmetric w.r.t. two particular...

PROBLEM STATEMENT: Determine if f(x,y) = x^2+y^2 has a maximum and a minimum when we have the constraint 2x^3+3x^{2}y+3xy^{2}+2y^3=1. (1) ATTEMPT TO SOLUTION: A standard way of solving these kinds of problems is by using the Lagrangian multiplier-method. It consists of comparing the gradient of...

Let a be the side of that isosceles triangle and b be the length of the rectangle and let h be the height of that triangle. Then the area A is: A(a,b,h) = 2ab + 2*h*\sqrt{a^2-h^2}. Great. Names. Woohoo. Now what? V = h*b*\sqrt{a^2-h^2}.

Give it a shot man/dude/girl! I'm in pain, i really want to fix this problem.

Been there done that. I don't get anything.

I've got a question that I don't know how to solve. The question is: We want to produce a tent, without a bottom part, which has two rectangular sides and two gables in the form of two isosceles triangles with the base against the ground. Determine the height of the tent, which has volyme V and...

Ok. But is it given that any curve in the plane can be parametized? If so, what theorems say this? For instance, what about the hyperbolae?

PROBLEM STATEMENT: I'm looking for a somewhat general method to find the expression for the distance (in \R^2 mortal, euclidean space) between a point in a certain curve and some point outside the line. ATTEMPTS TO SOLVE THE PROBLEM: In the case of the distance between the origin and some...

Very interesting! But I am somewhat confused. How do I actually use it? I was wondering how to find my matrix A out of some given polynomial - but that would require me to know it's roots, due to the design of the algorithm. For instance, if I have my matrix {{2,1},{1,2}} then it's...

Hahahaha! How brilliant. Okay. Now I can finally randomly create integer matrices A such that A = SDS^{-1} are integer matrices as well! Other questions: -How do I find a matrix A with integer elements, which has an inverse with rational elements? I get the feeling that it always is that a...

A follow-up question: how do I find a matrix with integer elements whose inverse also has integer elements? ^^

Jesus christ, I feel stupid. Thanks.

Hello guise. I am familiar to a method of diagonalizing an nxn-matrix which fulfills the following condition: the sum of the dimensions of the eigenspaces is equal to n. As to the algorithm itself, it says: 1. Find the characteristic polynomial. 2. Find the roots of the characteristic...

I was just thinking one thing... Let the set of points (region, whatever... you get the idea) which the first term is to be integrated over be denoted A. Then A = {(x,y): x ≤ y ≤ x^3, 1 ≤ x ≤ 2}. Let the set of points that the second term is integrated over be denoted B. Then B = {(x,y): x ≤ y≤...

I tried the substitution u= x^2, v= e^(y^2). The Jacobian had the value 1/(4xy*e^(y^2)). So far so good. But then I get... \frac{1}{4} \int_{1}^{4} (\int_{e^u}^{e^{u^3}}(\frac{u^{1/2}}{ln(v)^{1/2}})dv)du +\frac{1}{4} \int_{2}^{8^{2}} (\int_{e^u}^{e^{8^2}}(\frac{u^{1/2}}{ln(v)^{1/2}})dv)du...