Recent content by bengaltiger14

I am trying to come up with a design that would track the position of a wire. The wire will have a permanent magnet attached to its tip. I will use a electromagnet to move the wire in only 1 dimension. Here is what I was thinking... I would put a stationary aluminum plate some distance from...

Homework Statement The temperature in a room is given by T(x,y,z)=2x^2+3y^2 - 4z. A flying bug located at P(1,1,2) in the room desires to fly in such a direction that it will warm as soon as possible. In what direction must the bug fly? Taking the gradient of T: 4x(x hat)+6y(y hat)-4(z...

Still not getting correct answer. Lowly, you are saying the disregard the x hat and z hat component right?

Homework Statement A vector field is given by: A=2x(x hat) + 3(y hat) + 2y(z hat). A surface S is defined by 0<=x<=2m, y=5m, 0<=z<=2m. Find the flux of A through S. I plug the 5m into the z hat term to get 10(z hat) and then integrate. Integrating the (x hat) term I get 4. The...

Aha! Thank you

Homework Statement A position vector (between the origin and point (5,2,3) is expressed as r=5(x hat) + 2(y hat) + 3(z hat). Express vector in cylindrical coordinates. RHO = SQRT(5^2 + 2^2) FIE = tan-1(y/x) Z=3 Clearly, RHO = 5.385, FIE = 21.8, and Z=3. The answer is given is only...

That is: [1,0,0;4t,1,0;1t,0,1] The e^C*eB = [e^-2t,0,0;4te^-2t,e^-2t,0;te^-2t,0,e^-2t]

So, the resulting matrix would be: [e^-2t,0,0;4e^-2t,e^-2t,0;e^-2t,0,e^-2t] Does this look right?

e^C would be: C=[0,0,0;e^4t,0,0;e^-2t,0,0]

I am not sure how to split as you are talking. But the diagonal would just be a diagonal of e^-2t? And everything else just 0?

I think my prof. wants us to use the Eigenvectors, but i do not know how to split it the way you are talking of.

splitting the original matrix or the matrix with the -2 eigenvalue?

Homework Statement Given the matrix: A=[-2 0 0;4 -2 0;1 0 -2], find e^AT. I found the eigenvalues to be -2,-2,-2. How do I solve this problem with 3 identical eigenvalues? Do I cube to matrix after plugging in my eigenvalue -2 and then solve it that way? After plugging in the...

Homework Statement Show that f(t)=e^(5t) sin(t) satisfies the condition for the LaPlace transform to exist I can solve the Laplace and get 2/((s-5)^2 + 4) How do I show that the conditions exist? If it is solvable using the table, shouldn't that be enough?

Disregard that, I approached it entirely wrong. Sorry