Recent content by 1up20x6

Homework Statement [/B] Find the outward flux of the vector field ## \vec F = y^2e^{z^2+y^2} i + x^2 e^{z^2+x^2} j + z^2 e^{x^2+y^2} k## across that part of the ellipsoid $$ x^2 + y^2 + 4z^2 = 8$$ which lies in the region ##0 ≤ z ≤ 1## (Note: The two “horizontal discs” at the top and bottom are...

Homework Statement Evaluate \iiint z^2 \,dx\,dy\,dz over domain V, where V is the solid defined by 1 \leq x+y+3z \leq 20 \leq 2y-z \leq 3-1 \leq x+y \leq 1 Homework Equations The Attempt at a Solution I know how to do simple triple integrals, but all the variables in the inequalities are...

Homework Statement Find the inverse Laplace transform of F(s)=5e^(-8s)/(s2+36) Homework Equations The Attempt at a Solution I know that to find the inverse Laplace transform of this function, I start by factoring out (e^(-8s)) to end up with 5/(s^2+36), and that my final answer...

Using linear transformation reflection to find rotation Homework Statement Let T1 be the reflection about the line −4x−1y=0 and T2 be the reflection about the line 4x−5y=0 in the euclidean plane. The standard matrix of T1 \circ T2 is what? Thus T1 \circ T2 is a counterclockwise rotation...

Thanks for your responses. Are those equations self-evident or is there a proof that they apply for all values of n?

Homework Statement A = \begin{pmatrix} 1 & 4\\ 2 & -1 \end{pmatrix} Find A^n and A^{-n} where n is a positive integer. Homework Equations The Attempt at a Solution (xI - A) = \begin{pmatrix} x-1 & -4\\ -2 & x+1 \end{pmatrix} det(xI - A) = (x-3)(x+3) λ_1 = 3\quad...