Recent content by randomcat

Suppose that there are 2 apple trees. Tree A and tree B. A produces 0.7 of the farm's apples. And B produces 0.3. Out of the apples that tree A produces, 0.15 are bad. For B, 0.05 are bad. One package of goodies contains 3 apples. Given this information, what is the P(Tree A| at...

Homework Statement The divergence theorem states that ∫∫∫V div F dV = ∫∫S F(dot)Ndσ Suppose that div F = 1, then ∫∫∫V div F dV = ∫∫S F(dot)Ndσ If divF = 2, does the following hold true?∫∫∫V div F dV = 2∫∫S F(dot)Ndσ Homework Equations Since the divergence theorem computes the volume, if...

Hmm...I'm not sure where that leads me in the proof, could you please elaborate?

edit: vector* analysis; sorry for the typo Homework Statement Given that A = ||ru||2, B = ru\bulletrv, C = ||rv||2 surface area of S is Area(S) = \int^{d}_{c}\int^{b}_{a} = sqrt (AC - B2) dudv The Dirichlet energy can be thought of as a function as follows E(S) =...

Homework Statement Suppose that F = ∇f for some scalar potential function f(x, y) = 1/2(x2 + y2) Let C denote the positively oriented unit circle, parametrized by r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏. Compute the flux integral of \ointF\bulletN ds, where N is the outward unit normal to C.Homework...

Homework Statement A fluid as velocity field F(x, y, z) = (xy, yz, xz). Let C denote the unit circle in the xy-plane. Compute the circulation, and interpret your answer.Homework Equations The Attempt at a Solution Since the unit circle is a closed loop, I assumed that ∫ F * dr = 0 (the ∫ symbol...

Homework Statement Evaluate ∫ F ds over the curve C for: a) F = (x, -y) and r(t) = (cos t, sin t), 0 ≤ t ≤ 2∏ b) F = (yz, xz, xy) where the curve C consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) Homework Equations The Attempt at a Solution a) I first found the...