webwork math233 17742 huang s19 16.4 parametrized surfaces /1 16.4 Parametrized surfaces: Problem 1 Problem List Next Problem Previóus Problem (1 point) Show that Ф (u, u)-- (9u t-3, u-u, 17u t u)...
1 point) Show that Φ(u, u) (Au + 2, u-u, 7u + u) parametrizes the plane 2x -y-z = 4, Then (a) Calculate Tu T,, and n(u, v). þ(D), where D = (u, u) : 0 < u < 9,0 < u < 3. (b) Find the area of S (c) Express f(x, y, z in terms of u and v and evaluate Is f(x, y,z) ds. (a) Tu n(u,v)- T, (b) Area(S)- (c) JIs f(z, y,2) ds- 1 point)...
4. (1 pt) Calculate Tu, T, and n(u, v) for the parametrized surface at the given point Then find the equation of the tangent plane to the surface at that point Ф(и, у) %3D (2и + v, и — 4v, 5и); Ти The tangent plane: V u=4, v6 , n(u,v) TV =9z
HW09 12.7-12.8: Problem 18 Previous Problem Problem List Next Problem (1 point) Suppose a change of coordinates T : R2 + R2 from the uv-plane to the by-plane is given by I= -30 – 3u - 1. y = -1 +54 + 2v. (a) Find the absolute value of the determinant of the Jacobian for this change of coordinates a(z,y) a(u, v) det - 1 (b) If a region D* in the uv-plane has area 7.14, find the area of...
(1 point) Let S be the surface defined by ř(u, u)-< ucosu, u sinu, u > for (u,t) in D-((mu) : 0 < u < 3,0 < u < π} Evaluate the surface integral of F-<,z,y>upward across S. F-dS = (1 point) Let S be the surface defined by ř(u, u)- for (u,t) in D-((mu) : 0
Help would be greatly appreciated!! 1. Let S be the surface in R3 parametrized by the vector function ru, v)(,-v, v+ 2u) with domain D-{(u, u) : 0 u 1,0 u 2). This surface is a plane segment shaped like a parallelogram, and its boundary aS (with positive orientation) is made up of four line segments. Compute the line integral fos F -dr where F(z, y, z) = 〈エ2018 + y, 2r, r2-Ins). Hint: use Stokes' theorem to transform this...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
webwork / math315 may2019 73713 3: Problem 13 Previous Problem List Next 1 point) Solve the equation leaving your answer in implicit form. The solution is where C is a constant of integration. Note: Enter an answer that is a valid function of x and y in the whole plane. webwork / math315 may2019 73713 3: Problem 13 Previous Problem List Next 1 point) Solve the equation leaving your answer in implicit form. The solution is where C is a...
Section 16.8: Problem 5 Previous ProblemProblem List Next Problem (1 point) Let M be the capped cylindnical surface which is the union of two surfaces, a cylinder given by z+y-49,0 1, and a hemisphencal cap defined by Z2 + y2 + (z-1)2-49, z > 1. For the vector field F-(tr + z"y + 4y, zar + 72, z'z2), compute M(Vx F) dS in any way you like. Preview My Answers Submit Answers You hayi,attempted this problem 1 time. Your ovean...
11:57 X WeBWork HW09 Sec4.2 Homogeneous Li Real Roots: Problem 1 Previous Problem Problem List Next Problem (1 point) Find the general solution to y" +6y +9y=0. Enter your solution as y(x). .In your answer, use c, and c to denote arbitrary constants and x the independent variable. Enter c as cl and c2 as c2. Answer: yx) Done I'm ya I Q WERT YU P A S D F G H J K L X C Z V B...
Problem 1. Consider the nonhomogeneous heat equation for u,t) ut = uzz + sin(2x), 0<x<π, t>0 subject to the nonhomogeneous boundary conditions u(0, t) t > 0 u(n, t) = 0, 1, - and the initial condition Lee) Find the solution u(z, t) by completing each of the following steps: (a) Find the equilibrium temperature distribution ue(x). (b) Denote v(x, t) u(a, t) - e(). Derive the IBVP for the function v(x,t). (c) Find v(x, t) (d) Find u(, t)...