8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
1. For pdf f (r, y) = 1.22, 0 < x < 1,0 < y < 2, z +y > 1, calculate: EY) and () E (X2)
2. Solve the linear homogeneous IVP U+ rtuz = 0, u.1,0) = sinr, -o0<< 0, t> 0.
3. For the equation 24 = r, in 0 <<1,0<t<1, (1,0) = sin(x), on 0 SEST (0,1)=0, u(1. t) = 0, on 0 <t<1, (1) Using the separation of variables, find its solution.
2. Solve the initial-boundary value problem One = 48m2 for 0 < x < 8, t > 0, u(0, t) = u(8,t) = 0 for t > 0, u(2,0) = 2e-4x for 0 < x < 8. (60 pts.)
Solve the equation for all degree solutions and if 0° < θ < 360°. Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 2 sin -V3 (a) all degree solutions (Let k be any integer.) (b) 00 s 360°
Question 1 1 pts Let F= (2,0, y) and let S be the oriented surface parameterized by G(u, v) = (u? – v, u, v2) for 0 <u < 12, -1 <u< 4. Calculate | [F. ds. (enter an integer) Question 2 1 pts Calculate (F.ds for the oriented surface F=(y,z,«), plane 6x – 7y+z=1,0 < x <1,0 Sysi, with an upward pointing normal. (enter an integer) Question 3 1 pts Calc F. ds for the oriented surface F =...
Please need help in this problem it Resource Optimization problem Solve the following problem using Simplex method algebraic form Max Z = X1 +2x2 + 2x3 Subject to: 5x1 + 2x2 + 3x3 <= 15 X1 + 4X2 +2X3 12 X1 0 Xs>=0
1. Solve the following DE: (50 pts) (1, if 0<x51 a) y+ y = f(x), y(0) = 3 where f(x)= 0, if x>1 (10 pts)
Suppose that f (x II 2y), 0 < x < 1,0 < y < 1. Find EX + Y).