Classify the origin as an attractor, repeller, or saddle point of the dynamical system x + 1 = Axk. Find the directions of greatest attraction and/or repulsion.%3D1.0 0.4A =- 0.2 1.6.....Classify the origin as an attractor, repeller, or saddle point. Choose the correct answer below.O A. The origin is a repeller.O B. The origin is an attractor.C. The origin is a saddle point.

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Let V1, Vk be the points in R³ and suppose that for j = 1, ..., k an object with mass m; is located at point vj. Physicists call such objects point masses. The total mass of the system of point masses is m = m₁ + ... + mk. The center of gravity (or center of mass) of the system is 1 Point V₁ = (3,-5,3) V₂ = (6,3,-3) Mass 69 15g V3 ( 4, 3, 2) 6 g V4 = (-6,9,7) 3 g v = +... Compute the center of gravity of the system consisting of the point masses above.
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An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T,, ..., T4 denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes-to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T, .., 25° 25° T4. 4T, - T2 T4 = 40 15° 1 450 -T, + 4T2 - T3 = 70 15° 4 3 T2 +4T3 - T4 =80 450 T3 + 4T4 = 50 35° 35° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The unique solution of the system is ( ). (Type integers or decimals rounded to the nearest thousandth as needed.) O B. The system has infinitely many solutions. O C. The system has no solution. 2.
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