2) Given that the total flux across the surface, S of the tetrahedron bounded by the planesx = 0, y = 0, z = 0 and z=4-x-y as shown in Figure 2 with outward orientation is32.Use Gauss's theorem to evaluate fF.ds for vector field F = į+2yj+zk .Sz=4-x-y∙y4Figure 24X

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Answered: 2) Given that the total flux across the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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A vector field representing wind speeds is given by v = ry³ i + 3x³y³j. A walker can take one of two paths between points A(0,0) and B(1,1). Determine which path has more work done by the field? a) The first path follows y = x4. Find the work done by the field following this path. For path c1, v • dr =( )dr Sa v• dr = Note: Show solution to integral as answer rounded to 2 decimal places. b) The second path follows y = x. Find the work done by the field following this path. For path c2, v • dr =( )dx S,v• dr Note: Show solution to integral as answer rounded to 2 decimal places. c) Which path should you take if you want to put in less effort? O Path on curve 1 O Path on curve 2 O Either path, effort is the same.
1. State whether the following are scalar or vector quantities: (a) A temperature of 50 °C (b) A downward force of 80N (c) 300J of work (d) A south-westerly wind of 15 knots (e) 70m distance (f) An acceleration of 25m/s2 at 30 to the horizontal
b) The line integral F. dr is a scalar.
A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at each point by w(x, y, z) = 25 − 4(x² + y² + z²) °C. Use the fact that heat flow is given by the vector field F = -KVw and the rate of heat flow across a surface S within the solid is given by -K Vw ds. Find the rate of heat flow out of a sphere of radius 1 (centered at the origin) inside a large cube of copper (K = 400 kW/(m - K)). (Use symbolic notation and fractions where needed.) x J[, VW S -K Incorrect VwdS= 12800 kW
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Suppose f(z) = u(x, y) +iv(x, y) is differentiable at zo = xo+iyo, with f'(zo) # 0. Show that the vectors Vu(xo, yo) and Vv(xo, yo) are perpendicular and have the same magnitude. Express this magnitude in terms of f'(zo).
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Airodyne Wind, Inc., has wind tunnels that can operate vertically or horizontally for evaluating the effects of air flow on a component's PCB response and reliability. The company expects to build a new tunnel that will be outfitted with multiple sensor ports. For the estimates below, calculate the equivalent annual cost of the project. First Cost Replacement Cost, Year 2 AOC per Year Salvage Value Life, Years Interest Rate The equivalent annual cost of the project is $ $-250,000 $-330,000 $-940,000 $280,000 5 11%

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2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y = 0, z = 0 and z=4-x-y as shown in Figure 2 with outward orientation is 32. Use Gauss's theorem to evaluate fF.ds for vector field F = į+2yj+zk . S z=4-x-y ∙y 4 Figure 2 4 X