Question

In: Math

) Let S be the surface (with outward orientation) given by the boundary of the solid...

) Let S be the surface (with outward orientation) given by the boundary of the solid hemisphere x 2 + y 2 + z 2 ≤ 4 with z ≥ 0 (i.e., including the disk x 2 + y 2 ≤ 4). Use the Divergence Theorem to compute the flux of the vector field F = xyj + 2yzk over the surface S.

Solutions

Expert Solution


Related Solutions

Let ?be the solid region bounded by the surfaces ?=10−?2−?2and ?=1. Let ?be the boundary of...
Let ?be the solid region bounded by the surfaces ?=10−?2−?2and ?=1. Let ?be the boundary of ?. If ?⃗=<?,?,?>, compute the total flux over ?in two ways:(a)Directly as a surface integral.Include a sketch of ?in your answer (b)As a triple integral using the Divergence Theorem
Find the volume of the solid region inside of the surface given by ? 2 +...
Find the volume of the solid region inside of the surface given by ? 2 + ? 2 + ? 2 = 8 and between the upper and lower halves of the cone given by ? 2 = ? 2 + ? 2 by setting up and evaluating an appropriate triple integral (in the coordinate system of your choice).
Consider a surface S given by A point P on this surface is given by r(0,0,0, 3 (a) Find the norma...
Consider a surface S given by A point P on this surface is given by r(0,0,0, 3 (a) Find the normal curvature of the surface at an arbitrary point (θ,t) in terms of (d, d). (b) Find the principal curvatures of the surface at an arbitrary point (0, t) c)Find two unit tangent vectors to S at P that point in the principal directions. (d) The vector v (-4, 1,3) is tangent to S at P. Find the normal curvature...
Let the surface (S) be the part of the elliptic paraboloid z = x2 + 4y2lying...
Let the surface (S) be the part of the elliptic paraboloid z = x2 + 4y2lying below the plane z = 1. We define the orientation of (S) by taking the unit normal vector ⃗n pointing in the positive direction of z− axis (the inner normal vector to the surface). Further, let C denotes the curve of the intersection of the paraboloid z = x2 + 4y2 and the plane z = 1 oriented counterclockwise when viewed from positive z−...
A uniform solid sphere is rolling along a horizontal surface at 20. m/s. It approaches an...
A uniform solid sphere is rolling along a horizontal surface at 20. m/s. It approaches an incline surface making an angle of 30.° with the horizontal. How far along the incline (x) will the sphere travel before coming to a stop? Note: sinq = h/x             QIN = QOUT      KLinear + KRotational = UG
The surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase...
The surface energy of a single crystal depends on crystallographic orientation. Does this surface energy increase or decrease with an increase in planar density? Why? (Hint: Read “External Surface” part in S.4.6: Surface energy is proportional to the number of unsatisfied bonds of surface atoms) please clear hand writing, also plesae don't give me the book answer. Thank you.
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y <...
Find u(x,y) harmonic in S with given boundary values: S = {(x,y): 1 < y < 3} , u(x,y) = 5 (if y=1) and = 7 (when y=3) S = {(x,y): 1 < x2 + y2 < 4}, u(x,y)= 5 (on outer circle) and = 7 (on inner circle) I have these two problems to solve, and I'm not sure where to start. Any help would be appreciated. Thanks!
Let S1 be the level surface given by the equation f(x,y,z) =k1and letS2be the level surface...
Let S1 be the level surface given by the equation f(x,y,z) =k1and letS2be the level surface given by the equation g(x,y,z) =k2. Suppose that C is the curve of intersection of the surfacesS1andS2andassume that P is a point on C. show that any tangent vector to C at P must be parallel to∇f(P)×∇g(P)
What are the principles of surface sorption by solid?
What are the principles of surface sorption by solid?
1.evaginated gas exchange surface - a thin flap of the body wall extends outward for gas...
1.evaginated gas exchange surface - a thin flap of the body wall extends outward for gas exchange. This is only found in water living animals. Why? 2. invaginated gas exchange surface - the gas exchange surface is within the body but connected by passages to the outside environment. This is the usual respiratory system for a terrestrial animal. Why? Observe the demonstration of crayfish gills. Note their feathery appearance. This feathery nature greatly increases their surface area. Why is this...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT