9.) Let E be the tetrahedron with vertices: (0, 0, 0), (3, 2,0), (0, 3,0), (0, 0, 2).E is bounded by four planes: z = 0,x = 0,-2x + 3y = 0,T2313,2,0)(a) V(E)=Y(b) Average of f(x, y, z) = x + 2y - z on E is:2x+6y +9z = 18.

The tetrahedron bounded by the planes from the plane…

Answered: 9.) Let E be the tetrahedron with…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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EXERCISES: Find the absolute maximum and minimum of the functions on the given domains. 1) f(x, y) = 2x? plate bounded by the lines x = 0, y = 2, y = 2x in the first quadrant 4x + y2 - 4y + 1 on the closed triangular %3D %3D %3D
4.)It is known that the plane α passes through the point (2, 1, 3) and contains the line g with the equation x-1/2 = y-2/3 = z-4/5. Find the distance of the point (1, 1, 1) to the plane α
Find [x²ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to (3, 1,-2).
Show that there are point(s) (x, y, z) satisfying 2x − 3y + z − 5 = 0and lying on the line v = (5, −5, −6) + t(1, 1, 2).
The point(s) of intersection between the y-axis and the plane 2x-y-z=-6 is/are: O {(x, y, z): x = 2t-3, y=-t, z = t} O (-3,0,0) O {(x, y, z): x = 0, y =z=-6} O (0,-1,1) None of the given options IRIS is sharing your screen. Stop sharing Hide
The line of intersection of the planes x + y + z = 0 and x - y = 0 is ○ r(t) = (t, t, 1 — 2t) r(t) = (t, t, 0) r(t) = (t,0,−2t) O None of the above.
The line of intersection of the planes 2x +y – z= 4 and 4x – y+ 3z = 2 has equation %3D O a) (x, y, z) = (1, 2, 0) + t(1, –5, 1) O b) (x, y, z) = (1, –2,0) + t(2, –10, –6) O c) None of these O d) (x, y, z) = (1, 2, 0) + t(1, –5, -3)
Find a plane through the point (2,-3,7) and orthogonal to the line 3x - 3y -z = ·22 QUACLI x(t) = 4 + 3t y(t) = 2 - 3t z(t) = X -8-t
a) Compute the work done by F = (y², sin(z), x) along a straight line from (0,3,0) to (1, 0, 1). b) Compute the work done by F = (y², sin(z), x) along a triangular path from (0, 3, 0) to (1, 0, 1) to (0, 0, 2) and back to (0, 3, 0). c) Compute the work done by = (x, y², sin(z)) along a circular path of radius 3, centered at (0, 1, 0), in the plane y = 1, counterclockwise when viewed from the origin.

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9.) Let E be the tetrahedron with vertices: (0,0,0), (3, 2,0), (0,3,0), (0, 0,2). E is bounded by four planes: z = 0, x=0, -2x + 3y = 0, 2 3 (3,2,0) (a) V(E)= Y (b) Average of f(x, y, z) = x + 2y - z on E is: 2x + 6y +9z = 18.