Consider all tetrahedral regions with vertices (0, 0, 0), (a, 0, 0), (0, b, 0), and (0, 0, c) with a, b, c > 0.
Find the tetrahedron with the maximal flux if the vector field
is given as 
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Consider all tetrahedral regions with vertices (0, 0, 0), (a, 0, 0), (0, b, 0), and (0, 0, c) with a, b, c > 0. Find...
Evaluate the surface integral | Fids for the given vector field F and the oriented surface...
Evaluate the surface integral | Fids for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the JS positive (outward) orientation. F(x, y, z) = y i + (z - y)j + xk S is the surface of the tetrahedron with vertices (0, 0, 0), (4, 0, 0), (0, 4, 0), and (0, 0, 4)
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux...
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B)
(1 point) A uniform magnetic field B has constant strength b...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the f...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A-(7, 0, 6) , B-(7, 3, 0) , C-(0, 3, 0) , D- (0,0,6), F-(7,0,0) Flux(B)
(10 points) Un uniforme magnetic field B has constante strength...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vec...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
m sec sec Q4- Given A(0,0,0), B(1,-1,1), C(2,1,-2) and D(-1,2,-1) are vertices of tetrahedron. If the...
m sec sec Q4- Given A(0,0,0), B(1,-1,1), C(2,1,-2) and D(-1,2,-1) are vertices of tetrahedron. If the rate of increase in side AB = 0.5 m, BC = 0.3 and ACE 0.4 Find the change in altitude of tetrahedron ABCD to get the change in volume m3 0.1 m sec sec
q4 please thanks (1) Let A - (0,0), B- (1,1) and consider the veetor field f(r,...
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Verify Stokes' Theorem for the given vector field and surface, oriented with a downward-pointing normal. F = 〈ey-z, 0, 0), the square with vertices (6, 0, 6), (6, 6, 6), (0, 6, 6), and (O, O, 6)...
Verify Stokes' Theorem for the given vector field and surface, oriented with a downward-pointing normal. F = 〈ey-z, 0, 0), the square with vertices (6, 0, 6), (6, 6, 6), (0, 6, 6), and (O, O, 6) F·dS = aS curl(F) = curl(F) . dS =
Verify Stokes' Theorem for the given vector field and surface, oriented with a downward-pointing normal. F = 〈ey-z, 0, 0), the square with vertices (6, 0, 6), (6, 6, 6), (0, 6, 6), and...
Question 5. Let C be the tetrahedron in the positive orthant of points satisfying (a) Describe th...
Question 5. Let C be the tetrahedron in the positive orthant of points satisfying (a) Describe the sides (faces) of this tetrahedron and find the unit outward normal to b) What is the height of this tetrahedron from the origin to the face with r+y+z-1? (c) What is the area of the face r ty+z 1? (d) Find the flux of the field F of question 1 through this face? (e) Give a triple integral for the volume of this...
Consider the unit cube with vertices (corner points) (0, 0, 0), (0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (...
Consider the unit cube with vertices (corner points) (0, 0, 0),
(0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1),
(1, 1, 1). Let S be the boundary of the cube minus (i.e. not
including) the bottom square (the side which lies in the xy plane).
Orient S with the normal which points out of the cube. Let F =
<− y , x , y^2e^x . Evaluate (curl F) ·...
Evaluate the surface integral | Fids for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the JS positive (outward) orientation. F(x, y, z) = y i + (z - y)j + xk S is the surface of the tetrahedron with vertices (0, 0, 0), (4, 0, 0), (0, 4, 0), and (0, 0, 4)
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B)
(1 point) A uniform magnetic field B has constant strength b...
(10 points) Un uniforme magnetic field B has constante strength b teslas in the z-direction [i.e., B-(0,0, b) ] (a) Verity that A-Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A-(7, 0, 6) , B-(7, 3, 0) , C-(0, 3, 0) , D- (0,0,6), F-(7,0,0) Flux(B)
(10 points) Un uniforme magnetic field B has constante strength...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
m sec sec Q4- Given A(0,0,0), B(1,-1,1), C(2,1,-2) and D(-1,2,-1) are vertices of tetrahedron. If the rate of increase in side AB = 0.5 m, BC = 0.3 and ACE 0.4 Find the change in altitude of tetrahedron ABCD to get the change in volume m3 0.1 m sec sec
q4 please thanks
(1) Let A - (0,0), B- (1,1) and consider the veetor field f(r, y,z)vi+aj. Evaluate the line integral J f.dr )along the parabola y from A to B and (i)along the straight line from A to B. Is the vector field f conservative? (2) For the vector feld f # 22(r1+ gd) + (x2 + y2)k use the definition of line integral to (3) You are given that the vector field f in Q2 is conservative. Find...
Verify Stokes' Theorem for the given vector field and surface, oriented with a downward-pointing normal. F = 〈ey-z, 0, 0), the square with vertices (6, 0, 6), (6, 6, 6), (0, 6, 6), and (O, O, 6) F·dS = aS curl(F) = curl(F) . dS =
Verify Stokes' Theorem for the given vector field and surface, oriented with a downward-pointing normal. F = 〈ey-z, 0, 0), the square with vertices (6, 0, 6), (6, 6, 6), (0, 6, 6), and...
Question 5. Let C be the tetrahedron in the positive orthant of points satisfying (a) Describe the sides (faces) of this tetrahedron and find the unit outward normal to b) What is the height of this tetrahedron from the origin to the face with r+y+z-1? (c) What is the area of the face r ty+z 1? (d) Find the flux of the field F of question 1 through this face? (e) Give a triple integral for the volume of this...
Consider the unit cube with vertices (corner points) (0, 0, 0),
(0, 1, 0), (1, 0, 0), (1, 1, 0), (0, 0, 1), (0, 1, 1), (1, 0, 1),
(1, 1, 1). Let S be the boundary of the cube minus (i.e. not
including) the bottom square (the side which lies in the xy plane).
Orient S with the normal which points out of the cube. Let F =
<− y , x , y^2e^x . Evaluate (curl F) ·...
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