[10] (5) GIVEN: a>0, The surface, : x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F = (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- Here is the canonical parameterization of 22: Þ:D Q, Þ(x, y) = (x, y, a- x - y) where D = {(x, y)| 0 ≤ x ≤ a l xJ 0 ≤ y ≤a- FIND: The flux of F through with the given orientation. A X component. Add extra pages, as needed. A = (a,0,0) B = (0, a, 0) C = (0,0,a) B F = (x + y, z, y - x) Y
[10] (5) GIVEN: a>0, The surface, : x+y+z = a, x ≥ 0, y ≥ 0, z ≥ 0. Consider the 3D field: F = (x+y, z, y - x) Orient the surface so that its normal vector to it has a positive z- Here is the canonical parameterization of 22: Þ:D Q, Þ(x, y) = (x, y, a- x - y) where D = {(x, y)| 0 ≤ x ≤ a l xJ 0 ≤ y ≤a- FIND: The flux of F through with the given orientation. A X component. Add extra pages, as needed. A = (a,0,0) B = (0, a, 0) C = (0,0,a) B F = (x + y, z, y - x) Y
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For the first image attached please do thecalculations similar to the second image attached
Please answer fast super super fast as fast as possible. I need it before the end of the day
answer should be a^3/6
This is not a graded question
![[10] (5)
: x+y+z = a₁ x ≥ 0, y ≥ 0, z ≥ 0.
(x + y, z, y - x)
GIVEN: a>0, The surface,
Consider the 3D field: F
Orient the surface so that its normal vector to it has a positive z - component.
Here is the canonical parameterization of 22:
Þ:D, P(x, y) = (x, y, a- x - y)
where D =
=
0 ≤ x ≤ a l
{(x, y) ⁰ 0 ≤ y ≤ a-x]
FIND: The flux of F through
with the given orientation.
A
X
2
Ω
F
=
Add extra
pages, as
needed.
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
B
(x + y, z, y− x)
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4cd653b-3607-4828-91a1-c49e64d92fe8%2F7b1fc6e2-ade1-4471-95ee-a6b3115776d8%2F0o11gzp_processed.png&w=3840&q=75)
Transcribed Image Text:[10] (5)
: x+y+z = a₁ x ≥ 0, y ≥ 0, z ≥ 0.
(x + y, z, y - x)
GIVEN: a>0, The surface,
Consider the 3D field: F
Orient the surface so that its normal vector to it has a positive z - component.
Here is the canonical parameterization of 22:
Þ:D, P(x, y) = (x, y, a- x - y)
where D =
=
0 ≤ x ≤ a l
{(x, y) ⁰ 0 ≤ y ≤ a-x]
FIND: The flux of F through
with the given orientation.
A
X
2
Ω
F
=
Add extra
pages, as
needed.
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
B
(x + y, z, y− x)
Y
![[20] (2)
GIVEN: a > 0, The surface, Q2: x + y + z = a, x ≥ 0, y ≥ 0, z ≥ 0.
Consider the 3D field: F (x, 2x, 3x)
=
Orient the surface so that its normal vector has a positive z- component.
FIND: The flux of F through with the given orientation.
Parameterization of D. :
D= PROJ, :D
xy
= {(5₂₂) |05*{a-x}
y
Q
а-х-у
$(x,y)=(x, y, a-z-y)
⇒ = (1,0,-1)
y = (0,1,-1)
⇒x=(1,1,1)
canonical
||
3
a
X
parameterization
3
= 6 [−¾a³+ ½a³]
A
Z
Ω
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
B
F = (x, 2x, 3x)
D=
FLUX = √ F·Ã$ = √₂ (2,22,3x)-(1,1,1) dedy
= √₂ 6x4 dy = 65° 1² 727144
бу
dy
y=a-x
.a
= 6 √ ²x (a-x) & = 6 √ ² x ² + ax de
→L
Y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc4cd653b-3607-4828-91a1-c49e64d92fe8%2F7b1fc6e2-ade1-4471-95ee-a6b3115776d8%2F5kqkgsn_processed.png&w=3840&q=75)
Transcribed Image Text:[20] (2)
GIVEN: a > 0, The surface, Q2: x + y + z = a, x ≥ 0, y ≥ 0, z ≥ 0.
Consider the 3D field: F (x, 2x, 3x)
=
Orient the surface so that its normal vector has a positive z- component.
FIND: The flux of F through with the given orientation.
Parameterization of D. :
D= PROJ, :D
xy
= {(5₂₂) |05*{a-x}
y
Q
а-х-у
$(x,y)=(x, y, a-z-y)
⇒ = (1,0,-1)
y = (0,1,-1)
⇒x=(1,1,1)
canonical
||
3
a
X
parameterization
3
= 6 [−¾a³+ ½a³]
A
Z
Ω
A = (a,0,0)
B = (0, a, 0)
C = (0,0,a)
B
F = (x, 2x, 3x)
D=
FLUX = √ F·Ã$ = √₂ (2,22,3x)-(1,1,1) dedy
= √₂ 6x4 dy = 65° 1² 727144
бу
dy
y=a-x
.a
= 6 √ ²x (a-x) & = 6 √ ² x ² + ax de
→L
Y
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