For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 404. Let F ( x , y , z ) = 2 x i − 3 y j + 5 z k and let S be hemisphere z = 9 − x 2 − y 2 together with disk x 2 + y 2 ≤ 9 in the xy -plane. Use the divergence theorem.
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D . 404. Let F ( x , y , z ) = 2 x i − 3 y j + 5 z k and let S be hemisphere z = 9 − x 2 − y 2 together with disk x 2 + y 2 ≤ 9 in the xy -plane. Use the divergence theorem.
For the following exercises, use a CAS and the divergence theorem to compute the net outward flux for the vector fields across the boundary of the given regions D.
404. Let
F
(
x
,
y
,
z
)
=
2
x
i
−
3
y
j
+
5
z
k
and let S be hemisphere
z
=
9
−
x
2
−
y
2
together with disk
x
2
+
y
2
≤
9
in the xy-plane. Use the divergence theorem.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Finite Mathematics & Its Applications (12th Edition)
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