For the following exercises, approximate the mass of the homogeneous lamina that has the shape of given surface S . Round to four decimal places. 305. Compute ∬ s F ⋅ N d S , where F ( x , y , z ) = x y z i + x y z j + x y z k and N is an outward normal vector S , where S is the surface of the five faces of the unit cube 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 missing z = 0 .
For the following exercises, approximate the mass of the homogeneous lamina that has the shape of given surface S . Round to four decimal places. 305. Compute ∬ s F ⋅ N d S , where F ( x , y , z ) = x y z i + x y z j + x y z k and N is an outward normal vector S , where S is the surface of the five faces of the unit cube 0 ≤ x ≤ 1 , 0 ≤ y ≤ 1 , 0 ≤ z ≤ 1 missing z = 0 .
For the following exercises, approximate the mass of the homogeneous lamina that has the shape of given surface S. Round to four decimal places.
305. Compute
∬
s
F
⋅
N
d
S
, where
F
(
x
,
y
,
z
)
=
x
y
z
i
+
x
y
z
j
+
x
y
z
k
and N is an outward normal vectorS, where S is the surface of the five faces of the unit cube
0
≤
x
≤
1
,
0
≤
y
≤
1
,
0
≤
z
≤
1
missing
z
=
0
.
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.
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
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