For the following exercises, the heat flow vector field for conducting objects F = − k ∇ T , where T ( x , y , z ) is the temperature in the object and k > 0 is a constant that depends on the material. Find the outward flux of F across the following surfaces S for the given temperature distributions and assume k = 1 . 323. T ( x , y , z ) = In ( x 2 + y 2 + z 2 ) ; S is sphere x 2 + y 2 + z 2 = a 2 .
For the following exercises, the heat flow vector field for conducting objects F = − k ∇ T , where T ( x , y , z ) is the temperature in the object and k > 0 is a constant that depends on the material. Find the outward flux of F across the following surfaces S for the given temperature distributions and assume k = 1 . 323. T ( x , y , z ) = In ( x 2 + y 2 + z 2 ) ; S is sphere x 2 + y 2 + z 2 = a 2 .
For the following exercises, the heat flow vector field for conducting objects
F
=
−
k
∇
T
, where
T
(
x
,
y
,
z
)
is the temperature in the object and
k
>
0
is a constant that depends on the material. Find the outward flux of
F
across the following surfaces S for the given temperature distributions and assume
k
=
1
.
323.
T
(
x
,
y
,
z
)
=
In
(
x
2
+
y
2
+
z
2
)
;
S
is sphere
x
2
+
y
2
+
z
2
=
a
2
.
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.
Shading a Venn diagram with 3 sets: Unions, intersections, and...
The Venn diagram shows sets A, B, C, and the universal set U.
Shade (CUA)' n B on the Venn diagram.
U
Explanation
Check
A-
B
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3. A different 7-Eleven has a bank of slurpee fountain heads. Their available flavors are as follows: Mountain
Dew, Mountain Dew Code Red, Grape, Pepsi and Mountain Dew Livewire. You fill five different cups full
with each type of flavor. How many different ways can you arrange the cups in a line if exactly two Mountain
Dew flavors are next to each other?
3.2.1
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