Graphics Programs Reference
In-Depth Information
5.
a
r
T
T
A wirecarrying an electriccurrent issurrounded by rubberinsulation of outer
radius
r
. The resistance of the wire generates heat, which isconducted through
the insulation and convectedinto the surrounding air. The temperature of the
wirecan be shown to be
ln(
r
q
2
/
a
)
1
hr
T
=
+
+
T
∞
π
k
where
q
=
rate of heat generation in wire
=
50 W/m
a
=
radiusofwire
=
5mm
k
=
thermalconductivity of rubber
=
0
.
16 W/m
·
K
20 W/m
2
h
=
convectiveheat-transfer coefficient
=
·
K
T
∞
=
ambienttemperature
=
280K
Find
r
that minimizes
T
.
6.
Minimize the function
1)
2
1)
2
F
(
x
,
y
)
=
(
x
−
+
(
y
−
subject to the constraints
x
+
y
≤
1 and
x
≥
0
.
6.
7.
Find the minimum of the function
6
x
2
y
3
F
(
x
,
y
)
=
+
+
xy
≥
0. Verify the result analytically.
8.
SolveProb. 7 if the constraint ischanged to
y
in
y
≥−
2.
x
2
.
9.
Determine the smallest distance from the point(1
,
2) to the parabola
y
=
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