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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