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622
CHAPTER 15
DIFFERENTIATION IN SEVERAL VARIABLES
(ET CHAPTER 14)
50.
Find the change in elevation from
A
and
B
.
SOLUTION
The segment
AB
spans 7 level curves and the contour interval is 10 meters. Therefore, the change in
elevation from
A
to
B
is 10
·
7
=
70 m.
51.
Estimate the average ROC from
A
and
B
and from
A
to
C
.
The change in elevation from
A
to
B
is 70 m. The scale shows that
is approximately 1500 m. Therefore,
Average ROC from
A
to
B
=
70
1500
≈
0
.
047
.
The change in elevation from
A
to
C
is obtained by multiplying the number of level curves between
A
and
C
, which is 8,
by the contour interval 10 meters, giving 8
·
10
=
80 m. Using the scale, we approximate the distance
AC
by 3500 km.
Therefore,
Average ROC from
A
to
C
=
80
3500
≈
0
.
023
.
52.
Estimate the average ROC from
P
to points i, ii, iii, and iv.
The points i, ii, and iii are on a level curve adjacent to the level curve of
P
, hence the change in elevation
is 10 meters. Using the scale we approximate the distances from
P
to the points i, ii, and iii:
From
P
to i: 400 m
From
P
to ii: 400 m
From
P
to iii: 640 m
Therefore,
Average ROC from
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 Fall '09
 Park
 Multivariable Calculus

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