
Concept explainers
To show:
a) At any fixed time there are at least two diametrically opposite point on the equator that have exactly the same temperature.
To find:
b) If part a) holds for point lying on any circle on the earth’s surface.
c) If part a) holds for barometric pressure and for altitude above sea level.
a)
Explanation:
1) Concept: Intermediate value theorem
The intermediate value theorem states that if a continuous function,
2) Given:
Start form
3) Calculations:
The latitude
Let us define
Take any number
Case 1:
If
Case 2:
If
Since here
So by intermediate value Theorem
Hence two opposite point have same temperature.
b)
Explanation:
1) Concept: Intermediate value theorem
The intermediate value theorem states that if a continuous function,
2) Given:
Start form
3) Calculations:
Suppose the point lying on any circle on the earth’s surface.
The points are the latitude
Similarly solve by part a)
c)
Explanation:
1) Concept: Intermediate value theorem
The intermediate value theorem states that if a continuous function,
2) Given:
Start form
3) Calculations:
Barometric pressure fits the bill.
Altitude over the (vertical cliff) may be discontinues there for argument are not always hold.
Conclusion:
At any fixed time there are at least two diametrically opposite points on the equator that have exactly the same temperature. It also holds for barometric pressure.

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Chapter 1 Solutions
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