From the given function for the angle of elevation, we have that:
a) In Brownsville, the angle of elevation in the first day of summer is of 87.5º and of winter is of 40.9º.
b) In Nome, the angle of elevation in the first day of summer is of 49.5º and of winter is of 2.9º.
c) Both cities have the same change in the angle of elevation.
What is the function for the angle of elevation?
For this problem, the function for the angle of inclination is given as follows:
A(L,N) = 90 - L - 23.5cos[360(N + 10)/365]
In which:
- N is the day of the year.
Then, for items a and b, we find the numeric values of the multi-variable function, and for item c, we find the differences, considering that:
- The latitudes for each city are given.
- The days corresponding to the first day of summer and of winter are also given.
In item a, we have that the latitude is of L = 26, hence on the first day of summer, the angle is given by:
A(26, 172) = 90 - 26 - 23.5cos(360 x 182/365) = 87.5º.
On the first day of winter, the angle is given by:
A(26, 355) = 90 - 26 - 23.5cos(360 x 355/365) = 40.9º.
In Brownsville, the angle of elevation in the first day of summer is of 87.5º and of winter is of 40.9º.
In item b, we have that the latitude is of L = 64, hence on the first day of summer, the angle is given by:
A(26, 172) = 90 - 64 - 23.5cos(360 x 182/365) = 49.5º.
On the first day of winter, the angle is given by:
A(26, 355) = 90 - 64 - 23.5cos(360 x 355/365) = 2.9º.
In Nome, the angle of elevation in the first day of summer is of 49.5º and of winter is of 2.9º.
The changes are given as follows:
- Brownsville: 87.5 - 40.9 = 46.6º.
- Nome: 49.5 - 2.9 = 46.6º.
Both cities have the same change in the angle of elevation.
More can be learned about the numeric values of a function at brainly.com/question/28367050
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