3. -16 The number of hours of daylight at any point on Earth fluctuates throughout the year. At 40° north latitude, the length of a day is approximated by D(t) = 12- 3 cos (t + 10) where 2π 365 10)), D is measured in hours and t is measured in days, with t = 0 corresponding to January 1. a. Approximately how much daylight is there on September 1 (t = 243)? b. Find the rate at which the daylight is changing on September 1. Write your answer in a sentence, including appropriate units. c. The graph of D(t) is shown below. At what times of the year is the length of the day changing most rapidly? At what times is it changing least rapidly?
3. -16 The number of hours of daylight at any point on Earth fluctuates throughout the year. At 40° north latitude, the length of a day is approximated by D(t) = 12- 3 cos (t + 10) where 2π 365 10)), D is measured in hours and t is measured in days, with t = 0 corresponding to January 1. a. Approximately how much daylight is there on September 1 (t = 243)? b. Find the rate at which the daylight is changing on September 1. Write your answer in a sentence, including appropriate units. c. The graph of D(t) is shown below. At what times of the year is the length of the day changing most rapidly? At what times is it changing least rapidly?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3.
The number of hours of daylight at any point on Earth fluctuates throughout the year. At 40°
north latitude, the length of a day is approximated by D (t) = 12 - 3 cos ; (375 (t + 10)), where
D is measured in hours and t is measured in days, with t = 0 corresponding to January 1.
a. Approximately how much daylight is there on September 1 (t = 243)?
b. Find the rate at which the daylight is changing on September 1. Write your answer in a
sentence, including appropriate units.
c. The graph of D (t) is shown below. At what times of the year is the length of the day
changing most rapidly? At what times is it changing least rapidly?
180
200
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Expert Solution
Step 1
The length of a day is approximated by , where is measured in hours and is measured in days, corresponds to January .
We have to find how much daylight in September , the rate at which the daylight changing in September and the time of the year is the length of the day changing most rapidly and the changing least rapidly.
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