The number of hours of daylight varies throughout the course of a year (daylight is defined as the time between sunrise and sunset). It has been suggested to approximate the length of daylight in Maths city by the function: 5 f(t) = COS 1000+ 2a + b + 3c (365 (t- a + b + 3c)). +12, Ost≤ 365, 4 where f(t) is the number of daylight hours, t is time measured in days (t = 0 at January 1, 2022), and radian angle measure is used. (a) What is the lengths of daylight when t = 0 and t = a + b = c + 200? (b) What is the shortest length of daylight? What is the value of t then? (c) What is the longest length of daylight? What is the value of t then? (d) Find the domain and range of the function using interval notation.
The number of hours of daylight varies throughout the course of a year (daylight is defined as the time between sunrise and sunset). It has been suggested to approximate the length of daylight in Maths city by the function: 5 f(t) = COS 1000+ 2a + b + 3c (365 (t- a + b + 3c)). +12, Ost≤ 365, 4 where f(t) is the number of daylight hours, t is time measured in days (t = 0 at January 1, 2022), and radian angle measure is used. (a) What is the lengths of daylight when t = 0 and t = a + b = c + 200? (b) What is the shortest length of daylight? What is the value of t then? (c) What is the longest length of daylight? What is the value of t then? (d) Find the domain and range of the function using interval notation.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a=15, b=12, c=15
Transcribed Image Text:4. The number of hours of daylight varies throughout the course of a year (daylight is defined as
the time between sunrise and sunset). It has been suggested to approximate the length of
daylight in Maths city by the function:
5
f(t) = -cos (365 (t-
1000+ 2a + b +3c\
+ b + 3c)) +
+12,
Ost≤ 365,
4
where f(t) is the number of daylight hours, t is time measured in days (t = 0 at January 1,
2022), and radian angle measure is used.
(a) What is the lengths of daylight when t = 0 and t = a + b-c+200?
(b) What is the shortest length of daylight? What is the value of t then?
(c) What is the longest length of daylight? What is the value of t then?
(d) Find the domain and range of the function using interval notation.
(e) Use the information from (a) - (d) to sketch a graph of the function, including all relevant
information. (You can use technology)
(f) Find f"(t) (the second derivative of f(t)).
Note: (Show detailed working or explain your answer. Unsupported answers will not receive
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