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Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function F(t) = 12.25 -3.75 cos( in months and t= 0 corresponding to the winter solstice. (a) What is the average number of daylight hours per day over the course of a year? (b) At which times t, and t₂, where 0 ≤t₁ < t < 12 do the number of daylight hours equal the average number? 41- and 12 (c) Write and integral that expresses the total number of daylight hours in Seattle between f, and t₂ 2 with t given

Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function F(t) = 12.25 -3.75 cos( in months and t= 0 corresponding to the winter solstice. (a) What is the average number of daylight hours per day over the course of a year? (b) At which times t, and t₂, where 0 ≤t₁ < t < 12 do the number of daylight hours equal the average number? 41- and 12 (c) Write and integral that expresses the total number of daylight hours in Seattle between f, and t₂ 2 with t given

Advanced Engineering Mathematics
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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with t given Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function F(t) - 12.25 -3.75 cos ( in months and t = 0 corresponding to the winter solstice. (a) What is the average number of daylight hours per day over the course of a year? (b) At which times t; and t₂, where 0 ≤t₁ <t₂ < 12 do the number of daylight hours equal the average number? 41 and 2= (c) Write and integral that expresses the total number of daylight hours in Seattle between 1 and ₂. (d) Compute the average hours of daylight in Seattle between f, and t₂, where 0 < t < t < 12, and then between t2 and ty, and show that the average of the two is equal to the average day length. Average value of F(t) from 1 to ₂ using integration: Average:
Transcribed Image Text:with t given Suppose that the number of hours of daylight on a given day in Seattle is modeled by the function F(t) - 12.25 -3.75 cos ( in months and t = 0 corresponding to the winter solstice. (a) What is the average number of daylight hours per day over the course of a year? (b) At which times t; and t₂, where 0 ≤t₁ <t₂ < 12 do the number of daylight hours equal the average number? 41 and 2= (c) Write and integral that expresses the total number of daylight hours in Seattle between 1 and ₂. (d) Compute the average hours of daylight in Seattle between f, and t₂, where 0 < t < t < 12, and then between t2 and ty, and show that the average of the two is equal to the average day length. Average value of F(t) from 1 to ₂ using integration: Average:
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