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5. The water level of a restricted tidal basin is modeled with the function h(t) = sin (t) + where one tidal cycle passes every 27 time units. Two modification to the model are proposed: 1. a correction function g(t) = cos(2t) and 2. The addition of a function to account for development of a standing wave in the basin, f(t) = cos(t)³ sin(t) +1. (a) Calculate the average water level predicted from the original function over one tidal cycle, - h(t) dt. 27 (b) Calculate the average water level predicted from the addition of the correction function to the original function over one tidal cycle, r2x (h(t) + g(t) dt. (c) Calculate the average water level predicted from the addition of the standing wave function, E f(t)h(t) dt.

5. The water level of a restricted tidal basin is modeled with the function h(t) = sin (t) + where one tidal cycle passes every 27 time units. Two modification to the model are proposed: 1. a correction function g(t) = cos(2t) and 2. The addition of a function to account for development of a standing wave in the basin, f(t) = cos(t)³ sin(t) +1. (a) Calculate the average water level predicted from the original function over one tidal cycle, - h(t) dt. 27 (b) Calculate the average water level predicted from the addition of the correction function to the original function over one tidal cycle, r2x (h(t) + g(t) dt. (c) Calculate the average water level predicted from the addition of the standing wave function, E f(t)h(t) dt.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 18EQ
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The water level of a restricted tidal basin is modeled with the function h(t) sin (t) + where one tidal cycle passes every 27 time units. Two modification to the model are proposed: 1. a correction function g(t) = cos(2t) and 2. The addition of a function to account for development of a standing wave in the basin, f(t) = cos(t)³ sin(t) + 1. 5. (a) Calculate the average water level predicted from the original function over one tidal cycle, 1 -2x h(t) dt. (b) Calculate the average water level predicted from the addition of the correction function to the original function over one tidal cycle, -27 1 E (h(t) + g(t)) dt. (c) Calculate the average water level predicted from the addition of the standing wave function, -2x 1 : f(t)h(t) dt.
Transcribed Image Text:The water level of a restricted tidal basin is modeled with the function h(t) sin (t) + where one tidal cycle passes every 27 time units. Two modification to the model are proposed: 1. a correction function g(t) = cos(2t) and 2. The addition of a function to account for development of a standing wave in the basin, f(t) = cos(t)³ sin(t) + 1. 5. (a) Calculate the average water level predicted from the original function over one tidal cycle, 1 -2x h(t) dt. (b) Calculate the average water level predicted from the addition of the correction function to the original function over one tidal cycle, -27 1 E (h(t) + g(t)) dt. (c) Calculate the average water level predicted from the addition of the standing wave function, -2x 1 : f(t)h(t) dt.
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