1. The outside temperature of one day (from midnight to midnight) can be modeled as a sinusoidalfunction. Suppose you know the low temperature of 42°F occurs at midnight. The high temperatureis 58°F. Assuming 't' is the number of hours since midnight, find a SINE equation for thetemperature, T, in terms of t. Show all your planning and processing steps. Justify your answer.y = asin (c (x + ²)) + bOR y = a sin(cx + d) + b

The minimum and maximum temperature are 420F, 580F. The minimum temperature occurs at midnight. We…

Answered: 1. The outside temperature of one day…

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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At noon, the tide is at mid tide of 11 feet. At 6:00 pm, the tide is at low tide of 3 feet. At 6:00 am, the tide is at its high tide of 19 feet. It takes 24 hours for the tide to complete a full cycle. Determine a sinusoidal function that models the tide height h as a function of time t(in hours). Let t = 0 correspond to noon. - High tide Mid tide Low tide d
A gauge at the end of a pier measures and tracks the water depth d (in feet) over time. Regression analysis was performed to fit a trigonometric function to the data. The function d(t) models the depth of the water over time, d(t) = 11 sin(0.406t) + 21 where t represents the number of hours past midnight and 0 ≤ t ≤ 24. High tide occurs twice in a day. After how many hours will the second high tide occur? O 3.87 hours O 15.48 hours O 19.35 hours O 23.21 hours
The San Francisco Bay tides vary between 1 foot and 7 feet. The tide is at its lowest point when time (t) is 0 and completes a full cycle in 8 hours. What is the amplitude, period, and midline of a function that would model this periodic phenomenon? A. Amplitude = 6 feet; period = 8 hours; midline: y = 4 B. Amplitude = 6 feet; period = 4 hours; midline: y = 3 C. Amplitude = 3 feet; period = 8 hours; midline: y = 4 D. Amplitude = 3 feet; period = 4 hours; midline: y = 3
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 76 degrees at midnight and the high temperature is 86, at 6pm, while the low is 66 degrees, at 6am. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.D(t) =
A Ferris wheel has a radius of 30 m. Its center is 31 m above the ground. It rotates once every 40 s. Suppose you get on the bottom at t = 0. Write an equation that expresses your height as a function of elapsed time. Oh = 31 cos 2T- - O h = 30 cos 2T (t - 40) 40 = (t - 20) 40 Oh 31 cos 2T- = (t - 20) 40 (t – 20) 40 Oh 30 cos 2π- 2T +30 +1 +30 +31

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