Suppose a certain variable star has a period of 10 days. The average brightness of the staris 3.1 magnitudes, and the maximum variation from the average is 0.4 magnitude.Assuming that the variation in brightness is simple harmonic, find an equation that givesthe brightness of the star as a function of time. (Let y be the brightness in magnitudes andlet t be the time in days. Suppose that when t = 0 the brightness is 3.1 magnitudes andincreasing.)y =

According to the given problem, find the equation of y:

Answered: Suppose a certain variable star has a…

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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Outside temperature over the course of a day can be modeled as a sinusoids function. Suppose the temperature is 50 degrees at midnight and the high temperature for the day will be 60 degrees and low will be 40 degree ax Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.
During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)
Jerry is driving across the country at a constant speed. Jerry enters Intersate 90 and and starts a clock as he passes mile marker 52. After 5.4 hours, Jerry passes miles marker 484. Represent the time elapsed in hours using the independent variable t. Represent the mile marker passed at time t with the dependent variable x. At what speed is Jerry driving? miles per hour Write a formula to compute the mile marker x as a function of t. x= What mile marker is Jerry passing when 8.6 hours have elapsed?
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 85 degrees occurs at 4 PM and the average temperature for the day is 75 degrees. Find the temperature, to the nearest degree, at 7 AM.
The figure shows a page with 1-inch margins at the top and the bottom and half-inch side margins. A publishing company is willing to vary the page dimensions subject to the condition that the printed area of the page is 50 square inches. Express the total area of the page, A, as a function of the width of the rectangle containing the print, x.
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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