In each of the following problems you are given a function on the interval
Sketch several periods of the corresponding periodic function of period
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Mathematical Methods in the Physical Sciences
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- . Graph the function y = - 2 cos(2x - π).arrow_forward3. Suppose a sinusoidal function was created to model a yearly lynx population, due to a cyclical pattern of increasing and decreasing throughout each year. This function can take the form of y = a cos[ b (x - c)] + d Explain what the value of each parameter (a, b, c and d) would represent in the real-life context of analyzing lynx populations. If you were analyzing the function, consider what each parameter could tell you about the population or the time of research.arrow_forwardDetermine b4 of the periodic function as shown. Round-off to the nearest thousandths places.arrow_forward
- 1. -5TT/4 -8 -7- 6 5 WW -2 -3/4 -TT/2 -TT/4 0 -1- TT/4 Give the midline (vertical shift) of the function. d. Give the amplitude of the function. Amplitude = 3 TT/2 + a. On the graph shown, highlight one period of the function. b. Give the period of this function. 3TT/4 e. Find an equation for this graph of the form f(x)= a sin(b(x−c))+d (Bonus points if you can give more than one answer!) 3sin( f. Find an equation for this graph of the form f(x) = a cos(b(x-c))+d 577/4arrow_forward3. The water at a local beach has an average depth of 1 meter at low tide. The average depth of the water at high tide is 8 m. If one cycle takes 12 hours: (a) Determine the equation of this periodic function using cosine as the base function where o time is the beginning of high tide. (b) What is the depth of the water at 2 am? (c) Many people dive into the beach from the nearby dock. If the water must be at least 3 m deep to dive safely, between what daylight hours should people dive? Time (h) Height (m)arrow_forwardKk.342. If sin\theta =-(1)/(2) and 3\pi <\theta <(7\pi )/(2), thenarrow_forward
- Solve in 10 min plzarrow_forwardThe 10th problem.arrow_forwardThis problem is an example of critically damped harmonic motion. A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring feet. The ball is started in motion from the equilibrium position with a downward velocity of 5 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. Take as the gravitational acceleration 32 feet per second per second. (Note that the positive y direction is down in this problem.) y = learrow_forward
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