anonymous
  • anonymous
In Steinhatchee in July, high tide is at noon. The water level is 5 feet at high tide and 1 foot at low tide. Assuming the next high tide is exactly 12 hours later and the height of the water can be modeled by a cosine curve, find an equation for Steinhatchee's water level in July as a function of time (t).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
can some one explain how to solve this step by step???
anonymous
  • anonymous
The period of the time = 12 hours, therefore the coefficient of ( t ) in the cosine function is (2 pi ) / T = (2 pi)/ 12 = pi / 6 . Since the difference in water level is 5 - 1 = 4 feet, then the amplitude of the cosine is half that which is 2. f(t) = 2 cos pi over 6 t + 3 25. Maximum : 4 , Minimum : -2 , period : pi / 2 f(x) = a cos(k x) + b Maximum - Minimum = 4 - (-2) = 6 = 2 a , so a = 6/2 = 3 b = 1/2 (Maximum + Minimum) = 1/2 (4 + (-2) ) = 1 k = (2pi)/ T = (2pi)/ (pi/2) = 4 f(x) = 3 cos( 4 x) + 1 24. f(x) has the largest maximum equal to 7. 22. Rate of change = (y2 - y1) / (x2 - x1) = (-1 - 5 )/ (pi - 0) = = - 6 / pi
anonymous
  • anonymous
thank you soo much!!

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anonymous
  • anonymous
you're welcome :)! Medal?

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