Question

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).

Answer 1

can some one explain how to solve this step by step???

Answer 2

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

Answer 3

thank you soo much!!

Answer 4

you're welcome :)! Medal?