Throughout the day, the depth of water at the end of a dock varies with the tides. The function represents the height, in feet, of the water t hours after midnight. Which graph shows the height of the water at the dock at any time after midnight?
Question
Answer:
You forgot to include the function and the set of graphs from where select the right one.I did some research and found the function is:
h(t) = 5 cos (0.5t - 2) + 7
The graph for that function is in the figure attached. That is the answer.
To depict the grahp you can use this knowledge:
1) The maximum value of the cosine funcion is 1 and the minimum is - 1
2) Then, the maximum value of h(t) is 5(1) + 7 = 12
And that happens when the argument of the cosine is 0, which means:
0.5t - 2 = 0 => 0.5t = 2 => t = 2 / 0.5 = 4
So the maximum in the graph is the point (4, 12)
3) The minimum value of h(t) is 5(-1) + 12 = - 5 + 12 = 7.
And that happens when 0.5 t - 2 = Ο => 0.5t = Ο + 2 = (Ο + 2) / 0.5 β 10.3
So, the minimum in the graph is the point (10.3, 7)
4) The vertical axis - intercept is when t = 0 => h(0) = 5cos(0 - 2) + 7 β 4.9
With that you can choose the graph from your choices, and the result is the graph attached.
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11 months ago
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