wardlawshaliyah
01.08.2019 •
Mathematics
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?
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Ответ:
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 = π => 0.5t = π + 2 = (π + 2) / 0.5 ≈ 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 ≈ 4.9
With that you can choose the graph from your choices, and the result is the graph attached.
Ответ:
x = 3
Step-by-step explanation:
Given
4(x - 4) + 6x = 14 ← distribute and simplify left side
4x - 16 + 6x = 14
10x - 16 = 14 ( add 16 to both sides )
10x = 30 ( divide both sides by 10 )
x = 3