The height of the <em>water</em> depth is h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours, and the height of the Ferris wheel is h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds. Please see the image to see the figures.
<h3>How to derive equations for periodical changes in time</h3>
According to the two cases described in the statement, we have clear example of <em>sinusoidal</em> model for the height as a function of time. In this case, we can make use of the following equation:
h = a + A · sin (2π · t/T + B) (1)
Where:
- a - Initial position, in meters.
- A - Amplitude, in meters.
- t - Time, in hours or seconds.
- T - Period, in hours or seconds.
- B - Phase, in radians.
Now we proceed to derive the equations for each case:
Water depth (u = 20 m, l = 8 m, a = 14 m, T = 12 h):
A = (20 m - 8 m)/2
A = 6 m
a = 14 m
Phase
20 = 14 + 6 · sin B
6 = 6 · sin B
sin B = 1
B = π/2
h = 14 + 6 · sin (π · t/6 + π/2), where t is in hours.
Ferris wheel (u = 40 m, l = 2 m, a = 21 m, T = 40 s):
A = (40 m - 2 m)/2
A = 19 m
a = 21 m
Phase
2 = 21 + 19 · sin B
- 19 = 19 · sin B
sin B = - 1
B = - π/2
h = 21 + 19 · sin (π · t/20 - π/2), where t is in seconds.
Lastly, we proceed to graph each case in the figures attached below.
To learn more on sinusoidal models: brainly.com/question/12060967
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Answer:
$186.13
Step-by-step explanation:
15% = .15
218.98 * .15 = 32.847 = 32.85
218.98 - 32.85 = 186.13
Answer:
D. The area of the triangle is 9 square feet, because the area of the rectangle is 18 square feet.
Step-by-step explanation:
D = 2*3 -10 = -4
The n-th term of the sequence is
.. t[n] = 3 +d(n -1) = 7 -4n
Answer:
surface area = 136 m^2
Step-by-step explanation:
The prism has 5 faces.
Faces 1 and 2: The front and back faces are two congruent triangles with base 6 m and height 4 m.
Face 3: The bottom face is a rectangle with length 7 m and width 6 m.
Faces 4 and 5: The left and right inclined faces are two congruent rectangles with length 7 m and width 5 m.
area = area of faces 1 and 2 + area of face 3 + area of faces 4 and 5
area of triangle = bh/2
area of rectangle = LW
area = 2 * 6 m * 4 m / 2 + 7 m * 6 m + 2 * 7 m * 5 m
area = 24 m^2 + 42 m^2 + 70 m^2
area = 136 m^2
Answer: surface area = 136 m^2