Non-examples of least Common Multiple
2 answers:
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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:
The height of rocket is 102.7 meter.
Step-by-step explanation:
Given : Brynn and Denise launch their rockets at the same time.
The height of Brynn’s rocket, in meters, is given by the function , where x is the number of seconds after the launch.
The height of Denise’s rocket, in meters, is given by the function
, where x is the number of seconds after the launch.
There is a moment when the rockets are at the same height.
To find : The height
Solution :
When the rockets have same height
So,
Now, we put x value in any of the function to find height.
, x=1.52
Nearest tenth = 102.7
Therefore, The height of rocket is 102.7 meter.