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Sagot :
A sinusoidal function can be used to model the height because, the
height is given by the function; [tex]\underline{h = 13 \cdot sin \left(2\cdot t )\right) + 24}[/tex]
How can a sinusoidal function model the height of motion?
The time the cart takes to complete a full rotation = 2 seconds
The location of the center of the ride above the ground = 24 feet
The cart in the observation is cart X
Required:
The reason why a sinusoidal function can be used to model the height of
the cart X above the ground.
Solution:
In the diagram from a similar question, the radius is given as 13 feet
The height at a particular time depends on the angle of rotation which
depends on the time of rotation.
A sinusoidal function can be presented as follows;
[tex]y = \mathbf{A \cdot sin \left(\dfrac{2 \cdot \pi}{B} \cdot (x - C )\right) + D}[/tex]
Where;
y = h = The height
A = The radius = 13
C = 0
[tex]The \ \mathbf{period}, \ T = 2 = \dfrac{2 \cdot \pi}{B}[/tex]
x = t = The time in seconds
D = 24
Which gives;
[tex]h = \mathbf{13 \cdot sin \left(2\cdot t )\right) + 24}[/tex]
Therefore, the height can be modelled using the following sinusoidal
function; [tex]\underline{h = 13 \cdot sin \left(2\cdot t )\right) + 24}[/tex]
Learn more about sinusoidal functions here:
https://brainly.com/question/4599331
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