Respuesta :
Answer:
The required function is [tex]h(t)=-25\cos(\pi t)+29[/tex].
Step-by-step explanation:
The general form of cosine function is
[tex]y=A\cos(Bt+C)+D[/tex]
where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and D is midline.
It is given that the Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. So the minimum value of the function is 4 and maximum value is 50+4=54.
[tex]D=\frac{Maximum+Minimum}{2}=\frac{54+4}{2}=29[/tex]
It takes six minutes to do three revolutions on the Ferris wheel. So, period of the function is
[tex]period=\frac{6}{3}[/tex]
[tex]period=2[/tex]
The period of a cosine function is
[tex]\frac{2\pi}{B}=2\Rightarrow B=\pi[/tex]
The function have no phase shift. So, C=0.
Substitute y=h(t), B=π, C=0 and D=29 in equation (1) to find the function.
[tex]h(t)=A\cos(\pi t+0)+29[/tex]
It is given that the ride is at the low point whet t=0, it means the function passes through the point (0,4).
Substitute t=0 and h(t)=4 in the above function.
[tex]4=A\cos(\pi (0)+0)+29[/tex]
[tex]4=A+29[/tex]
Subtract 29 from both the sides.
[tex]4-29=A+29-29[/tex]
[tex]-25=A[/tex]
The amplitude of the function is -25.
Substitute y=h(t), A=-25 B=π, C=0 and D=29 in equation (1) to find the function.
[tex]h(t)=-25\cos(\pi t)+29[/tex]
Therefore the required function is [tex]h(t)=-25\cos(\pi t)+29[/tex].
