MATH SOLVE

4 months ago

Q:
# a ferris wheel rotates around in 30 seconds. the maximum height above theground is 55 feet and the minumum height above the ground is 5 feet. what function would model the height as a funtion of T in seconds

Accepted Solution

A:

Answer:The required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].Step-by-step explanation:The general sine function is[tex]y=A\sin (Bx+C)+D[/tex] .... (1)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 maximum height above the ground is 55 feet and the minimum height above the ground is 5 feet. The amplitude of the function is[tex]A=\frac{Maximum+Minimum}{2}=\frac{55+5}{2}=30[/tex]The Midline of the function is[tex]D=\frac{Maximum-Minimum}{2}=\frac{55-5}{2}=25[/tex]A ferris wheel rotates around in 30 seconds. So, the period of the function is 30.[tex]\frac{2\pi}{B}=30\Rightarrow B=\frac{2\pi}{30}=\frac{\pi}{15}[/tex][tex]2\pi=30B[/tex]Substitute A=30, [tex]B=\frac{\pi}{15}[/tex], C=0 and D=25 in equation (1), to find the required function.[tex]y=30\sin (\frac{\pi}{15}x+0)+25[/tex]The required variable is T. Replace the variable x by T. So the height function is[tex]h(T)=30\sin (\frac{\pi}{15}T+0)+25[/tex]Therefore the required function is [tex]h(T)=30\sin (\frac{\pi T}{15})+25[/tex].