Respuesta :
The correct option is (b) h=0.5cos([tex]\pi[/tex]/6t)+9.5.
The equations can be used to model the height as a function of time, t, in hours is h=0.5cos([tex]\pi[/tex]/6t)+9.5.
Equation of cosine function:
The following is a presentation of the cosine function's generic form;
y = a + cos(bx - c) + d
amplitude = a
b = cycle speed
Calculation for the model height;
The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.
Obtain amplitude 'a' as
[tex]\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}[/tex]
The time 'T' is calculated as-
[tex]\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}[/tex]
Now, calculate 'd'
[tex]\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}[/tex]
Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:
h=0.5cos([tex]\pi[/tex]/6t)+9.5
To know more about the general equation of a cosine function, here
https://brainly.com/question/27587720
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The complete question is-
The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.
A. h=0.5cos([tex]\pi[/tex]/12t)+9.5
B. h=0.5cos([tex]\pi[/tex]/6t)+9.5
C. h=cos([tex]\pi[/tex]/12t)+9
D. h=cos([tex]\pi[/tex]/6t)+9
