Question

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(pi/12t)+9.5
B. h=0.5cos(pi/6t)+9.5
C. h=cos(pi/12t)+9
D. h=cos(pi/6t)+9

Answer 1

We can tell from the data that there is a midpoint between the lowest and highest point of the clock, which is at a height of 9.5 feet.
Moreover, the lowest point occurs at 6 o clock, and the highest occurs at 12 o clock.
The amplitude of variation from the mid-point is 0.5 feet given by (10 - 9) / 2.
Finally, the time period for the equation is 12 hours. Thus, the answer is:
h = 0.5cos(πt/6) + 9.5, option B

Answer 2

The equations can be used to model the height as a function of time, t, in hours is $\rm h=0.5cos \left (\dfrac{\pi }{6}t\right )+9.5$, the correct option is B.

Equation of cosine function

The general form of the cosine function is presented as follows;

y = a cos(bx - c) + d

Where amplitude = a

Given information

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

The value of a is given by;

$\rm a =\dfrac{Maximum \ value -Minimum \ value}{2}\\\\a=\dfrac{10-9}{2}\\\\a=\dfrac{1}{2}\\\\a=0.5$

Here, b = The cycle speed

The period, T, is given as follows;

$\rm T=\dfrac{2\pi }{b}\\\\12=\dfrac{2\pi }{b}\\\\b = \dfrac{2\pi }{12}\\\\b=\dfrac{\pi }{6}$

And the value of d is given by;

$\rm d =\dfrac{Maximum \ value +Minimum \ value}{2}\\\\d=\dfrac{10+9}{2}\\\\d=\dfrac{19}{2}\\\\d=9.5$

The following equations can be used to model the height as a function of time, t, in hours is;

$\rm h=0.5cos \left (\dfrac{\pi }{6}t\right )+9.5$

Hence, The equations can be used to model the height as a function of time, t, in hours is $\rm h=0.5cos \left (\dfrac{\pi }{6}t\right )+9.5$.

To know more about the cosine function click the link given below.

https://brainly.com/question/4458343