Which of the following is a sixth-degree polynomial function? Select all that apply.2 answers

The equation that can be used to models the height as a function of time, based on the given options, is presented as follows; $\displaystyle \underline{ H = 0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

Reasons:

The given parameters are;

The variation of the height of the tip of the hour hand = 9 feet to 10 feet

At t = 0, the time = 12.00 a.m.

Required: The equation that can be used to model the height as a function of time.

Solution:

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

y = a·cos(b·x - c) + d

The amplitude = a

$\displaystyle a = \mathbf{ \frac{Maximum \ value -Minimum \ value}{2}}$

Therefore;

$\displaystyle a = \frac{10 -9}{2} = 0.5$

b = The cycle speed

The period, T, is given as follows;

$\displaystyle T = \mathbf{ \frac{2 \cdot \pi}{b}}$

The period of a block, T = 12 hours

Therefore;

$\displaystyle b = \frac{2 \cdot \pi}{T}$

$\displaystyle b = \frac{2 \cdot \pi}{12} = \mathbf{ \frac{ \pi}{6}}$

$\displaystyle d = \mathbf{ \frac{Maximum \ value +Minimum \ value}{2} = \frac{10 + 9 }{2}} = 9.5$

At t = 0, H = The highest point = 10 ft.

Which gives;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \times 0 -c\right) + 9.5} = 10$

$\displaystyle cos \left( -c\right) = \frac{0.5}{0.5} = 1$

-c = arcos(1) = 0

-c = 0

c = 0

The equation is therefore;

$\displaystyle H = \mathbf{0.5 \cdot cos \left(\frac{\pi}{6} \cdot t \right) + 9.5}$

The above equation is the same as; <u>H = 0.5cosine (StartFraction pi Over 6 EndFraction t) + 9.5</u>

Learn more about the cosine function here:

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Y_Kistochka [10]

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MaRussiya [10]

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