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Sonbull
4 days ago
13

Amare wants to ride a Ferris wheel that sits four meters above the ground and has a diameter of 50 meters. It takes six minutes

to do three revolutions on the Ferris wheel. Complete the function, h(t), which models Amare's height above the ground, in meters, as a function of time, t, in minutes. Assume he enters the ride at the low point when t = 0.
Mathematics
2 answers:
tester [8.8K]4 days ago
7 0
The distance from the bottom of the wheel to a point on the ground can be expressed using the sine function h(t) = a*sin(kt) + b, where b represents the height of the wheel at 4m. The radius a is calculated as 50/2 = 25m. Since it takes 6 minutes for 3 complete rotations, the period can be derived from 2π/k, giving us k = π. Thus, h(t) = 25*sin(π*t) + 4. 
babunello [8.4K]4 days ago
5 0
The desired function is h(t) = h(t)=-25\cos(\pi t)+29. The cosine function's standard form is , where A is the amplitude, \frac{2\pi}{B} indicates the period, C is the phase shift, and D denotes the midline. With a Ferris wheel height of 4m and a diameter of 50m, the minimum value is 4 and the maximum is 54. Since the full 3 revolutions take 6 minutes, the period is determined accordingly. There is no phase shift here, so C = 0. We can substitute y=h(t), B=π, C=0, and D=29 into the general equation to find the function, ensuring it starts at the lowest point when t=0.
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Answer:

P\left(8\right)=0

Step-by-step explanation:

Assuming a fair die is rolled.

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Let X represent the collection of all outcomes. Let A represent a specific outcome.

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                        P\left(A\right)=\frac{|A|}{|X|}

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Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =
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Answer:

Attached is the question in consideration.

m\angle CEA =90 \ (deg)

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The options 1,4,5,6 represent the correct answers.

Step-by-step explanation:

⇒ Given that \ ray\ AE  is ⊥FEC it constitutes a right triangle, leading to m\angle CEA =90\ (deg).

⇒ The measure for \angle BEF =135\ (deg) equals \angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg) as \angle AEB bisects \angle AEC, implying that \angle AEB is half of \angle AEC, thus  \angle AEB = 45\ (deg).

⇒\angle CEF represents a straight line, as the angle measures across it yield 180\ (deg).

⇒ The angle measure for \angle AEF = 90\ (deg) is derived from the linear pair concept.

Since \angle CEA + \angle AEF = 180\ (deg), inserting the values of  m\angle CEA =90\ (deg) leads to \angle AEF = 90\ (deg).

The other two options are incorrect as:

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  • Also, m\angle CEB=2(m\angle CEA) is inaccurate.

     As \angle CEA = 90\ (deg) and \angle CEB=45\ (deg)

Thus, we have a total 4 valid answers.

The confirmed options are 1,4,5,6.

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