Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.


Emily is on a Ferris wheel and her height is modeled by the equation
27
y = 30.48 cos2pi/4.25 (x - 2) + 34.27 where x = the number of minutes since the
ride began and y = the height in feet of Emily.
a) What is the radius of the Ferris wheel?
b) How long does it take Emily to make one rotation?
The radius is______
feet and it takes Emily_____
minutes for one rotation.

Emily Is On A Ferris Wheel And Her Height Is Modeled By The Equation 27 Y 3048 Cos2pi425 X 2 3427 Where X The Number Of Minutes Since The Ride Began And Y The class=

Sagot :

The given function for the height of the Ferris wheel is a sinusoidal equation.

  • a) The radius is 30.48 feet and it takes Emily 4.25 minutes for one rotation

Reasons:

The function that gives the height of the Ferris wheel is presented as follows;

[tex]\displaystyle y = 30.48 \cdot cos \frac{2\cdot \pi }{4.25} \cdot \left(x - 2 \right) + 34.27[/tex]

Where;

x = The number of minutes since the ride began

y = The height in feet of Emily

a) Required:

The radius of the Ferris wheel

Solution:

Comparing the given equation with the general equation of a Ferris wheel, we have;

[tex]\displaystyle f(t) = \mathbf{A \cdot trig\left(B \cdot \left(t + C\right) \right) + D}[/tex]

The amplitude of the Ferris wheel = A = 30.48

The amplitude, A = The largest distance from the center = The radius, r

A = r

Therefore;

The radius of the Ferris wheel, r = A = 30.48 feet

b) The time it takes the Emily to make one rotation is given by the period, T, of the motion of the Ferris wheel as follows;

[tex]\displaystyle T = \mathbf{\frac{2 \cdot \pi}{B}}[/tex]

By comparison, we have;

[tex]\displaystyle B = \frac{2 \cdot \pi}{4.25}[/tex]

Therefore;

[tex]\displaystyle The \ period, \, T = \frac{2 \cdot \pi}{\left(\frac{2 \cdot \pi}{4.25} \right)} = 4.25[/tex]

The time it takes Emily to make one rotation, T = 4.25 minutes

Learn more here:

https://brainly.com/question/21165143

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.