. The London Eye is a popular tourist attraction in London, England and is one of the largest Ferris Wheels in the world. It has a diameter of 135 meters and makes one revolution (counterclockwise) every 30 minutes. It is constructed so that the lowest part of the Eye reaches ground level, enabling passengers to simply walk on to, and off of, the ride. Find a sinsuoid which models the height h of the passenger above the ground in meters t minutes after they board the Eye at ground level.

Answer:

[tex]y=-67.5[cos(\frac{\pi}{15}t)-1][/tex]

Step-by-step explanation:

We can start solving this problem by doing a drawing of London Eye. (See attached picture).

From the picture, we can see that the tourists will start at the lowest point of the trajectory, which means we can make use of a -cos function. So the function will have the following shape:

[tex]y=-Acos(\omega t)+b[/tex]

where:

A=amplitude

[tex]\omega[/tex] = angular speed.

t= time (in minutes)

b= vertical shift.

In this case:

A= radius = 67.5 m

[tex]\omega=2\pi f[/tex]

where the frequency is the number of revolutions it takes every minute, in this case:

[tex]f=\frac{1}{30} rev/min[/tex]

so:

[tex]\omega=2\pi (\frac{1}{30})[/tex]

[tex]\omega=\frac{\pi}{15} rad/min [/tex]

and

b= radius, so

b=A

b=67.5m

so we can now build our equation:

[tex]y=-67.5cos(\frac{\pi}{15} t)+67.5[/tex]

which can be factored to:

[tex]y=-67.5[cos(\frac{\pi}{15}t)-1][/tex]

You can see a graph of what the function looks like in the end on the attached picture.

The required sinusoidal equation is  [tex]y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

Given that,

It has a diameter of 135 meters and makes one revolution (counterclockwise) every 30 minutes.

It is constructed so that the lowest part of the Eye reaches ground level, enabling passengers to simply walk on to, and off of, the ride.

We have to find,

A sinusoidal  which models the height h of the passenger above the ground in meters t minutes after they board the Eye at ground level.

According to the question,

The tourists will start at the lowest point of the trajectory, which means we can make use of a -cos function. So the function will have the following shape:

[tex]y = -Acos(wt) + b[/tex]

Where,  A=amplitude ,  [tex]\omega[/tex] = angular speed, t= time (in minutes) , b= vertical shift.

Then,

[tex]Radius = \dfrac{diameter}{2}\\\\Radius = \dfrac{135}{2}\\\\Radius = 65.5m[/tex]

The frequency is the number of revolutions it takes every minute is determined by the formula is,

[tex]\omega = 2\pi f[/tex]

Where,

[tex]f = \dfrac{1}{30} revolution \ per \ minute[/tex]

Then,

[tex]\omega = 2\pi \times \dfrac{1}{30}\\\\\omega = \dfrac{\pi }{15}\ radian \ per\ minute[/tex]

Here, The sinusoidal equation can be written as;

[tex]y = -67.5cos\dfrac{\pi t}{15} + 67.5\\\\y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

Hence, The required sinusoidal equation is  [tex]y = -67.5 (cos\dfrac{\pi t}{15} -1)[/tex]

To know more about Frequency click the link given below.

https://brainly.com/question/9661952

In the song, 7 pounds, 5 ounces was the median weight of the students at birth. Which of these is correct?

james jogged around the track 0.68 hours at an average speed 28.9 miles per hour how far did he jog?

A lottery game requires that 3 different numbers are picked from 1 to 9 if someone picks all 3 winning numbers the person wins 9 million complete parts a and b

You have 33 nickels and quarters whose value is $3.85. Find the number of nickels and quarters that
you have.
What is the answer

Find the zeros of the function below.

\small -7x=x^2+12

Find the measure of the arc.
D
А
146°E
B
mĒDF = [?]°
Enter

What’s the answer to 7x when x=8 I need help please

19.214÷13
pls someone help me

ramu and ravi borrowed rs 8000​

What is the value of x in the figure below?

AY
1500-
1400
1300
Optional: How much compound
interest is earned at 35 years?
(looks to be in the middle)
compound interest
Total amount (dollars)
1200
1100
1000
900
800
700
600
500
400
300
200
100
Optional: How much simple
interest is earned at 35 years?
(looks close to the whole number)
simple interest
(a) How much more compound
interest than simple interest is
earned after 35 years?
0
5 10 15 20 25 30 35 40 45 50
Number of years

Help for brainiest
please explain how you got it :D it would help so I can understand how to do the rest

Need answers right away due tonight please. Geometry composite shapes.

Use the table that shows the results of a class poll.
Question
Yes
No
Do
you walk to school?
18% yes
82% no
Is there a pet in your home?
14
—— yes
25
11
—— no
25
Do you play on a sports team?
0.42 yes
0.58 no
Which category in the table shows the least portion of the class?

The owner of a restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a drink from the beverage fountain instead of filling the cup with water. The owner randomly selected 90 people who order a water cup and found that 21 of those customers filled the cup with a soft drink.a. Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. b. The owner estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.35. Suppose that in the month of June 2,500 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.

Select all the statements that are true about the triangles

Please help me with the question

Simplify the following expression.

Nathan bought 4 pounds of chicken for $8. How many pounds can he buy for $20? *

Find the value of −12 + 8 −(−9). Question 20 options: −13 −5 13 5

For which value of k does the system has no solutions?
Equation:
3x + y = 4
kx + y = −2
Answers:
A: -3
B: -2
C: 3
D: 4

If you are given the diameter, how can you calculate the radius

-3/4 ( 8y - 12 ) + 1/5 ( 15y - 30 )

A rectangular prism has a length of 11 centimeters, a height of 13 centimeters, and a width of 2 centimeters. What is its volume, in cubic centimeters?

I need the answer for this one please

A large school district is considering implementing a program that, if successful, would improve the reading scores of its students by 10 points. The current reading scores for the district are normally distributed with a mean of 25 and a standard deviation of 8. The administrators decide to test the new program in one school of 200 students. What is the standard deviation of the comparison distribution

find the surface area of a cylinder with the height of 10 inches and a base diameter of 6 in ​

HELPP!! I report wrong answers!!

PRETTY MUCH A FREE BRAINLIEST IF UR RIGHT, GOOD LUCK :D. Value of x is greater than or equal to 14

Options:

x>14

x<14

x≥14

x≤14

During a competition, numismatist Aditi has been given Rs. 200 in Rs.1 denominations. The judge asks Aditi to allocate the Rs. 1 denominations into a number of pouches such that any amount required between Rs.1 & Rs. 200 can be given by giving out a certain number of pouches without opening them. Aditi thinks and asks the judge to give her 'x' number of pouches to keep the money, where 'x' is the minimum number of bags required to keep the total money. Can you guess the value of 'x'?