The figure below is a model of a Ferris wheel. The diameter of the wheel is 191 feet, and one complete revolution takes 15 minutes. The bottom of the wheel is 11 feet above the ground. Complete the table below. (Round your answers to two decimal places.)

t H
0 min 11 ft
1.875 min HOW DO I FIND?
3.75 min 106.5 ft (the baseline, 202-95.5)
5.625 min HOW DO I FIND?
7.5 min 11 + 191 = 202 ft
9.375 min HOW DO I FIND?
11.25 min 106.5 ft
13.125 min HOW DO I FIND?
15 min 11 ft

if the diameter is 191, then the radius is 191/2 = 95.5

That is the amplitude of the sin/cos curve

Add 11 to that since the wheel doesn't scrape the ground.

H = 95.5 sin(kt) + 106.5

Since H is at its minimum at t=0, it will look like

H = -95.5 cos(kt) + 106.5

since cos(x) is at its max when x=0.

Since the period is 15 minutes

H(t) = -95.5 cos(2πt/15) + 106.5

Now just plug in values for t to fill in the table. For example, when

t = 3.75 = 15/4,
H = -95.5 cos pi/2 + 106.5 = 106.5

Well, well, well, it seems like you're having trouble finding the heights for certain times. Don't worry, I'm here to bring some laughter and assistance!

To find the heights at the given times, we need to use a little bit of math and imagination. Since one complete revolution of the Ferris wheel takes 15 minutes, we can divide the total height (191 ft) by the total time (15 min) to find the rate of change in height per minute.

So, you can calculate the rate as 191 ft divided by 15 min, which gives you approximately 12.73 ft/min. Keep this number in your clown toolbox - I mean, calculator.

To find the height at a specific time, you want to determine how many minutes have passed since the ride started and then multiply that by the rate of change.

For example, at 1.875 minutes:
1.875 min * 12.73 ft/min = approximately 23.80 ft. Ta-da!

Similarly, you can use this method to find the heights at 5.625, 9.375, and 13.125 minutes. Just replace the time in the equation and let the math work its magic.

I hope this helps you complete the table with a smile on your face! Remember, math can be a ride of its own, so buckle up and enjoy the journey!

To find the height of the Ferris wheel at different times, we need to understand the relationship between time and height. We know that one complete revolution takes 15 minutes, so we can use this information to find the height at specific times.

To find the height at 1.875 minutes:

1. Calculate the fraction of a complete revolution that has elapsed: 1.875 minutes / 15 minutes = 0.125.
2. Multiply this fraction by the circumference of the wheel to find the distance traveled: 0.125 * 191 feet = 23.875 feet.
3. Subtract this distance from the starting height of 11 feet: 11 feet - 23.875 feet = -12.875 feet.

Therefore, the height at 1.875 minutes is -12.875 feet.

To find the height at 5.625 minutes:

1. Calculate the fraction of a complete revolution that has elapsed: 5.625 minutes / 15 minutes = 0.375.
2. Multiply this fraction by the circumference of the wheel to find the distance traveled: 0.375 * 191 feet = 71.625 feet.
3. Subtract this distance from the starting height of 11 feet: 11 feet - 71.625 feet = -60.625 feet.

Therefore, the height at 5.625 minutes is -60.625 feet.

To find the height at 9.375 minutes:

1. Calculate the fraction of a complete revolution that has elapsed: 9.375 minutes / 15 minutes = 0.625.
2. Multiply this fraction by the circumference of the wheel to find the distance traveled: 0.625 * 191 feet = 119.375 feet.
3. Subtract this distance from the starting height of 11 feet: 11 feet - 119.375 feet = -108.375 feet.

Therefore, the height at 9.375 minutes is -108.375 feet.

To find the height at 13.125 minutes:

1. Calculate the fraction of a complete revolution that has elapsed: 13.125 minutes / 15 minutes = 0.875.
2. Multiply this fraction by the circumference of the wheel to find the distance traveled: 0.875 * 191 feet = 167.125 feet.
3. Subtract this distance from the starting height of 11 feet: 11 feet - 167.125 feet = -156.125 feet.

Therefore, the height at 13.125 minutes is -156.125 feet.

By following the steps outlined above, you can complete the table with the requested values.

To complete the table, we need to find the height (H) of the Ferris wheel at different time intervals.

At the start of the table, it is given that at 0 minutes, the height (H) is 11 feet.

To find the height at 1.875 minutes, we need to determine how much the Ferris wheel has rotated since the starting position. Since one complete revolution takes 15 minutes, we divide 1.875 by 15 to get the fraction of rotation that has occurred.

1.875 / 15 = 0.125

Now, we need to find the corresponding height of the Ferris wheel when it has completed 0.125 rotations. We can calculate this by multiplying the fraction of rotation (0.125) by the circumference of the wheel.

Circumference of a circle = π * diameter

Given that the diameter of the Ferris wheel is 191 feet:

Circumference = π * 191 = 600.095 feet (rounded to two decimal places)

Now, we multiply the circumference by the fraction of rotation:

600.095 * 0.125 = 75.012 feet (rounded to two decimal places)

Therefore, at 1.875 minutes, the height of the Ferris wheel is approximately 75.01 feet.

Similarly, you can use the same method to find the heights at 5.625 minutes and 9.375 minutes by calculating the fraction of rotation and multiplying it by the circumference of the wheel as explained above.