Question

the revolving restaurant in the cn tower completes 5 6 of a revolution every hour. if shani and laszlo at dinner at the restaurant from 19: 15 to 21: 35, through what angle did their table rotate during the meal? express your answer in radian measure in exact form and in approximate form, to the nearest tenth.

Answer 1

The table rotated approximately 12.13 radians during the meal.

Step-by-step explanation:

To calculate the angle of rotation, we need to determine the fraction of a revolution completed during the time at the restaurant. The restaurant completes 5/6 of a revolution every hour, so in 2 hours and 20 minutes, it would complete:

2 hours + 20 minutes = 2.33 hours

Angle of rotation = (2.33 hours) x (5/6 of a revolution per hour) x (2π radians per revolution)

Angle of rotation = 3.86π radians

To approximate this value, we can use 3.14 as an approximation for π:

Angle of rotation ≈ 3.86 x 3.14 = 12.13 radians (rounded to the nearest tenth)

Answer 2

Shani and Laszlo's table rotated approximately 12.05 radians during their meal at the CN Tower's revolving restaurant.

Solving for the Angle Through Rotation:

1. Convert revolutions to radians:

Since 1 revolution equals 2π radians, 5/6 of a revolution is:

(5/6) * 2π radians = 5π/3 radians

2. Calculate the total time in hours:

The duration of the meal is 21:35 - 19:15 = 2 hours and 20 minutes.

3. Convert minutes to hours:

20 minutes is equal to 20/60 hours = 1/3 of an hour.

4. Calculate the total time as a fraction of an hour:

Total time = 2 hours + 1/3 hour = 7/3 hours

5. Find the total angle of rotation:

The angle rotated each hour is 5π/3 radians.

Multiply this by the total time in hours:

Total angle = (5π/3 radians) * (7/3 hours) = 35π/9 radians

Answer:

In exact form: 35π/9 radians

In approximate form: 12.05 radians (rounded to the nearest tenth)