A ferris wheel has 16 cars spaced equal distances apart. The cars are numbered in order from 1-16. What is the measure of the angle of rotation that will map the position of car 16 onto the position of car 13?
A) 22.5
B) 45
C) 67.5
D) 90
I think it's D
the cars are 360/16 = 22.5° apart.
car 16 is 3 positions from car 13. So, a rotation of 67.5° will move car 16 to car 13's position.
To find the angle of rotation that will map the position of car 16 onto the position of car 13, we can use the concept of rotational symmetry.
The ferris wheel has 16 cars spaced evenly, so each car is separated by an angle of 360°/16 = 22.5°.
To get from car 16 to car 13, we need to rotate counterclockwise, so we need to calculate how many cars/carriages we need to pass through to reach car 13.
To find the number of cars we need to pass through, we can subtract the car numbers:
Number of cars = 16 - 13 = 3
Since each car is separated by 22.5°, the angle of rotation required to map car 16 onto car 13 is:
Angle of rotation = Number of cars × Angle between cars = 3 × 22.5° = 67.5°
Therefore, the correct answer is C) 67.5.
To find the measure of the angle of rotation that will map the position of car 16 onto the position of car 13, we need to determine the number of cars that need to be rotated.
Since the ferris wheel has 16 cars spaced equally apart, and the cars are numbered from 1 to 16, the distance between car 16 and car 13 can be calculated as follows:
Distance = 16 - 13 = 3 cars
Therefore, to map car 16 onto car 13, we need to rotate the ferris wheel by 3 cars.
Since there are 16 equally spaced cars, one complete rotation of the ferris wheel would cover all the cars. Therefore, one complete rotation is equal to 360 degrees.
To find the measure of the angle of rotation for 3 cars, we can set up a proportion:
3 cars / 16 cars = x degrees / 360 degrees
Cross-multiplying, we get:
3 cars * 360 degrees = 16 cars * x degrees
1080 degrees = 16x degrees
Now, solving for x:
x = 1080 degrees / 16
x ≈ 67.5 degrees
Therefore, the measure of the angle of rotation that will map the position of car 16 onto the position of car 13 is approximately 67.5 degrees.
So the correct answer is C) 67.5.
thank you !
Well, let's take a spin and find out! If car 16 needs to be mapped onto car 13, we need to figure out how many cars we have to rotate. Since the ferris wheel has 16 cars spaced equally apart, we can calculate that each car is rotated by an angle of 360 degrees divided by 16, which is 22.5 degrees. So, to go from car 16 to car 13, we need to rotate 3 cars, which is a total rotation of 3 times 22.5 degrees, equaling 67.5 degrees.
So, the correct answer is C) 67.5 degrees. By the way, I hope they serve popcorn and cotton candy on your ferris wheel ride to keep you entertained!