Acarnival ride is in the shape of a wheel with a radius of 15 feet. the wheel has 24 cars attached to the center of the wheel. what is the central angle, arc length, and area of a sector between any two cars? round answers to the nearest hundredth if applicable. you must show all work and calculations to receive credit. (10 points)

1) Given that there are 24 cars equally divided, each space between two adjacent cars is the 1 /24 of the total space.

2) Central angle of a sector between to adjacent cars:

=> divide the angle of the whole circle by 24 => 360° / 24 = 15°

3) arc length between two adjacent cars:

=> divide the total length of the circle by 24.

The total length of the circle is the circumference = 2π(radius) = 2π(15 feet)

total length = 94.25 feet

=> arc length = 94.25 feet / 24 = 3.93 feet

4) area of a sector between two adjacent cars:

=> divide the area of the circle by 24

area of the circle = π(radius)^2 = π(15 feet)^2 = 706.86 feet^2

=> area of the sector = 706.86 feet^2 / 24 = 29.45 feet^2

Logical equivalent of the give question is its contrapositive