(09.04 mc)
a carnival ride is in the shape of a wheel with a radius of 25 feet. the wheel has 20 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)

In this problem, we assume that cars are separated by an equal distance between.

First, we have to find the angle assigned to each car. If the whole central angle is 360° and there are 20 cars, then each car would be:

This means that there's 18° per car. That is, each car represents a circular sector with an angle of 18°.

The arc length is given by this formula:

Where is the arc length, the radius, and is the angle of the sector.

Replacing values we have:

So, the arc length to each sector is

The area of a circular sector is given by the formula:

Therefore, the area of the circular sector is

All the problem is done based on the equality of each sector, and the distance between cars.

central angle=18

arc length=2.5 π feet

area of a sector=31.25π square feet

Step-by-step explanation:

Given

wheel radius=25 feet

attached cars=20

Space between cars along the circumference of wheel= 360/20

                                                                                           =18

Finding arc length:

arc length= radius x angle(in radians)

 angle in radian = 18 x π/180 = 0.1π radians

arc length   = 25 x 0.1π

                  =2.5π feet  

Area of the circle = πr^2

Area of the circle = π(25)^2

Area of the circle = 625π square feet.  

As the ratio of the central angle to the full circle angle is proportional to the area of the sector to the complete circle:

central angle/360=area of sector/area of circle

Area of sector= area of circle x 18/360

                        = 625π(1/20)

                         =31.25π !

answer: 2x + 2 − 2 = 10 − 2; subtraction property of equality

step-by-step explanation: