Adding and Subtracting Rational Expressions

The video tutorial covers how to calculate the arc length and area of sectors in a circle. It explains the formulas for arc length and sector area, emphasizing the use of radians. The tutorial includes several example problems, demonstrating how to find arc length given the radius and angle, and how to convert between degrees and radians. It also explores real-world applications, such as calculating distances between cities and the path of a merry-go-round. The video concludes with methods to find the area of a sector using the central angle and radius.

What is the formula to calculate the length of an intercepted arc?

• s = R + theta

• s = R / theta

• s = R * theta

• s = R - theta

How is the angle measure theta always expressed in the formula for arc length?

• Turns

• Gradients

• Radians

• Degrees

If a circle's radius is 8 meters and the central angle is 2pi radians, what is the arc length?

• 16pi meters

• 8pi meters

• 16 meters

• 4pi meters

To convert degrees to radians, which of the following is used?

• Divide by 180 and multiply by pi

• Multiply by 180 and divide by pi

• Multiply by pi and divide by 180

• Divide by pi and multiply by 180

What is the area of a sector formula?

• 1/2 * theta * R^2

• R^2 / (2 * theta)

• theta / (2 * R^2)

• 1/2 * theta * R

What is the measure of theta in radians if a circle of radius 6 meters has an intercepted arc length of 10 meters?

• 3/5 radians

• 6/10 radians

• 10/6 radians

• 5/3 radians

How far apart are Cincinnati and Atlanta if the earth's radius is 3960 miles and the difference in latitude is 5.4 degrees?

• 396 miles

• 540 miles

• 5.4 miles

• 373.2 miles

What is the radius of a circle if the area of a sector is 134 feet squared and the central angle is 240 degrees?

• 12 feet

• 10 feet

• 16 feet

• 8 feet

For a merry-go-round rotating 2808 degrees per ride, how far does a rider seated 8 feet from the center travel?

• 280.8 feet

• 78pi feet

• 704 feet

• 392.1 feet

What is the area swept by a 32-inch long windshield wiper arm through an angle of 125 degrees?

• 32 inches squared

• 132 inches squared

• 985 inches squared

• 1117 inches squared