Determine the linear velocity of a point rotating at the given angular velocity at a distance r from the center of the rotating object. Round to the nearest tenth. $\omega=36$ radians per second, $r=12$ inches

Determine each angular velocity. Round to the nearest tenth. 100 revolutions in 16 minutes

Determine each angular velocity. Round to the nearest tenth. 28.4 revolutions in 19 seconds

Determine each angular velocity. Round to the nearest tenth. 17.2 revolutions in 12 seconds

A sector has a central angle of $135^{\circ}$ and arc length of 114 millimeters. Find the radius of the circle.

A sector has a central angle of $135^{\circ}$ and arc length of 114 millimeters. Find the area of the sector.

A sector has area of 15.3 square meters. The radius of the circle is 3 meters. Find the degree measure of the central angle.

Given the measurement of a central angle, find the length of its intercepted arc in a circle of radius 14 centimeters. Round to the nearest tenth. $282^{\circ}$

A sector has arc length of 6 feet and central angle of 1.2 radians. Find the area of the sector.

The diameter of a circle is 22 inches. If a central angle measures $78^{\circ},$ find the length of the intercepted arc.

Determine each angular displacement in radians. Round to the nearest tenth. 50.4 revolutions

Determine each angular displacement in radians. Round to the nearest tenth. 13.2 revolutions

Write an equation of a sine function with amplitude 20, period 1, phase shift 0, and vertical shift 100.

Write an equation for the given function given the period, phase shift, and vertical shift. cosecant function, period $=3 \pi,$ phase shift $=\frac{\pi}{3},$ vertical shift $=-4$