Particle travels along a circular path that has a radius of 3 feet. the angular velocity of the particle is 18 radians per minute. the linear velocity of the particle is feet per minute.

We know that

[length of a circumference ]=2*pi*r
for r=3 ft

[length of a circumference ]=2*pi*3> 18.84 ft

The angular velocity of the particle is 18 radians per minute.

if 2pi radians  (full circle)> 18.84 ft
18 radians> X
X=18*18.84/(2*pi)> X=54 ft
so
The linear velocity of the particle is 54 ft/minute

the answer is
54 ft/min