Answer:
The angular velocity is 6.72 π radians per second
Step-by-step explanation:
The formula of the angular velocity is ω =
, where v is the linear velocity and r is the radius of the circle
The unit of the angular velocity is radians per second
∵ The diameter of the tire is 25 inches
∵ The linear velocity is 15 miles per hour
- We must change the mile to inch and the hour to seconds
∵ 1 mile = 63360 inches
∵ 1 hour = 3600 second
∴ 15 miles/hour = 15 × 
∴ 15 miles/hour = 264 inches per second
Now let us find the angular velocity
∵ ω =
∵ v = 264 in./sec.
∵ d = 25 in.
- The radius is one-half the diameter
∴ r =
× 25 = 12.5 in.
- Substitute the values of v and r in the formula above to find ω
∴ ω = 
∴ ω = 21.12 rad./sec.
- Divide it by π to give the answer in terms of π
∴ ω = 6.72 π radians per second
The angular velocity is 6.72 π radians per second
|12x + 1| = 10
Remove the absolute value term and make two equations:
12x +1 = 10
12x +1 = -10
Now solve for both x values:
12x +1 = 10
Subtract 1 from both sides:
12x = 9
Divide both sides by 12:
x = 9/12
12x +1 = -10
Subtract 1 from both sides:
12x = -11
Divide both sides by 12:
x = -11/12
The answer would be (-11/12, 912)
Answer: 560 tickets
Step-by-step explanation:
3/4 = 420/x; now cross multiply:
3x = 4(420)
3x = 1,680; now divide both sides by 3, and you get x = 560