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
For 61 you can change it to √25/√49. √25=5 and √49=7 so it would simplify to 5/7.
Answer:
I'm getting stuck by

Sorry I can't help you out, if you find the answer through FP lmk
Answer:
The line passes (2, 5) and (4, 7) has slope:
S = (7 - 5)/(4 - 2) = 2/2 = 1
The line passes (1, 7) and (-4, 2) has slope:
S = (2 - 7)/(-4 - 4) = 5/-5 = -1
The multiplication of two slope is 1 x (-1) = -1
=> Two lines are perpendicular
Hope this helps!
:)