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
The white Christmas tree is 7.55m
Green Christmas tree is twice as tall as white Christmas tree: 7.55 * 2 = 15.1m
High golden Christmas tree: 15.1m - 0.454m = 14.646m
The total height of 3 Christmas trees is: 7.55m + 15.1m + 14.646m = 37.296m
Choose: A 37.296m
Answer:
Let the two supplementary angles be
we know sum of two supplementary angles is 180
2x + 3x = 180
5x = 180
x = 180/5
x = 36
2*36 = 72
3*36 = 108
Therefore the two supplementary angles are 72 and 108
<span>By similarity of triangles we have the following relationship:</span>
<span> (x) / (6) = (18) / (9)</span>
<span> Simplifying we have:</span>
<span> (x) / (6) = 2</span>
<span> Clearing the value of x we have:</span>
<span><span> x = 6 * 2</span></span>
<span><span> X = 12</span></span>
<span><span> Answer:</span></span>
<span><span> The value of x for this case is equal to:</span></span>
<span><span> <span>X = 12</span></span>
</span>
D, he is moving at a constant spees
