The area of the circle with radius r is
A = πr²
The rate of change of area with respect to time is
![\frac{dA}{dt} = \frac{dA}{dr} . \frac{dr}{dt} =2 \pi r. \frac{dr}{dt}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20%5Cfrac%7BdA%7D%7Bdr%7D%20.%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D2%20%5Cpi%20r.%20%5Cfrac%7Bdr%7D%7Bdt%7D%20)
The rate of change of the radius is given as
![\frac{dr}{dt} =-2 \, \frac{ft}{s}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdr%7D%7Bdt%7D%20%3D-2%20%5C%2C%20%20%5Cfrac%7Bft%7D%7Bs%7D%20)
Therefore
![\frac{dA}{dt} =-4 \pi r \, \frac{ft^{2}}{s}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D-4%20%5Cpi%20r%20%5C%2C%20%20%5Cfrac%7Bft%5E%7B2%7D%7D%7Bs%7D%20)
When r = 10 ft, obtain
![\frac{dA}{dt}|_{r=10 \, ft} = -40 \pi \, \frac{ft^{2}}{s}](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%7C_%7Br%3D10%20%5C%2C%20ft%7D%20%3D%20-40%20%5Cpi%20%20%5C%2C%20%20%5Cfrac%7Bft%5E%7B2%7D%7D%7Bs%7D%20%20)
Answer: - 40π ft²/s (or - 127.5 ft²/s)
D is the correct answer!!
Answer:
magnitude of the frictional torque is 0.11 Nm
Explanation:
Moment of inertia I = 0.33 kg⋅m2
Initial angular velocity w° = 0.69 rev/s = 2 x 3.142 x 0.69 = 4.34 rad/s
Final angular velocity w = 0 (since it stops)
Time t = 13 secs
Using w = w° + §t
Where § is angular acceleration
O = 4.34 + 13§
§ = -4.34/13 = -0.33 rad/s2
The negative sign implies it's a negative acceleration.
Frictional torque that brought it to rest must be equal to the original torque.
Torqu = I x §
T = 0.33 x 0.33 = 0.11 Nm
Answer:
1.85c
Explanation:
a photon moves at c, the electron is moving at 0.85c, and since they are moving in opposing directions, the relative speed would be 1.85c
Answer:
1.a storm with a violent wind, in particular a tropical cyclone in the Caribbean.
2.The Eye of a Hurricane. The eye is the region at the center of the hurricane, which is roughly circular in shape and usually has calm weather.
3.Hurricanes form over the ocean, often beginning as a tropical wave—a low pressure area that moves through the moisture-rich tropics, possibly enhancing shower and thunderstorm activity.
4.When the surface water is warm, the storm sucks up heat energy from the water, just like a straw sucks up a liquid. This creates moisture in the air. If wind conditions are right, the storm becomes a hurricane. This heat energy is the fuel for the storm.
5.a rising of the sea as a result of atmospheric pressure changes and wind associated with a storm.
6.A hurricane dies down when it loses its energy source, which is usually warm water at the surface of the ocean.
7.Hurricane Katrina was so destructive because of a bunch of events that happened in just the right way. First, understand that Katrina was at one point a Category 5 storm and was predicted to hit New Orleans as a Category 4. It weakened to a Cat 3 and veered ever so slightly to the east, making the damage far less than it could have been.
Explanation:
hope this helps