Wind farms are a source of renewable energy found around the world. The power p (in kilowatts) generated by a wind turbine varies directly as the cube of the wind speed v (in meters per second).

Question

love_333 · Answer

Question: If a turbine generates 500kW in a 10m/s wind, how much power does it generate in a 12m/s wind?

sunnnystrong · Answer

$$p=.5v^3$$

p=power (kW)
v= wind speed (m/s)

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Let v=12 & solve for p

love_333 · Answer

p = 864?

sunnnystrong · Answer

Yep. When they say it varies... that means that there is a constant factor in front of v (: because they gave you a point (10, 500) we were able to find the constant
...
$$p = kv^3$$

where k=constant

$$500 = k10^3$$
... solving for k you get .5 (:

love_333 · Answer

Great! Thanks!!