To solve this problem, we can set up a proportion using the given information.
First, let's define the relationship between power and wind speed using the direct variation equation:
P = kv^3
where P is the power generated in kilowatts, v is the wind speed in meters per second, and k is the constant of variation.
Given that the turbine generates 500 kW in a 10 m/s wind, we can use this information to find the value of k:
500 = k * 10^3
500 = k * 1000
k = 500 / 1000
k = 0.5
Now we can use the value of k to find the power generated in a 12 m/s wind:
P = 0.5 * 12^3
P = 0.5 * 1728
P = 864
Therefore, the turbine generates 864 kW of power in a 12 m/s wind.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
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). If a turbine generates 500kW in a 10m/s wind, how much power does it generate in a 12m/s wind?
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