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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 in v (in meters per second). If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12m/s wind?

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MissPhiladelphia
If a turbine generates 500kW in a 10m/s wind, how much power does it generate in 12m/s wind?
first solve the proportionality constant k
P = kv^3
500 = k (10^3)k = 500 / 10^3k = 0.5
so when v = 12 m/s
P = 0.5(12^3)p = 864 kW is the power generated by a 12 m/s wind

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