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 700kW in a 5m.s wind, how much power does it generate in a 14m/s wind?

Not the real answer but what I think bobpursley is trying to convey

P=v^3x
500=20^3x
500=8000x
1/16=x
P=10^3(1/16)
P=1000(1/16)
P=62.5

power=k*speed^3

k=power/speed^3=700kw/125

now figure power
power=k*15^3

i don't understand

To find out how much power the turbine generates in a 14 m/s wind, we can use the concept of direct variation and the given information about the relationship between power and wind speed.

Given:
Power generated (P1) = 700 kW
Wind speed (v1) = 5 m/s

We can set up a proportion using the direct variation relationship:
(P1 / v1^3) = (P2 / v2^3)

Now we can substitute the given values into the equation:
(700 / 5^3) = (P2 / 14^3)

Simplifying the equation:
(700 / 125) = (P2 / 2744)

To find P2, we can cross multiply:
700 * 2744 = P2 * 125

Solving for P2:
P2 ≈ 3875.84 kW

Therefore, the turbine will generate approximately 3875.84 kW of power in a 14 m/s wind.