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22 March, 19:51

The power P produced by a wind turbine is directly proportional to the cube of the wind speed S. A wind speed of 37 miles per hour produces a power output of 750 kilowatts. Find the output for a wind speed of 40 miles per hour.

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  1. 22 March, 22:47
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    Answer:the output for a wind speed of 40 miles per hour is 810.8 kilowatts.

    Step-by-step explanation:

    The power P produced by a wind turbine is directly proportional to the cube of the wind speed S. This means that

    P is directly proportional to S

    Introducing a constant of proportionality, k, it becomes

    P = kS

    A wind speed of 37 miles per hour produces a power output of 750 kilowatts. This means that

    750 = k * 37

    k = 750/37 = 20.27

    The expression becomes

    P = 20.27S

    Therefore, the output for a wind speed of 40 miles per hour would be

    P = 20.27 * 40

    P = 810.8
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