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 700 kW in a 12 m/s wind, how much power does it generate in a 6 m/s wind? (The formula for P as a power function of v is P = a ⋅ v3.

A. 88 kW

B. 175 kW

C. 125 kW

D. 1050 kW

New power = 88 Kw (Approx.)

Step-by-step explanation:

Given:

P = a(v³)

Old power p = 700 Kw

Old wind speed v = 12 m/s

Find:

New power when v = 6m/s

Computation:

P = a(v³)

700 = a(12³)

a = 0.4050 m²

New power = a(v³)

New power = (0.4050)(6³)

New power = 87.48

New power = 88 Kw (Approx.)

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step-by-step explanation:

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.