Question 980442


The condition of this problem means &nbsp;<U>exactly the following</U>:


The power produced by a windmill &nbsp;<B>is proportional to the product of the square of its diameter and the cube of the wind speed</B>. 


In other words, 


{{{P}}} = {{{k}}}.{{{D^2}}}.{{{w^3}}}, 


where &nbsp;{{{P}}}&nbsp; is the power produced by a windmill, &nbsp;{{{D}}}&nbsp; is a windmill diameter, &nbsp;{{{w}}}&nbsp; is the wind speed, &nbsp;and &nbsp;{{{k}}} is the proportionality coefficient which is the constant value for the selected unit system. 


Therefore, &nbsp;the proportion is valid

{{{P[2]/P[1]}}} = {{{(D[2]/D[1])^2}}}.{{{(w[2]/w[1])^3}}} = {{{(4/2.5)^2}}}.{{{(5/4)^3}}} = {{{1.6^2}}}.{{{1.25^3}}} = 2.56*1.953 = 5. 


where the index &nbsp;"1"&nbsp; relates to the &nbsp;"smaller windmill", &nbsp;and the index &nbsp;"2"&nbsp; relates to the &nbsp;"larger windmill".


Finally, &nbsp;its gives {{{P[2]}}} = {{{5}}}.{{{P[1]}}} = 5*560 watts = 2800 watts.