To express: The given expression as equation.
The equation of given expression is .
The given expression is,
Power from a windmill is directly proportional to cube of the wind speed .
If the quantities and are related by the equation then for , is directly proportional to and is called constant of proportionality.
So, is directly proportional to cube of .
Write the given expression as,
is the power obtained from windmill.
is the wind speed.
is constant of proportionality.
Thus, the equation of given expression is .
To find: The constant of proportionality for the windmill.
The constant of proportionality of given windmill is .
Power produced by windmill is .
Speed of the wind is .
In equation (1) substitute for and for and solve for .
Thus, the value of proportionality constant is .
To find: Power produced by windmill.
The power produced is .
The wind speed is increased to .
Wind speed is increased to , Now the value of is 30.
Substitute for and for from equation (2) in equation (1).
Thus, the value of power is .
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