The power P (in watts) generated by a windmill that has efficiency E is given by the formula P = 0.31ED^2V^3, where D is the diameter (in feet) of the windmill blades and V is the wind velocity (in ft/sec). Approximate the wind velocity necessary to generate 30,000 watts if E = 41% and D = 17

To approximate the wind velocity necessary to generate 30,000 watts, we can rearrange the given formula and solve for V.

The formula for power is P = 0.31ED^2V^3.

Given values:
P = 30,000 watts
E = 41% (0.41 as a decimal)
D = 17 feet

Substituting the given values into the formula, we have:

30,000 = 0.31 * 0.41 * 17^2 * V^3

First, we can simplify the equation:

(0.31 * 0.41 * 17^2) * V^3 = 30,000

Next, we can solve for V by isolating it:

V^3 = 30,000 / (0.31 * 0.41 * 17^2)

Now, we can calculate the right side of the equation:

V^3 ≈ 386.6463415 (rounded to 9 decimal places)

To find the cube root of this value, you can use a calculator or math software. The cube root of 386.6463415 ≈ 7.233313139 (rounded to 9 decimal places).

Therefore, the wind velocity necessary to generate approximately 30,000 watts is roughly 7.233 ft/sec.