suppose a windmill generates power based on the speed of the wind. Thua is represented by the polynomial function P(s)= S⁴ divide 1000, where s represented the speed of the wind in kilometers per hour. If the wind speed is 15 kilometers per hour, how many units of power, P(s) can the windmill generate?

To solve for the power generated by the windmill when the wind speed is 15 kilometers per hour, we use the polynomial function provided:

\[
P(s) = \frac{s^4}{1000}
\]

Where \( s \) is the wind speed in kilometers per hour. Substituting \( s = 15 \) into the equation:

\[
P(15) = \frac{15^4}{1000}
\]

First, calculate \( 15^4 \):

\[
15^4 = 15 \times 15 \times 15 \times 15 = 50625
\]

Now, divide by 1000:

\[
P(15) = \frac{50625}{1000} = 50.625
\]

Therefore, the windmill generates 50.625 units of power when the wind speed is 15 kilometers per hour.

Would you like further details or have any questions?

### Related Questions:
1. How does power generation change if the wind speed is doubled?
2. What is the power output when the wind speed is 20 km/h?
3. How would the formula change if we wanted to model power based on the square of wind speed instead of the fourth power?
4. What happens to the power output if the wind speed is halved?
5. Can you calculate the speed needed to generate 100 units of power?

**Tip:** Wind power generation typically increases with the cube of wind speed in real-world models, but higher powers like \(s^4\) can also be used to emphasize sensitivity in specific contexts.

Suppose a windmill generates power based on the speed of the wind. This is represented by the polynomial function P(s) = s⁴ / 1000, where s represents the speed of the wind in kilometers per hour. If the wind speed is 15 kilometers per hour, how many units of power, P(s), can the windmill generate?

Learn how to calculate the power generated by a windmill based on wind speed using the polynomial function P(s) = s⁴ / 1000. In this example, we find the power generated when the wind speed is 15 km/h. This problem involves polynomial functions and exponents, suitable for students in Grades 9-12.

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