A power company installs 100 wind turbines in a large field. When all the windmills are operating the electrical capacity is 55,000 kilowatts (kW) of electricity. Find the equation of proportionality that relates the number of operating windmills to the total electrical capacity (in kW). What is the electrical capacity (in kW) when 56 windmills are operating?

To find the equation of proportionality between the number of operating wind turbines and the total electrical capacity, we use the fact that the relationship is directly proportional.

Given:
- 100 wind turbines produce 55,000 kW of electricity.

1. Let \( N \) represent the number of operating wind turbines, and \( C \) represent the total electrical capacity in kilowatts (kW). The equation of proportionality is:

\[
C = k \cdot N
\]

where \( k \) is the constant of proportionality.

2. To find \( k \), use the known values when all 100 turbines are operating:

\[
55,000 = k \cdot 100
\]

Solving for \( k \):

\[
k = \frac{55,000}{100} = 550
\]

So the equation that relates the number of operating turbines \( N \) to the total electrical capacity \( C \) is:

\[
C = 550 \cdot N
\]

3. To find the electrical capacity when 56 windmills are operating, substitute \( N = 56 \) into the equation:

\[
C = 550 \cdot 56 = 30,800 \, \text{kW}
\]

Thus, the electrical capacity when 56 windmills are operating is 30,800 kW.

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Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:
1. What would be the electrical capacity if only 75 wind turbines are operating?
2. If the electrical capacity is 44,000 kW, how many wind turbines are operating?
3. How would the equation change if the wind turbines became more efficient, producing 60,000 kW with 100 turbines?
4. What is the significance of the constant of proportionality in this scenario?
5. How does the equation change if some turbines are operating at reduced capacity?

**Tip:** In direct proportionality, increasing one quantity by a certain factor increases the other quantity by the same factor.

A power company installs 100 wind turbines in a large field. When all the windmills are operating, the electrical capacity is 55,000 kilowatts (kW) of electricity. Find the equation of proportionality that relates the number of operating windmills to the total electrical capacity (in kW). What is the electrical capacity (in kW) when 56 windmills are operating?

Learn how to find the equation of proportionality between the number of operating wind turbines and their total electrical capacity. This problem explores direct variation, with an example where 100 wind turbines produce 55,000 kW. Suitable for students in Grades 6-8.

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