https://file.aiquickdraw.com/mathbot/file/1727659696042q6ui74bq.jpg

The question asks for the amount of hydroelectric power produced, given that the power produced by a dam is proportional to the flow rate of water. Specifically, it provides:

- **Known values**: 35,700 kW of power is produced when the flow rate is 2260 cubic feet per second (ft³/s).
- **Find**: The power produced when the flow rate is 2180 ft³/s.

Since power is proportional to the flow rate, we can set up a ratio between the two scenarios. This can be solved using direct proportion.

The ratio is:

\[
\frac{35,700 \text{ kW}}{2260 \text{ ft}^3/\text{s}} = \frac{x \text{ kW}}{2180 \text{ ft}^3/\text{s}}
\]

Now, solve for \( x \):

\[
x = \frac{35,700 \times 2180}{2260}
\]

I'll calculate that for you.The amount of power produced when the flow rate is 2180 ft³/s is approximately **34,436 kW**.

Do you have any questions, or would you like a detailed breakdown of the solution? Here are five related questions to consider:

1. How does proportionality help in solving real-world problems?
2. What would happen if the flow rate increased by 10%?
3. How would you calculate the power for a different flow rate, such as 2000 ft³/s?
4. What does "direct proportionality" mean in mathematical terms?
5. How would errors in measuring the flow rate affect the power calculation?

**Tip:** In problems involving proportionality, always make sure to maintain the ratio correctly between known and unknown values!

The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces 35,700 kW of power when the flow rate is 2260 ft³/s, how much power will be produced if the flow rate is 2180 ft³/s?

Learn how to calculate hydroelectric power produced by a dam using flow rate proportionality. This example shows how 35,700 kW of power is produced when the flow rate is 2260 ft³/s, and how to find the power produced for a flow rate of 2180 ft³/s. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation