Question

solve the given applied problems involving variation. The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces $35,800 \mathrm{kW}$ of power when the flow rate is $2250 \mathrm{ft}^{3} / \mathrm{s}$, how much power will be produced if the flow rate is $2150 \mathrm{ft}^{3} / \mathrm{s} ?$

Name: Problem 31, Chapter 18: Basic Technical Mathematics with Calculus
Uploaded: 2021-06-15T05:36:59-08:00
Duration: 2 min 44 s
Channel: Dwijendra Rao
Description: solve the given applied problems involving variation. The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces 35,800 kW of power when the flow rate is 2250 ft^3 / s, how much power will be produced if the flow rate is 2150 ft^3 / s ?

   solve the given applied problems involving variation.
The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces $35,800 \mathrm{kW}$ of power when the flow rate is $2250 \mathrm{ft}^{3} / \mathrm{s}$, how much power will be produced if the flow rate is $2150 \mathrm{ft}^{3} / \mathrm{s} ?$

Basic Technical Mathematics with Calculus

Allyn J. Washington,… 11th Edition

Chapter 18, Problem 31

Instant Answer

Solved by Expert Dwijendra Rao

06/15/2021

Step 1

Step 1: Given that the amount of hydroelectric power produced by a dam is proportional to the flow rate of the water, we can write this relationship as $P = kQ$, where $P$ is the power produced, $Q$ is the flow rate, and $k$ is the constant of proportionality. Show more…

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solve the given applied problems involving variation. The amount of hydroelectric power produced by a dam is proportional to the flow rate of the water. If a particular dam produces $35,800 \mathrm{kW}$ of power when the flow rate is $2250 \mathrm{ft}^{3} / \mathrm{s}$, how much power will be produced if the flow rate is $2150 \mathrm{ft}^{3} / \mathrm{s} ?$

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Key Concepts

Solving Applied Variation Problems

In applied problems involving variation, the approach is to first determine the proportionality constant from provided values and then use that constant to calculate unknown amounts. This technique is useful across many fields where one quantity directly affects another.

Direct Variation

Direct variation describes a relationship where one variable is a constant multiple of another. It is typically expressed as y = kx, meaning as one variable increases, the other increases at a fixed rate determined by the constant k.

Proportionality Constant

The proportionality constant is the constant factor (k) that links two variables in a direct variation. Once this constant is found using known values, it can be used to predict other corresponding values in the relationship.

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