solve for r

Guri Bee

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19-10-2024

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Solving for 'r': Unraveling the Mystery of the Variable

In the world of mathematics, solving for a specific variable is a fundamental skill. One common variable you might encounter is 'r'. This variable often represents a rate, radius, or even a correlation coefficient, depending on the context of the equation. This article will delve into the process of solving for 'r' in different scenarios, providing you with the tools to tackle this challenge.

1. Solving for 'r' in a Simple Equation

Let's start with a basic example:

Equation: 2r + 5 = 11

Goal: Solve for 'r'

Steps:

1. Isolate the 'r' term: Subtract 5 from both sides of the equation. This gives us: 2r = 6

2. Solve for 'r': Divide both sides by 2. This gives us: r = 3

2. Solving for 'r' in a More Complex Equation

Here's an example involving a bit more algebra:

Equation: 3(r - 2) = 9

Goal: Solve for 'r'

Steps:

1. Distribute: Multiply 3 by both terms inside the parentheses. This gives us: 3r - 6 = 9

2. Isolate the 'r' term: Add 6 to both sides of the equation: 3r = 15

3. Solve for 'r': Divide both sides by 3: r = 5

3. Solving for 'r' in a Formula

Let's take a real-world example:

Formula: A = πr² (Area of a circle)

Goal: Solve for 'r' (radius)

Steps:

1. Isolate the 'r' term: Divide both sides of the equation by π: A/π = r²

2. Solve for 'r': Take the square root of both sides of the equation: √(A/π) = r

4. Solving for 'r' in a System of Equations

Here, we encounter a scenario where 'r' is part of a system of equations. Let's consider:

Equation 1: 2r + 3s = 10 Equation 2: r - s = 2

Goal: Solve for 'r'

Steps:

1. Solve for 's' in Equation 2: s = r - 2

2. Substitute: Substitute the value of 's' from Equation 2 into Equation 1: 2r + 3(r - 2) = 10

3. Simplify and solve for 'r': 2r + 3r - 6 = 10 5r = 16 r = 16/5

Finding Resources and Further Exploration:

The world of solving for 'r' is vast. To explore further, consider the following resources:

• Online Calculators: Numerous websites offer equation solvers that can handle complex equations.
• Khan Academy: Provides excellent video tutorials on solving for variables.
• Math Stack Exchange: A platform where you can ask and answer math-related questions.

Key Takeaway: Solving for 'r' is a key skill in mathematics, applicable to various fields. By understanding the basic steps involved and using the right tools, you can confidently tackle this challenge.