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Chapter 9: Problem 354

In the following exercises, solve. Solve the formula \(C=\pi d\) for \(\pi\)

Short Answer

Expert verified
\(\pi = \frac{C}{d}\)

Step by step solution

01

Identify the given formula

The given formula is: \(C = \pi d\)
02

Rearrange the formula

We need to solve for \(\pi\). To do this, isolate \pi on one side of the equation. Since \pi is multiplied by \(d\), we can divide both sides of the equation by \(d\) to isolate \pi. \(\pi = \frac{C}{d}\)
03

Final formula

The formula solved for \pi is: \(\pi = \frac{C}{d}\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving Equations
Solving equations is a fundamental skill in mathematics. It involves finding the value of one or more variables that make the equation true. In this exercise, we start with the equation given: \(C = \pi d\).
To solve for a specific variable, we perform operations that will isolate this variable on one side of the equation. By carefully following each step, we transform the equation into a simpler form, ultimately revealing the value of the unknown variable we're looking for.
Formula Manipulation
Formula manipulation is all about rearranging an equation to solve for a specific variable. This is done through various arithmetic operations such as addition, subtraction, multiplication, and division.
In our exercise, we solved for \(\pi\) in the formula \(C = \pi d\). The goal was to make \(\pi\) the subject of the formula.
Here are the steps again in more detail:
  • Identify the original formula and note which variable you need to solve for.
  • If the required variable is being multiplied or divided by another term, use the inverse operation to isolate it.
  • Simplify the equation and ensure the variable stands alone on one side.
This process is essential in various areas of math and science and helps us understand and work with different formulas more effectively.
Division in Equations
Division in equations is used to isolate a variable when it is multiplied by another term. It is the inverse of multiplication, which means it undoes the multiplication effect.
In our example: \(C = \pi d\), \(\pi\) is multiplied by \(d\). To solve for \(\pi\), we need to get rid of \(d\) on the right side. We do this by dividing both sides of the equation by \(d\). Mathematically, this looks like: \[ \pi = \frac{C}{d} \].

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