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Chapter 7: Problem 84

Solve. See the Concept Check in this section. Solve \(D=R T\) for \(T\)

Short Answer

Expert verified
\( T = \frac{D}{R} \).

Step by step solution

01

Identify the Formula

We are given the formula to solve: \( D = R T \). This is the equation that needs to be rearranged to solve for \( T \).
02

Isolate T

To solve for \( T \), we need to rearrange the equation so that \( T \) is by itself on one side of the equation. Since \( T \) is multiplied by \( R \), we can divide both sides of the equation by \( R \). This gives us: \( T = \frac{D}{R} \).
03

Conclusion

Now the formula is rearranged to solve for \( T \), so \( T = \frac{D}{R} \) is the solution. This means if you know the values of \( D \) and \( R \), you can substitute them into the formula to find \( T \).

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Key Concepts

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

Rearranging Formulas
Rearranging formulas is all about changing the form of an equation to isolate and solve for a specific variable. This skill is vital in math and science as it enables you to approach and solve problems more flexibly. For instance, given a formula like \( D = RT \), our goal is to rewrite it so we can easily find the value of \( T \) when \( D \) and \( R \) are known.
  • If you want to solve for a particular variable, identify that variable in the equation.
  • Think of the equation as a balance. Whatever you do to one side, you must do to the other to keep it balanced.
  • Apply basic arithmetic operations like addition, subtraction, multiplication, or division to rearrange the formula.
By rearranging formulas, you develop a deeper understanding of the relationships within the equations themselves.
Isolating Variables
Isolating variables involves manipulating an equation to get one variable alone on one side. To better illustrate, take the equation \( D = RT \), where we want to isolate \( T \). Here, \( T \) is currently multiplied by \( R \). To isolate it, divide both sides of the equation by \( R \), effectively separating \( T \) from \( R \).
  • Understand what operations are being performed on the variable you want to isolate.
  • Use inverse operations to reverse these actions until the variable stands alone.
  • The equation should retain its meaning, so make sure each step maintains equality.
This practice strengthens your algebraic thought process, making it easier to solve varied mathematical problems.
Algebraic Manipulation
Algebraic manipulation refers to using algebraic operations to simplify or rewrite equations and expressions. This concept is often used when rearranging formulas or isolating variables. When transforming \( D = RT \) into \( T = \frac{D}{R} \), we're using algebraic manipulation to divide both sides by \( R \), maintaining the equation's equality.
  • Ensure each manipulation respects the equality of the equation.
  • Break down complex expressions into simpler parts to manage them more easily.
  • Regularly check your work to avoid errors during manipulation.
Mastering algebraic manipulation is crucial for solving not just equations but also for tackling real-world problems using algebra.

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Most popular questions from this chapter

Perform the indicated operations. $$ \frac{-2 x}{x^{3}-8 x} \div \frac{3 x}{x^{3}-8 x} $$

Find the \(L C D\) for each list of rational expressions. $$ \frac{4}{x^{2}+4 x+3}, \frac{4 x-2}{x^{2}+10 x+21} $$

In your own words, describe how to add or subtract two rational expressions with the same denominator.

Perform each indicated operation. $$ \frac{13}{20} \div \frac{2}{9} $$

Find the \(L C D\) for each list of rational expressions. $$ \frac{19}{2 x}, \frac{5}{4 x^{3}} $$
See all solutions

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