In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R

Verified step by step guidance

1. Start with the formula: $D=RT$.
2. To solve for $R$, you need to isolate $R$ on one side of the equation.
3. Divide both sides of the equation by $T$ to get $R$ by itself: $\frac{D}{T}=R$.
4. Rearrange the equation to express $R$ explicitly: $R=\frac{D}{T}$.
5. This formula is the classic distance-rate-time relationship, where $D$ is distance, $R$ is rate (or speed), and $T$ is time.

Key Concepts

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation. Understanding how to manipulate equations is essential for solving for a variable, as it allows one to express the variable in terms of others.

Formulas and Their Applications

Formulas are mathematical expressions that describe relationships between variables. In this case, the formula D = RT relates distance (D), rate (R), and time (T). Recognizing the context of a formula helps in understanding its application, such as calculating speed or travel time, which is crucial for interpreting the problem correctly.

Isolating Variables

Isolating a variable means rearranging an equation so that the variable of interest stands alone on one side. In the equation D = RT, isolating R involves dividing both sides by T, resulting in R = D/T. This concept is fundamental in algebra as it allows for solving equations and understanding how changes in one variable affect others.