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 given formula: $D\; =\; R\; \backslash cdot\; T$. This formula is commonly known as the distance formula, where D represents distance, R represents rate (or speed), and T represents time.
2. To solve for R, isolate R on one side of the equation. Since R is multiplied by T, divide both sides of the equation by T to undo the multiplication.
3. The equation becomes: $R\; =\; \backslash frac\{D\}\{T\}$. This expresses the rate (R) as the distance (D) divided by the time (T).
4. Check the formula to ensure it makes sense conceptually. The rate is indeed calculated by dividing the distance traveled by the time taken.
5. Recognize that this formula is used in problems involving motion, where you need to find the speed or rate of an object given the distance it travels and the time it takes.

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.