(b) Make $r$ The Subject Of The Formula $T=\frac{r}{4}-p$.
Solving for r in the Formula T = (r/4) - p
In mathematics, solving for a variable in a formula is an essential skill that is used in various mathematical operations. In this article, we will focus on solving for the variable r in the formula T = (r/4) - p. This formula is commonly used in physics and engineering to calculate the time it takes for an object to travel a certain distance.
Understanding the Formula
The formula T = (r/4) - p is a linear equation that relates the time T, the radius r, and the distance p. To solve for r, we need to isolate the variable r on one side of the equation. This can be done by performing algebraic operations such as addition, subtraction, multiplication, and division.
Step 1: Add p to Both Sides
To solve for r, we need to get rid of the negative sign in front of the p term. We can do this by adding p to both sides of the equation. This will give us:
T + p = (r/4) - p + p
Simplifying the equation, we get:
T + p = (r/4)
Step 2: Multiply Both Sides by 4
To isolate the variable r, we need to get rid of the fraction (1/4) in front of the r term. We can do this by multiplying both sides of the equation by 4. This will give us:
4(T + p) = 4(r/4)
Simplifying the equation, we get:
4T + 4p = r
Step 3: Divide Both Sides by 1
Finally, to solve for r, we need to get rid of the constant term 4p on the left-hand side of the equation. We can do this by dividing both sides of the equation by 1. This will give us:
r = 4T + 4p
In this article, we have solved for the variable r in the formula T = (r/4) - p. We have used algebraic operations such as addition, subtraction, multiplication, and division to isolate the variable r on one side of the equation. The final solution is r = 4T + 4p.
Let's use an example to illustrate the solution. Suppose we have the following values:
T = 5 p = 2
Substituting these values into the formula, we get:
5 = (r/4) - 2
Adding 2 to both sides, we get:
7 = (r/4)
Multiplying both sides by 4, we get:
28 = r
Therefore, the value of r is 28.
- When solving for a variable in a formula, it's essential to isolate the variable on one side of the equation.
- Use algebraic operations such as addition, subtraction, multiplication, and division to simplify the equation.
- Make sure to check your solution by plugging it back into the original equation.
- Not isolating the variable on one side of the equation.
- Not using algebraic operations to simplify the equation.
- Not checking the solution by plugging it back into the original equation.
The formula T = (r/4) - p has various real-world applications in physics and engineering. For example, it can be used to calculate the time it takes for an object to travel a certain distance, or to determine the radius of a circle given the time and distance.
In conclusion, solving for r in the formula T = (r/4) - p is a straightforward process that involves algebraic operations such as addition, subtraction, multiplication, and division. By following the steps outlined in this article, you can easily solve for r and apply the formula to real-world problems.
Q&A: Solving for r in the Formula T = (r/4) - p
In our previous article, we solved for the variable r in the formula T = (r/4) - p. In this article, we will answer some frequently asked questions about solving for r in this formula.
Q: What is the formula T = (r/4) - p used for?
A: The formula T = (r/4) - p is used to calculate the time it takes for an object to travel a certain distance. It is commonly used in physics and engineering to determine the time and distance of an object's motion.
Q: How do I solve for r in the formula T = (r/4) - p?
A: To solve for r, you need to isolate the variable r on one side of the equation. This can be done by performing algebraic operations such as addition, subtraction, multiplication, and division. The steps to solve for r are:
- Add p to both sides of the equation.
- Multiply both sides by 4.
- Divide both sides by 1.
Q: What if I have a negative value for p?
A: If you have a negative value for p, you can simply add it to both sides of the equation as you normally would. The formula will still work, and you will get the correct value for r.
Q: Can I use this formula to solve for p?
A: No, this formula is specifically designed to solve for r. If you want to solve for p, you will need to use a different formula.
Q: What if I have a fraction for T?
A: If you have a fraction for T, you can simply multiply both sides of the equation by the denominator of the fraction to eliminate it. Then, you can proceed with solving for r as usual.
Q: Can I use this formula to solve for r in a different context?
A: Yes, this formula can be used to solve for r in a variety of contexts, such as calculating the time it takes for a car to travel a certain distance or determining the radius of a circle given the time and distance.
Q: What are some common mistakes to avoid when solving for r?
A: Some common mistakes to avoid when solving for r include:
- Not isolating the variable r on one side of the equation.
- Not using algebraic operations to simplify the equation.
- Not checking the solution by plugging it back into the original equation.
Q: How do I check my solution to make sure it is correct?
A: To check your solution, you can plug it back into the original equation and make sure that it is true. If the equation is true, then your solution is correct.
In conclusion, solving for r in the formula T = (r/4) - p is a straightforward process that involves algebraic operations such as addition, subtraction, multiplication, and division. By following the steps outlined in this article and avoiding common mistakes, you can easily solve for r and apply the formula to real-world problems.
- For more information on solving for r in the formula T = (r/4) - p, check out our previous article on the topic.
- For more information on algebraic operations and how to use them to solve equations, check out our article on the topic.
- For more information on real-world applications of the formula T = (r/4) - p, check out our article on the topic.