To find $r$, the variable you want to solve for, depends on the type of equation or formula it is involved in. Here are some common contexts and ways to solve for $r$:

1. Solving for $r$ in a Linear Equation

If you have a simple linear equation like $ar + b = c$, you can solve for $r$ using the following steps: $ar + b = c$

• Subtract $b$ from both sides: $ar = c - b$
• Divide both sides by $a$: $r = \frac{c - b}{a}$

2. Solving for $r$ in a Circle's Equation

If you're given the formula for the circumference or area of a circle, you can solve for the radius $r$:

• Circumference: $C = 2\pi r$ $r = \frac{C}{2\pi}$

• Area: $A = \pi r^2$ $r = \sqrt{\frac{A}{\pi}}$

3. Solving for $r$ in Interest Formulas

In financial mathematics, when using formulas for simple or compound interest, you may need to solve for $r$:

• Simple Interest: $I = Prt$ (where $I$ is interest, $P$ is principal, $r$ is the rate, and $t$ is time) $r = \frac{I}{Pt}$

• Compound Interest: $A = P(1 + r/n)^{nt}$ (where $A$ is the amount, $P$ is the principal, $r$ is the interest rate, $n$ is the number of times interest is compounded per year, and $t$ is time in years)

4. Solving for $r$ in the Distance Formula

If you are solving for $r$ as a distance (e.g., in 3D space):

• $d = \sqrt{x^2 + y^2 + z^2}$, where $d$ is distance $r = \sqrt{x^2 + y^2 + z^2}$

5. Solving for $r$ in the Quadratic Formula

If $r$ is a root of a quadratic equation $ax^2 + bx + c = 0$, use the quadratic formula: $r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

If you have a specific formula or context for $r$, I can help you further with that.

Would you like more details or clarifications?

Here are 5 related questions for you to explore:

1. How do you solve for $r$ in the surface area of a sphere formula?
2. What is the role of $r$ in the Pythagorean theorem?
3. Can you derive the formula for $r$ in terms of volume for a cylinder?
4. How is the variable $r$ used in polar coordinates?
5. What are the steps to solve for $r$ in a logarithmic equation?

Tip: Always isolate the variable you're solving for by reversing operations in the equation systematically (addition, subtraction, multiplication, division, powers, etc.).