# Ch 21: NY Regents - Well-Known Equations: Tutoring Solution

### About This Chapter

## How it works:

- Begin your preparation for the NY Regents integrated algebra exam.
- Identify the well-known equations concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.

## Who's it for?

This chapter of our NY Regents Exam - Integrated Algebra tutoring solution will benefit any student who is trying to learn well-known equations and earn passing scores on the exam. This resource can help students including those who:

- Struggle with understanding the theory of relativity, the Pythagorean theorem, the quadratic formula or any other well-known equations topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves struggling with preparations for the NY Regents integrated algebra exam
- Cope with ADD or ADHD
- Want to get ahead in preparing for the NY Regents integrated algebra exam
- Don't have access to NY Regents integrated algebra prep materials

## Why it works:

**Engaging Tutors:**We make learning well-known equations simple and fun.**Cost Efficient:**For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.**Consistent High Quality:**Unlike a live algebra tutor, these video lessons are thoroughly reviewed.**Convenient:**Imagine a tutor as portable as your laptop, tablet or smartphone. Learn well-known equations on the go!**Learn at Your Pace:**You can pause and rewatch lessons as often as you'd like, until you master the material.

## Learning Objectives

- Explain the theory of relativity.
- Understand the Pythagorean theorem.
- Define the value of e.
- Describe the relationship between diameter and circumference and pi.
- Learn how to use Isaac Newton's formula for the force of gravity.
- Discuss Euler's identity.
- Examine Fermat's last theorem.
- Understand how to calculate monthly loan payments.
- Define the absolute-value inequality.
- Learn how to use the quadratic formula.

### 1. Theory of Relativity: Definition & Example

Einstein's special theory of relativity explains how energy and mass are related and how objects seem to behave as they approach the speed of light. Learn to define Einstein's theory of relativity, and use examples to explain the speed of light and Einstein's mass-energy equivalence equation and how it is used.

### 2. Pythagorean Theorem: Definition & Example

Pythagorean theorem, named after the mathematician Pythagoras, shows the relation between the sum of the squares of each of the three sides of a right triangle. Learn about the definition of the Pythagorean theorem, discover how a right triangle and sides of a triangle are used in the equation of the theorem, and explore the application of the Pythagorean theorem through relevant examples.

### 3. The Value of e: Definition & Example

The mathematical constant e was coined by the 18th-century Swiss mathematician, Leonhard Euler. Learn the definition of the value of e, what makes e an irrational number, and study an example of e.

### 4. Diameter and Circumference Related with Pi

In mathematics, pi is a constant that is equal to approximately 3.14, though the number actually is infinite. Learn about the definition of pi and explore its relationship to the diameter and circumference of a circle, the formula for calculating circumference, and also practice finding the circumference or diameter of a circle.

### 5. Isaac Newton's Formula for the Force of Gravity: Definition & Example

As the man who created the law of universal gravitation, Isaac Newton is one of the most renowned scientists to ever live. In this lesson, explore the definition of the force of gravity, the relationship of two objects, Newton's formula for the force of gravity, and an example of finding the force.

### 6. Euler's Identity: Definition & Example

As a famous mathematical equation, Euler's identity is often referred to as a mathematical jewel. Learn the definition of Euler's identity, explore why it is important, and discover how to apply the formula of Euler's identity formula with a provided example.

### 7. Fermat's Last Theorem: Definition & Example

Fermat's Last Theorem asserts that the sum of two positive numbers taken to a power greater than 2 will be equal to a third positive number taken to the same power greater than 2. Learn the definition of Fermat's Last Theorem, which was discovered in the margins of a book and remained unsolved for more than 300 years, and see how it relates to the Pythagorean Theorem.

### 8. Calculating Monthly Loan Payments

For most loans, such as a mortgage loan to purchase a house, the lender requires the borrower to make monthly loan payments, which include payments on the interest charged for the borrowed money. Explore the formula to calculate the amount of monthly interest and the number of payments required to repay a loan. Use the formula to find the monthly payment amount.

### 9. The Absolute-Value Inequality: Definition & Example

Absolute value inequalities are types of problems that may seem complicated from the outset but are relatively simple to solve with the right understanding. Take a closer look at the definitions of the absolute value and the absolute value inequality, followed by an example of how to set up and solve these types of problems.

### 10. The Quadratic Formula: Definition & Example

The quadratic formula is arguably one of the most well-known and important formulas in math. In this lesson, look at the definition of the quadratic formula, its standard form, how to plug in your values, and an example of the formula in action.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Tutoring Solution course

- NY Regents - Number Theory & Basic Arithmetic: Tutoring Solution
- NY Regents - Problems with Decimals and Fractions: Tutoring Solution
- NY Regents - Problems with Percents: Tutoring Solution
- NY Regents - Problems with Exponents: Tutoring Solution
- NY Regents - Problems with Exponential Expressions: Tutoring Solution
- NY Regents - Problems with Radical Expressions & Equations: Tutoring Solution
- NY Regents - Problems with Algebraic Expressions and Equations: Tutoring Solution
- NY Regents - Distributing Terms in Algebra: Tutoring Solution
- NY Regents - Algebraic Linear Equations & Inequalities: Tutoring Solution
- NY Regents - Matrices and Absolute Value: Tutoring Solution
- NY Regents - Overview of Functions: Tutoring Solution
- NY Regents - Factoring with Variables: Tutoring Solution
- NY Regents - Quadratics & Polynomials: Tutoring Solution
- NY Regents - Rational Expressions: Tutoring Solution
- NY Regents - Graphing Functions: Tutoring Solution
- NY Regents - Calculations with Ratios, Percent & Proportions: Tutoring Solution
- NY Regents - Sets: Tutoring Solution
- NY Regents - Probability and Statistics: Tutoring Solution
- NY Regents - Probability Mechanics: Tutoring Solution
- NY Regents - Working with Data: Tutoring Solution
- NY Regents - Intro to Trigonometry: Tutoring Solution
- NY Regents - Measurement for Algebra Students: Tutoring Solution
- NY Regents - Geometry for Algebra Students: Tutoring Solution