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NY Regents Exam - Algebra II: Test Prep & Practice16 chapters | 114 lessons | 7 flashcard sets

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you'll learn how you can use your math skills to solve real world problems. Learn how you can mathematically model your problem so you can use appropriate equations to find the solution.

Did you know that you can use math to help you model a real world problem making it easier to solve? That's right. Once you've created your mathematical model, you'll be able to use the associated mathematical equations for that model to help you solve your problem. This process of creating a mathematical model is referred to as **descriptive modeling**.

Let's take a look at how this process can make your life a whole lot easier.

Imagine that you are a forensic scientist who has just been called out to the scene of an accident. When you arrive at the scene of the accident, you see the two cars. A blue car has hit a red car in the side. The red car's side has an indent that's 1.2 inches deep.

Your job now is to determine just how fast the other car was going before it hit the other car. This information will help the car insurance companies figure out just who is responsible and how much to pay out.

After you've gathered all your information, you now have the hard task of finding your answer.

To help you, you create a descriptive model of the situation. This is what you do.

You first find a mathematical model for your problem. You ask yourself, just what kind of math is involved here. You decide on a physics model that shows the force of impact when objects collide with each other.

Next, you label your variables according to the model. In your case, you have the mass of the two cars, the force of impact, and the speed of travel for each car.

Then you use your variables and other information to solve the problem. Once you've labeled your variables and other information, you can then follow the model to solve the problem. In your case, you'll follow the physics model for determining the force of impact of a traveling object. You use the appropriate equation, plug everything in, and solve.

For your problem, you'll use this equation to determine just how fast the car was going when it collided.

The *F* stands for the force of impact, the *d* stands for the distance the car crumpled or dented (this could be either the car itself or the object that got hit), the *m* stands for the mass of the car that caused the crash, and the *v* stands for the velocity or directional speed of the car.

You decided to use this equation because you have all the information except the velocity of the car which you want to find. So, you can plug in all your known values and then solve for the velocity. From studying the scene and from prior experience, you can tell that a force of impact of roughly 250,000 foot pounds per second squared was needed to indent the red car. The distance that the red car dented is 1.2 inches (0.1 feet). The mass of the blue car is 3000 pounds. Plugging this information into the formula and then solving for the velocity, you get this.

So, the blue car was traveling at 2.78 miles per hour when it hit the red car causing a dent of 1.2 inches.

Now, you try picking a mathematical model to use to help you solve a problem.

Here is your problem. You are trying to figure out just how much carpet you need to carpet your whole home. Your home has 5 rooms total with 1 long hallway.

What kind of mathematical model would you choose to help you solve this problem?

If you try and visualize this problem in your head or on paper, you'll see that to find how much carpet you need is the same as finding the area of your home, of your five rooms plus the hallway to be exact. You can narrow this down further by taking a look at the floorplan of your home. You'll see that your five rooms and hallway are all rectangles, so to find the area of these places will mean finding the area of these rectangles. And there you have your mathematical descriptive model. All you need to solve this problem is to find your dimensions for each of these places. Then you'll use the formula to find the area of rectangles for each room and hallway and then add them all up to get your answer.

Let's review.

The process of creating a mathematical model is referred to as **descriptive modeling**. By creating such a model, it helps you to find solutions to real-world problems. What you do is 1) you first find a mathematical model that is similar to the real world problem, 2) label all your variables that are part of your problem, and 3) use the equations that are part of your mathematical model and the values that you have to find your solution.

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NY Regents Exam - Algebra II: Test Prep & Practice16 chapters | 114 lessons | 7 flashcard sets

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