Polynomial Applications Worksheet Answers – In this section, we’ll explore how polynomials are used in perimeter, area, and volume applications. First we will see how polynomials can be used to describe the perimeter of a rectangle.

A rectangular garden has one side of length [latex]k+7[/latex] and one side of length [latex]2x + 3[/latex]. Find the perimeter of the park.

The following video shows you how to find the perimeter of a triangle whose sides are defined by a polynomial.

#### Lesson Video: Graphs Of Polynomial Functions

Determine and translate:  The larger circle has radius = r and the smaller circle has radius= 3.  If we find the area of ​​the larger circle, subtract the area of ​​the smaller circle, the remaining area will be the shaded area. . . First determine the area of ​​the larger circle:

In the following video, an example of determining the area of ​​a rectangle whose sides are defined by polynomials will be shown.

It’s easy to confuse pi as a variable because we use Greek letters to represent it. We use Greek letters instead of numbers because no one has been able to find the end of pi. To be precise and complete, we use Greek letters to say, “we’ve included all the digits of pi without having to write them out.” The expression for the area of ​​the shaded area in the previous example also includes the variable r, which represents the unknown radius and the number pi. If we need to use this expression to make a physical object or instruct a machine to cut certain dimensions, we will round pi to the appropriate number of decimal places.

In the following example, we will write the area of ​​a rectangle in two different ways, one as the product of two binomials and the other as the sum of four rectangles. Since we describe the same shape in two different ways, we should end up with the same expression regardless of how we define the area.

## Polynomial Expressions, Equations, & Functions

Write two different polynomials that represent the surface of the image. For one expression, think of the rectangle as a large figure, and for another expression, think of the rectangle as the sum of 4 different rectangles.

Reading and Comprehension: We were asked to write an expression for the area in the picture above. The area of ​​a rectangle is given as [latek]A=lv[/latek]. We have to consider all the figures in our dimension.

Define and translate: Use the formula for area: [latex]A=lv[/latex], the sides of a figure are the sum of certain sides. [latex]beginl=left(i+7right)\v=left(i+9right)end[/latex]

We can use any method we have learned to multiply binomials to simplify this expression, we will use a table.

### Applications Of Polynomials

Now we will find an expression for the area of ​​the whole figure, which consists of the area of ​​four rectangles added together.

Read and understand: The area of ​​a rectangle is given as [latex]A=lv[/latex]. First we must determine the area of ​​each rectangle and then add them all together to get the area of ​​the whole figure. It helps to mark four rectangles on the image to be able to resize it.

Note that we usually write another constant multiplied by [latek]pi[/latek] in front of it. Now we can distribute [latek]7pi[/latek] in each term of the polynomial.

Notice again how we left [latex]pi[/latex] as a Greek letter. If we were to use this calculation to measure ingredients, we would either round pi, or the computer would round it for us.

#### Multiply Polynomials (with Examples): Foil & Grid Methods

In this last video, we present another example of finding the volume of a cylinder whose dimensions include polynomials.

In the section on systems of linear equations, we discussed how a firm’s costs and revenues can be modeled using two linear equations. We find that the company’s profit area is the area between the two lines where the company will make money based on how much is produced. In this section we will see that polynomials are sometimes used to describe costs and revenues.

Profit in business is usually defined as the difference between the amount of money earned (revenue) by producing some items and the amount of money needed to produce that number of items. When you’re in business, you definitely want to see a profit, so it’s important to know what your expenses and income are.

For example, say that it costs the producer to produce certain things C, and the revenue generated by selling those things R. The profit, P, can be defined as

### Polynomial Equation Word Problems (video Lessons, Examples And Solutions)

Read and understand: Profit is the difference between revenue and costs, so we need to define P = R – C for the business.

Mathematical models are great when you use them to learn important information. A cell phone manufacturing company can use the profit equation to find out how much profit it will make on the number of phones it produces. In the following example we will explore some profit values ​​for this company.

We will immediately write and solve because we already have a polynomial. It is probably easier to use a calculator since the numbers in this problem are very large.

Interpretation: If the number of calls generated is 100, the company’s profit is -\$250,000. That’s not what we want! The company must produce more than 100 phones to make a profit.

### Solve Polynomial Equations By Factoring

Interpretation: If the number of calls produced is 25,000, the company’s profit is \$118,130,000. It’s more like that! If a company makes 25,000 calls, it will make a profit after paying all its bills.

If this is true, then the company needs to make more phones to make more money, right? In fact, something different happens as the quantity of goods produced increases forever.

Interpretation: If the number of calls produced is 60,000, the company’s profit is -\$24,750,000. Wait a minute! If a company makes 60,000 calls it will lose money, what happens? At some point, the cost of producing the phone will exceed the amount of profit the company can make. If you found this interesting, you might like to read about economics and business models.

We show that profit can be modeled by a polynomial and that the profit a company can make from this business model is finite.

#### Preworksheet 11.11 Applications Of Taylor Polynomials

In this section, we define a polynomial that represents the perimeter, area, and volume of known shapes. We also introduce some conventions on how to use and write [latek]pi[/latek] when combined with other constants and variables. The following application will introduce you to cost and revenue polynomials. We explored cost and revenue equations in the Systems of Linear Equations module, now we will see that they can be more than linear equations, they can be polynomial. This product should only be used by the teacher who purchased it. This product cannot be shared with other teachers. Please purchase the correct number of licenses if using by multiple teachers.

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