Lesson 2.4 Using Polynomials in word problems

 

Please note in order to move to the next Lessons you will have to let me know that you have finished this Lesson 2.4.    

           Please email me  sojohnsey@gmail.com

 

You must be sure to complete the quiz at then end of this lesson.  Then send me the email I asked for above.  I will review the quiz before allowing you to move to SECTION 3.   If you can not complete the quiz with at least 85% then you are not ready for Section 3.

It is Section 2 in reverse!

 

Polynomials can also be used to solve word problems.

There are 4 diagrams and 1 video in this lesson.  If you do not see them then please let me know.

 

In this lesson we will learn to write the equations, but we will wait until the next chapter to solve them.

 

 

VIEW this video here if you do not see one above:  http://www.youtube.com/v/9pEN8lMkxDA  

 

 

EXAMPLE R:   The length of a rectangle is 3x - 2  meters. The width is x+5 meters. 

Write an equation for its perimeter. 

Perimeter  is the sum of the measures of ALL the sides.

Perimeter = 3x - 2 + 3x - 2 + x+5 + x+5= 6x - 4 +2x +10 

or Perimeter = 2(3x-2) + 2(x+5)= 8x + 6.

 

                                                                                                              

Now find the area of the rectangle.                                                                              

Area = length times width.                                                            

Area = (3x-2)(x+5)= 3x²+15x -2x -10  = 3x²+13x -10.

 

Box  EXAMPLE :     The corners (small squares) are cut from a rectangular piece of cardboard that measures

8 inches by 12 inches.  The sides are folded up on the dotted lines to make a shoe box. 

Write an equation to find the volume of the box.

The small squares will be cut  out to allow the needed folding.   They measure x by x.  

 

 

Volume =  (Area of the bottom) * HEIGHT 

 

Length of rectangle is 12 but the box will require the ends to be bent upwards.  

Thus the length will be come 2x shorter.   We will bend up x inches on each end.  

Thus length of box is 12-2x.

 

Width of rectangle is 8 but the box will require the ends to be bent upwards.   Thus the width will be come 2x shorter.  

We will bend up x  inches on each end.   Thus width of box is 8 -2x.

 

Area of the bottom = length * width = (12-2x)(8 -2x).  

The bottom area is 96 - 40x +4x²  inches squared. 

 

Height  is x inches.  Study this diagram  carefully.  You will cut out the small squares and then you will

fold the cardboard up to form a box whose height is the determined by the size of the squares you cut out. 

Get a piece of cardboard or paper and try this. 

 

The Volume is the area of the bottom which is (96 -40x+4x²) TIMES the HEIGHT which is x.

 

V = (96 -40x+4x²)x = 96x -40x²+4x³  inches cubed. 

If we write this polynomial in descending order we will have V = 4x³-40x²+96x in³.

 

 

 

Field  Example :  An athletic field has dimensions of 30 yards by 100 yards. 

An end zone is w yards wide and there is an end zone at each end of the field . 

Find the total area of the field and its 2 end zones.

 

 

There are 3 rectangles so the area for each is length times width.

Field = 30 times 100 = 3000 sq. yards

end zone = 30 times w = 30w

Total = 3000 +30w  +30w

        = 3000 + 60w sq. yards

 

 

NOW LOOK at CIRCLES.

 

The radius of a circle is half of its diameter. 

The area of a circle is found by using the formula 3.14 times radius times radius. 

Please do not try using the diameter in the formula for finding the area of a circle.  

You must change the diameter to a radius before using this formula. 

Remember the radius is half of the diameter.

 

Circle Example :   Find the area of a circle whose diameter is 2x+64 feet.  

 To find the area we need the radius of the circle.  

The radius is half of the diameter; thus, the radius is x+32 feet.

Area of circle = radius²times pi.   Recall pi is approximately 3.14.

Area = (x+32)²times 3.14.   

the r squared is NOT  (x²+ 1024) 

Instead it is =  (x+32) (x+32) (3.14)

                 = (x²+32x +32x + 1024) (3.14)

                 =  (x²+64x + 1024) (3.14)          

 I hope you see where the 64x came from.

 

ASSIGNMENT 2.4

 

Write an equation for each and then simplify by multiplying or combining like terms.

 

1.  Find the area of the figure .

All measurements are given in feet.  

Be careful finding the width of the green rectangle.

 

 

2.  The radius of a circle is 8x-4 inches.  Find its area. 

     Area = radius²; times π  or  r²; times 3.14.

 

3. The diameter of a circle is 16v-8.  Find its area

 

4. The length of the side of a square is 15m+6.  Find its perimeter and then find its area.

 

5. The length of a rectangle is 20x and its width is x -9.  Find its perimeter then find its area.

 

6.   In Box Example of Lesson 2.4, find the volume if the rectangular piece of cardboard is changed to 5 inches by 10 inches.  

        You must state your expressions for the length, width, and volume.

 

 

This link will help you review the beginning of the SECTION 2;   do good on it.   

 

Polynomials 1 ii c2 http://www.quia.com/quiz/1532692.html

 This is at the web site called QUIA. You do NOT need to join QUIA; I am the member.  You can play this for free.