Inequalities

 

Inequalities

 

Read the following instructions in order to complete this assignment, and review the example of how to complete the math required for this assignment:

Read the article about Body Mass Index (BMI) on page 151 of Elementary and Intermediate Algebra. Use the formula given using pounds and inches for finding the BMI at the end of the first paragraph in order to find the four intervals the article mentions:

 

17 < BMI < 22      might have a longer life span than average 

 

23 < BMI < 25      probably not overweight

 

25 < BMI < 29.9   probably overweight 

 

     BMI > 30       obese

You will use your height to plug into the formula to solve for W, the weight range that will go with each category. You may prefer to solve the formula for the variable W before plugging in values, which is fine.

Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the Instructor Guidance and be concise in your reasoning.  In the body of your essay, please make sure to include:

 

Your solution to the above problem, making sure to include all mathematical work

 

A discussion on the computed weight ranges and some reasons why they could be misleading

 

An evaluation of the regions outside of the “probably not overweight” range using both set notation and interval notation. Include a simple graph of the regions. (See Instructor Guidance example for some ideas of how to do this.) 

 

The incorporation of the following five math vocabulary words into your discussion. Use bold font to emphasize the words in your writing (Do not write definitions for the words; but integrate them into your discussion.):

 

Inequality 

 

Equivalent 

 

Compound inequality 

 

Interval 

 

Infinity

 

My height=5’7″ or 67 inches 

INSTRUCTORGUIDANCE EXAMPLE: Week 2 Written Assignment (paper)

Students, you are perfectly welcome to format your math work just as I have done in

these examples. However, the written parts of the assignment MUST be done in your

own words. You are NOT to simply copy my wording into your posts!

[The introductory paragraph must be written by each individual student and the content

will vary depending on what the student decides to focus on in the general information of

the topic.]

On page 151 of our textbook we find the formula for Body Mass Index or BMI as

follows:

BMI = 703W

H

2

Where W = one’s weight in pounds, and

Where H = one’s height in inches.

We are asked to calculate four intervals based on our own height. My height is 67.25

inches. The specified intervals include three compound “between” inequalities, and

one regular inequality. Everywhere “BMI” shows up in the inequalities I will substitute

the formula and solve the inequality for W to specify the weight ranges which fit each

category for my height.

The first interval shows who might have a longer life span than average. The compound

inequality for this is:

17 < BMI < 22

17 < 703W < 22 This is an equivalent inequality replacing BMI with the formula.

H
2

17 < 703W < 22

67.25
2
H

2
has been replaced by my height in inches.

17 < 703W < 22

4522.5625 The next step I multiply all three terms by the denominator.

17(4522.5625) < 703W(4522.5625) < 22(4522.5625) Cancelling is done.

4522.5625

76883.5625 < 703W < 99496.375 The multiplications were carried out.

76883.5625 < 703W < 99496.375 All three terms divided by 703 to isolate W.

703 703

703

109 < W< 141.5

People of height 67.25 inches might have a longer than average life span if they weigh

between 109 lbs and 141.5 lbs.

I am now going to do something different. I am going to solve the second inequality

formula for W before I plug in the values to find W.

23 < 703W < 25 First, multiply all terms by H 2 to take it out of the denominator.

H
2

23H
2
< 703W < 25H

2
Divide all terms by 703 to isolate W.

23H
2
< W < 25H

2

703 703 This is an equivalent inequality to solve for the second weight

interval.

I will now plug in my height squared (4522.5625) to find the second weight interval.

23(4522.5625) < W < 25(4522.5625)

703 703

104018.9375 < W < 113064.0625 Multiplication carried out.

703 703

148 < W < 161 Division carried out.

People of height 67.25 inches who weigh between 148 lbs and 161 lbs are probably not

overweight.

This method is much more efficient than the first method so I will use it to find the next

two intervals as well. The third weight interval indicates the range for probably

overweight for this height. I will plug 25.1 and 29.9 into the above compound

inequality in place of 23 and 25.

25.1(4522.5625) < W < 29.9(4522.5625)

703 703

113516.31875 < W < 135224.61875 Multiplications carried out.

703 703
161.5 < W < 192 Division carried out

People of height 67.25 inches who weigh between 161.5 and 192 are probably

overweight.

The fourth weight interval indicates the range for those who are obese at this height.

This is not a compound inequality so I only need to use the middle and right terms of

the basic inequality with the opposite pointing arrow and substitute 30 for 29.9.

W ≥ 30(4522.5625)

703

W ≥ 135676.875 Multiplication carried out.

703

W ≥ 193 Division carried out.

People of height 67.25 inches who weigh 193 or above are most likely obese and would

benefit from some serious life-style changes. Although this interval theoretically extends

to positive infinity, we know that the weight of a human is eventually self-limiting.

[Student answers to part 3 are going to vary according to their math and understanding

of the article.]

In English I have written the following: People of height 67.25 inches who weigh

between 148 lbs and 161 lbs are probably not overweight. In set notation this could be

written as follows:

Let X = the set of those who are probably not overweight for the specified height.

Then X = {w | w < 148 or w > 161} where w represents the weight of the individual.

In interval notation this would be written as follows: X = (- , 148) (161, )

Graphed on a number line this interval could look like this:

<-------------)--------------------------------(-------------------->

148 161

[The conclusion paragraph must be written by each individual student and the content

will vary depending on what the student decides to include in their summary. NOTE:

this example does not demonstrate APA format for a paper. The student is responsible

for the proper formatting of his or her own work.]

Tipsfor Writing in Math Classes

In addition to the weekly homework, lab, and discussion posts, the Math courses at Ashford also include

written assignments. Do not let this intimidate you. While this may be unlike other math classes in the

past, the purpose of this is let you examine a math concept that has a direct correlation to the use of

mathematics in the “real world,” and to have you explain how and why you solved a problem in a

particular way, allowing you to further develop your critical thinking skills with regard to mathematics.

The purpose of this short “guide” is to prepare you for completing these writing assignments, since the

format will be slightly different than the other writing assignments you have here at Ashford. However,

the basic 5 paragraph essay should still be the basis for your written assignments in Math.

Introduction:

Your introduction needs to do three main things:

 Introduce the specific concept examined in the assignment (i.e. inequalities, Pythagorean

quadratics, etc).

 Introduce or reference the specific question or real world application being asked (i.e. BMI,

navigation)

 Have a clear statement that describes how the concept examined in the assignment is important to

a “real world” setting.

As with all introductions, this should be about 5-6 sentences in length.

Body Paragraphs:

This is where your assignment diverges from a more traditional essay. Here is where you will solve the

specific problem being asked, and explain how and why this is important.

In order to do this, you will need to:

 Restate the problem in your own words. Solve the problem demonstrating your understanding of

the concepts examined in the essay, making sure to include each mathematical step (in other

words, show your work). This will count as a “paragraph.”

If there is a visual that you used that would like to include, you may attach a scanned

copy of it separately, and reference it here (i.e. see attached visual). Please note that this

visual must be created by you and cannot be a scanned copy of the text or other class

wide visual.

 Include a discussion that incorporates the answers of each additional question asked in the

prompt. Depending on the questions asked, this will usually be 2 paragraphs in length.

 In your discussion, make sure to incorporate the weekly vocabulary terms listed in the

assignment, and place these in bold type. These should be fully integrated into your discussion,

and should not just be definitions.

Conclusion

Your conclusion should be a paragraph (at least 5 sentences) that includes the following:

 An application of the concept examined to the particular problem solved

 A summary of the problem and your method of solving it

 A statement of what you learned

 A statement of how this concept can be used in the real world.

APA format:

All assignments submitted at Ashford must be in APA format. Therefore, please make sure to include a

properly formatted reference and title page, and make sure your paper is in an APA font, such as 12 pt.

Courier New or Times New Roman. With regard to internal citations, you don’t need to cite the textbook

if the problem you are solving is from the textbook, but you will need to cite any outside sources. Please

make sure that the text is listed in your reference section however, along with any other sources you used

in working on the assignment.

Plagiarism:

Plagiarism, or the use of another person’s words are thoughts, is academically and intellectually dishonest

and not permitted at Ashford. Please make sure everything you turn in is new and original work, and is

written in your own words. Copy and pasting portions of your discussion off the internet will result in

automatically failing the assignment.