Model Matrix Worksheet Humanities Assignment Help

Calculus I (MAT 221)

Mathematica Project 2

For this project, we will be looking at implicitly defined curves. The goal is to be able to plot an implicit curve using Mathematica, find the derivative of that implicit curve, and then plot tangent lines together with the original curve. We will be using the operation ContourPlot to graph these implicit functions. For example, to plot the unit circle x^2+y^2 = 1 on a window of −1.5 ≤ x ≤ 1.5 and −1.5 ≤ y ≤ 1.5, we would write the code as:

ContourPlot[x^2 + y^2 == 1 , {x,−1.5,1.5} , {y,−1.5,1.5}]

1) Let’s start by looking at the the basic hyperbola, x^2−y^2 = 1.

a) Plot this hyperbola.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Using this, find the derivative at the point (−2,√3). (-2, radical (3))

e) Graph the tangent line on the same plot as the hyperbola.

2) A famous implicitly defined curve is the Lemniscate of Bernoulli. This curve is defined by: (x^2 + y^2)^2 = 4(x^2 −y^2).

a) Plot the Lemniscate of Bernoulli.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Find the derivatives (yes plural) when x = 1. Look at the function, how many points have an x-coordinate of 1?

e) Graph the tangent lines at these points on the same set of axes as the Lemniscate.

3) Now let’s look at another famous implicitly defined curve, the folium of Descartes. This curve is defined by: x^3 + y^3 = 6xy.

a) Plot the folium of Descartes.

b) In Mathematica write a detailed step by step process on how to find the derivative, dy/dx, by using implicit differentiation.

c) Using the Derivative operation in Matheamtica, confirm your derivative from the previous step.

d) Find all points where dy/dx = 0 (horizontal tangent lines). You should use Mathematica and the Solve or Reduce options.

e) Plot the horizontal tangent lines on the same plot as the folium.

f) We could also find the vertical tangent lines by looking where dy/dx is undefined. But, this function is its own inverse so if you reflex your horizontal tangent lines over the line y = x, you will find your vertical tangent lines. Try this to get the vertical tangent lines and plot them to confirm they are the vertical tangent lines.

Write a full four pages essay. Answering the prompt question in bold as I attached below. Below are two readings that need to be connect and compare with each other. In the essay, there are a few points should be include:

1. A clear, arguable thesis in the introduction paragraph.

2. Three Topic sentences that reflect the thesis in three body paragraph.

3. Three body paragraphs total, each body paragraph should contain two quotes, one quote from one reading and one from the other.

4. Introducing the quote first and explain it. Then, find out if the connections between two quotes from two authors.( It could be similarities or contradictions).

5. Important: avoid summary, write more about own ideas. And focus on the idea each paragraph.

Reflection involves critical thinking, which means rethinking your existing knowledge and previously held opinions in light of what we have learned about theories of ethics, logic, and reasoning. You will need to question your existing knowledge and beliefs. Why do you feel the way you do about prenatal testing?

Of the four responses offered in the Prenatal Testing scenario, which do you feel is the most ethical and why?

To complete this assignment:

• Complete the entire scenario.
• Compose your reflection in a Word document. Of the four responses offered in the scenario, which do you feel is the most ethical and why?
• Support your conclusions with evidence and specific examples from the textbook, as well as other sources as needed.
• Your reflection must be at least 250 words in length and follow APA (6th ed.) formatting and citation guidelines as appropriate.

Assignment #4 False or Misleading Food Advertising and Labels

This assignment is about business ethics. Marketing of food is a huge business. Marketing uses many techniques to make a product appealing including indicating it is a healthy choice.

Your analysis must be at least 3 pages, single spaced with a minimum of 5 separate identified sources.

For example the dairy industry is now challenging the term milk on soy milk and almond milk products which contain zero animal milk. McDonalds recently got into difficulty when it advertised that its fries were cooked in vegetable oil, but didn’t readily disclose that the fries were flavored with beef tallow. McDonald’s was sued by several vegetarians and Hindus who do not eat meat for ethical and/or religious reasons.

Look in your kitchen cupboard, refrigerator, or a cabinet and choose 5 from these listed products: cereal, yogurt, cheese food, (Velveeta or most pre-sliced cheeses), bread, an item labeled fat free or low fat, frozen food with a healthy sounding brand name (healthy choice for example), chicken fingers, or processed meat (deli type meats) and a snack food.

If you are in a dorm you can use labels from food you have purchased or keep handy.

1. Look at the photo on the front of the package if there is one. Describe it in comparison what you learn from the below analysis.

2. For each product, record the serving size. Does 1 tablespoon or ½ slice sound like an average serving to you? In other words, is the serving size reasonable?

3. Then check the serving size content of fat, saturated fat, partially hydrogenated oils, salt, sugars, high fructose corn syrup, dextrose, sucrose, fructose and other sugars, and mono and di-glycerides. Compare that to the daily recommended allowance on the same chart. Look up any ingredients that you do not recognize. How many of the ingredients do you need to research to understand? What are they? Would you buy them in a grocery store? Are they in your kitchen? How many of the ingredients do you need to research to understand?

4. Does this product appear to be a good source of healthy food? Are the pictures representative of the product or have other items been added? Does the packaging seem deceptive, misleading, confusing, hard to read, or otherwise false?

5. Does the mandatory (government required) nutritional information provide you with sufficient information to make an informed choice? Is the print prominent enough, large enough? Clear?

There will be a discussion of the assignment in class.