MAT 262 – Estimating the Area Under a Curve with MatLab
Part 1
The first new idea here is how to use subscripts within MatLab. Outside of the MatLab environment, a row vector x with n components would look like
x = [ x1x2 … xn -1xn ]
where each entry in the vector would be a number. In MatLab, however, we write x(1), x(2), …, x(n – 1), x(n) to represent subscript notation, which allows us to manipulate entries individually instead of the vector as a whole.
We may know what this vector looks like entry by entry, but it may not be very practical to do monotonous calculations with each entry within the script with respect to some function over and over again. Instead, we can compute what the function would look like for each component by setting up a pattern for MatLab to follow inside of what is called a for loop. A for loop is a way to essentially tell MatLab to do the same operation for a predetermined amount of calculations to a set of values until all of the calculations are done, and then MatLab stops. The example below demonstrates both of these ideas together. I have left notes as comments.
% the function in this code is the standard Normal curve from x = -5 to x = 5; we are going to discretize the horizontal axis, then evaluate the value of each value on the standard Normal curve
xmin = -5; % this is the smallest value in our domain; it is suppressed so it won’t output to the CW
h = 1; this is our step size for this example; h or are common variables to use for step size
xmax = 5; % this is the largest value in our domain, also suppressed
n = (xmax – xmin)/h; this generates how many entries there are in our vector, which is 10
x(1) = xmin; % our first entry is -5, as mentioned earlier, so this is x1, but written so MatLab understands
y(1) = (1/(sqrt(2*pi)))*exp(-((xmin).^2)/2); % the value of written into MatLab
for i=1:n % don’t suppress the condition for the for loop
x(i+1) = x(i) + h; % this is the pattern for going from one x entry to the next; suppress it
y(i+1) = (1/(sqrt(2*pi)))*exp(-((x(i+1)).^2)/2); % same deal as the line above
end % once MatLab goes through all of the entries, you have to tell it to stop operating in the for loop
One of the reasons we are working with subscripts and for loops is to enable us to estimate areas under curves, which is the purpose of this second MatLab project. As such, it would be nice to visualize how these values in the for loop are advantageous to estimating the area under a given curve. One way to do this is to create the histogram that is associated with the left-hand and right-hand estimates. As seen in class, depending upon which estimate we use, we could be using an overestimate or an underestimate.
Even though there are built-in histogram functions in MatLab, none of them work quite as easily as the line command. The line command allows the user to dictate exactly where the line starts and ends. In particular, it creates a line between two points in the xy-plane using the pattern below.
line([starting x coordinate; ending x coordinate],[starting y coordinate, ending y coordinate])
This lends itself to creating either vertical, horizontal, or diagonal lines. We are only really concerned with creating the former two, since we are mimicking a histogram. These can be manipulated inside of a for loop to create a collection of lines as needed (hint for the next part).
Two final commands that need to be mentioned are the sum command and the trapz command.
The sum command is exactly what it sounds like it is: a cumulative sum of a collection of quantities, which could be a collection of subscripted quantities (hint for the next part). If, for example, you wanted to add up all of the areas of the individual bars of a histogram, a single equation in a for loop could collect all of the areas and a short, unsuppressed command after the end of the for loop of the form sum( ) could generate that sum.
Lastly, the trapz command is a method to finding the “exact” area under a given curve. It is displayed and executed in the same format as the plot command: trapz(x vector, y equation). Leave it unsuppressed so the output is displayed in the CW.
Part 2 – Estimating the Area Under a Curve (30 pts)
Consider a simple LRC series electrical circuit connected to a 9V battery. This circuit has an inductance of 0.2 H (henries), a resistance of 5 (ohms), and capacitance 0.0 F (farads). If this circuit stays closed indefinitely (so current runs through the circuit all the time), starting at time t = 0 seconds, with an initial charge of 0 C (coulombs), then the function that gives the current for all nonnegative times t is
i(t) = .
2A) (4 pts) Plot the current function above from t = 0 seconds to t = 1 seconds with an adequately small step size. Label each of the axes as to what they represent and title the graph. Make it look nice.
Now, this function above, i(t), gives us the current throughout the circuit, but it does not explicitly tell us much about the charge in the circuit. The relationship between distance, velocity, and time is very similar to the relationship between charge, current, and time. Using this knowledge, we are going to utilize subscripts and for loops to estimate the area under the curve generated by the current function, i(t) in a similar fashion as the example provided earlier.
2B) (10 pts) Use a for loop to calculate the left-hand estimate for the area under the curve. Use a step size of either 0.1 or 0.2 in your code. Create vertical and horizontal lines mimicking what the left-hand estimate would look when drawn over the top of the original function (like examples from class). Create these lines within the for loop. Lastly, calculate the area of each column for the estimate, and sum the results outside of the for loop using a sum command.
Hint: Set up the first subscripted entry before the for loop like in the example above. It may be useful to draw a picture by hand first to help with how line commands should work.
2C) (10 pts) Do the same thing as in 2B, but for the right-hand estimate for the area under the curve.
Hint: Once you get 2B, you only need a few minor modifications to knock this one out.
2D) (6 pts) Compare the estimated results from parts 2B and 2C. Are they close? Do they make sense based on the original plot? Now, compute the exact area under the curve with the trapz command with the original vector and function. Are your estimates close to the actual area under the curve? Finally, what does the area under the curve represent for this problem? Provide a careful, thoughtful answer within the context of the problem.
MY ANSWER SO FAR:
% Part 2A
%sets the range
%this is the equation
%stops from listing the variables
%creates the graph
%Part 2B
%defines the for loop
%coordinates into the loop
%this part is supposed to split the graph into sections
%finds left sum
%Part 2C
%Part 2D
%finds the exact area under a curve
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Mastery Objectives Develop One Mastery Concept And 5 Mastery Objectives For Your
/in Uncategorized /by developerMastery Objectives
Mastery Objectives
Third Grade ELA Mastery concept: Students will identify the main idea and concept presented in text, identify and assess evidence that support the ideas.Students will learn the definition of the main idea. Students will be able to identify the main idea and supporting details of a fiction or non-fiction passage. Use strategies to practice finding a main idea independently. Identify the main idea and concept presented in text, identify and assess evidence that support the ideas.
Five Mastery Objectives
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Mat 114 Quantitative Reasoning Spring 2017 Project Two The Objective Of This Pro
/in Uncategorized /by developerI just need the anwsers to this:) It is a pretty hard project
EAGLESA study was conducted on Admiralty Island in southeast Alaska using time-lapse photography todocument Bald Eagle incubation, brooding (sitting on eggs to hatch them), prey deliveries and…
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Mat 116 Week 8 Real World 12 60 11 55 10 50 Grade Scale Number Correct 9 8 7 6
/in Uncategorized /by developerCan you help with these 12 questions?
MAT/116 – Week 8 Real World1260 1155 1050 Grade Scale (Number Correct)987654454035302520 315 210 15 Complete this project to apply the skills learned in Chapter 8 and Chapter 9 to a real-life situationThis document is copy-protected. Please answer the following questions in a Word document (.doc or .docx) attachment statingyour name, problem number, and answers. You may show work if you choose.You are required to use Equation Editor, if necessary, to write mathematical expressions and equations (such as fractions, squareroots, etc.).Submit the document in your Assignment Section by Week 8, Day 7 (Sunday) A Great InvestmentFor most people, buying a house is a great investment that can offer security in an uncertain world, but buying a house is also acommitment. Suppose you are in the market for a new home and are interested in a new housing community under construction ina different city.1.2.3.4.5.6. The sales representative informs you that there are two floor plans still available, and that there are a total of 65 housesavailable. Use x to represent floor plan #1 and y to represent floor plan #2. Write an equation that illustrates the situation.The sales representative later indicates that there are 4 times as many homes available with the second floor plan than the first.Using the same variables you used in question #1, write an equation that illustrates this situation..Use the equations from questions #1 and #2 of this exercise as a system of equations. Use substitution to determine how manyof each type of floor plan is available.What are the intercept(s) of the equation in question #1 of this problem?What are the intercept(s) in question #2 of this problem?Where would the two lines intersect if you solved the system by graphing? As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decideto inquire about it.7.8. 9. The sales representative here tells you they also have two floor plans available, but they only have 40 homes available. Write anequation that illustrates the situation. Use m to denote floor plan #1 and n to denote floor plan #2.The representative tells you that floor plan #1 sells for $175,000 and floor plan #2 sells for $200,000. She also mentions that allthe available houses combined are worth $7,625,000. Write an equation that illustrates this situation. Use the same variablesyou used in question #7.Use elimination to determine how many houses with each floor plan are available. You recently started the paperwork to purchase your new home, and you were just notified that you can move in to the house in 2weeks. You decide to hire a moving company, but are unsure which company to choose. You search online and are interested incontacting two companies, Heavy Lifters and Quick Move, to discuss their rates. Heavy Lifting charges $60 per hour with noadditional fees. Quick Move charges a $75 fee plus $35 per hour.10. Which mover provides a better deal for 2 hours of work?11. Which mover provides a better deal for 15 hours of work?12. For what value of h (hours), does Quick Move and Heavy Lifting offer the same (equal) deal? MAT/116 – Week 8 Real World Rev: 8/2010 (Hoyer)
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Mat 172 Final Exam Study Guide You May Use You Calculator On The Final Exam But
/in Uncategorized /by developerplease workout and thoroughly explain number 6-11 in the document attached
This is only a study guide but a study guide doesn’t do much good If I don’t know how to approach or do numbers 6-11 , please help
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Mat 262 Estimating The Area Under A Curve With Matlab Part 1 The First New Ide
/in Uncategorized /by developerMAT 262 – Estimating the Area Under a Curve with MatLab
Part 1
The first new idea here is how to use subscripts within MatLab. Outside of the MatLab environment, a row vector x with n components would look like
x = [ x1x2 … xn -1xn ]
where each entry in the vector would be a number. In MatLab, however, we write x(1), x(2), …, x(n – 1), x(n) to represent subscript notation, which allows us to manipulate entries individually instead of the vector as a whole.
We may know what this vector looks like entry by entry, but it may not be very practical to do monotonous calculations with each entry within the script with respect to some function over and over again. Instead, we can compute what the function would look like for each component by setting up a pattern for MatLab to follow inside of what is called a for loop. A for loop is a way to essentially tell MatLab to do the same operation for a predetermined amount of calculations to a set of values until all of the calculations are done, and then MatLab stops. The example below demonstrates both of these ideas together. I have left notes as comments.
% the function in this code is the standard Normal curve from x = -5 to x = 5; we are going to discretize the horizontal axis, then evaluate the value of each value on the standard Normal curve
xmin = -5; % this is the smallest value in our domain; it is suppressed so it won’t output to the CW
h = 1; this is our step size for this example; h or are common variables to use for step size
xmax = 5; % this is the largest value in our domain, also suppressed
n = (xmax – xmin)/h; this generates how many entries there are in our vector, which is 10
x(1) = xmin; % our first entry is -5, as mentioned earlier, so this is x1, but written so MatLab understands
y(1) = (1/(sqrt(2*pi)))*exp(-((xmin).^2)/2); % the value of written into MatLab
for i=1:n % don’t suppress the condition for the for loop
x(i+1) = x(i) + h; % this is the pattern for going from one x entry to the next; suppress it
y(i+1) = (1/(sqrt(2*pi)))*exp(-((x(i+1)).^2)/2); % same deal as the line above
end % once MatLab goes through all of the entries, you have to tell it to stop operating in the for loop
One of the reasons we are working with subscripts and for loops is to enable us to estimate areas under curves, which is the purpose of this second MatLab project. As such, it would be nice to visualize how these values in the for loop are advantageous to estimating the area under a given curve. One way to do this is to create the histogram that is associated with the left-hand and right-hand estimates. As seen in class, depending upon which estimate we use, we could be using an overestimate or an underestimate.
Even though there are built-in histogram functions in MatLab, none of them work quite as easily as the line command. The line command allows the user to dictate exactly where the line starts and ends. In particular, it creates a line between two points in the xy-plane using the pattern below.
line([starting x coordinate; ending x coordinate],[starting y coordinate, ending y coordinate])
This lends itself to creating either vertical, horizontal, or diagonal lines. We are only really concerned with creating the former two, since we are mimicking a histogram. These can be manipulated inside of a for loop to create a collection of lines as needed (hint for the next part).
Two final commands that need to be mentioned are the sum command and the trapz command.
The sum command is exactly what it sounds like it is: a cumulative sum of a collection of quantities, which could be a collection of subscripted quantities (hint for the next part). If, for example, you wanted to add up all of the areas of the individual bars of a histogram, a single equation in a for loop could collect all of the areas and a short, unsuppressed command after the end of the for loop of the form sum( ) could generate that sum.
Lastly, the trapz command is a method to finding the “exact” area under a given curve. It is displayed and executed in the same format as the plot command: trapz(x vector, y equation). Leave it unsuppressed so the output is displayed in the CW.
Part 2 – Estimating the Area Under a Curve (30 pts)
Consider a simple LRC series electrical circuit connected to a 9V battery. This circuit has an inductance of 0.2 H (henries), a resistance of 5 (ohms), and capacitance 0.0 F (farads). If this circuit stays closed indefinitely (so current runs through the circuit all the time), starting at time t = 0 seconds, with an initial charge of 0 C (coulombs), then the function that gives the current for all nonnegative times t is
i(t) = .
2A) (4 pts) Plot the current function above from t = 0 seconds to t = 1 seconds with an adequately small step size. Label each of the axes as to what they represent and title the graph. Make it look nice.
Now, this function above, i(t), gives us the current throughout the circuit, but it does not explicitly tell us much about the charge in the circuit. The relationship between distance, velocity, and time is very similar to the relationship between charge, current, and time. Using this knowledge, we are going to utilize subscripts and for loops to estimate the area under the curve generated by the current function, i(t) in a similar fashion as the example provided earlier.
2B) (10 pts) Use a for loop to calculate the left-hand estimate for the area under the curve. Use a step size of either 0.1 or 0.2 in your code. Create vertical and horizontal lines mimicking what the left-hand estimate would look when drawn over the top of the original function (like examples from class). Create these lines within the for loop. Lastly, calculate the area of each column for the estimate, and sum the results outside of the for loop using a sum command.
Hint: Set up the first subscripted entry before the for loop like in the example above. It may be useful to draw a picture by hand first to help with how line commands should work.
2C) (10 pts) Do the same thing as in 2B, but for the right-hand estimate for the area under the curve.
Hint: Once you get 2B, you only need a few minor modifications to knock this one out.
2D) (6 pts) Compare the estimated results from parts 2B and 2C. Are they close? Do they make sense based on the original plot? Now, compute the exact area under the curve with the trapz command with the original vector and function. Are your estimates close to the actual area under the curve? Finally, what does the area under the curve represent for this problem? Provide a careful, thoughtful answer within the context of the problem.
MY ANSWER SO FAR:
% Part 2A
%sets the range
%this is the equation
%stops from listing the variables
%creates the graph
%Part 2B
%defines the for loop
%coordinates into the loop
%this part is supposed to split the graph into sections
%finds left sum
%Part 2C
%Part 2D
%finds the exact area under a curve
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Mat 350 Any Documents Needed To Complete The Assignment Questions Are Attached B
/in Uncategorized /by developerMAT 350
Any documents needed to complete the assignment questions are attached below.
Essay #1: The Gallup organization releases the results of recent polls at its website, www.gallup.com. Visit this site and read an article of interest.
A Gallup poll indicated that 74% of Americans who had yet to retire look to retirement accounts (such as 401(k), IRA, and Keogh account) as major funding sources when they retire. Interestingly, 40% also said that they looked to stocks or stock market mutual fund investments as major funding sources when they retire. (data extracted from D. Jacobs, “Investors Look Beyond Social Security to Fund Retirement,” www.gallup.com, March 28, 2011). The results are based on telephone interviews conducted March 24, 2011, with 1,000 or more adults living in the United States, aged 18 and older.
Essay #2: A manufacturer of cat food was planning to survey households in the United States to determine purchasing habits of cat owners. Among the variables to be collected are the following:
Essay #3: In 2008, a university in the mid-western United States surveyed its full-time first-year students after they completed their first semester. Surveys were electronically distributed to all 3,727 students, and responses were obtained from 2,821 students. Of the students surveyed, 90.1% indicated that they had studied with other students, and 57.1% indicated they had tutored another student. The report also noted that 61.3% of the students surveyed came to class late at least once, and 45.8% admitted to being bored in class at least once.
Essay #4: The Data and Story Library (DASL) is an online library of data files and stories that illustrate the use of basic statistical methods. Visit Data and Story Library, click DASL and explore a data set of interest to you.
Essay #5: A sample of 62 undergraduate students answered the following survey:
Based on your study of the survey and the results provided, answer the following:
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Mat 510 Homework Assignment Homework Assignment 8 Due In Week 9 And Worth 30 P
/in Uncategorized /by developerI need help with answering the questions, I have no problems with the charting. I’m confused on what the questions is asking. Iv’e already constructed the 95% confidence interval for the difference between the proportions of service. Should there be more to answer on question 1? On question two I’m I answering what the difference between the actual machines, or the confidence interval?
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Mat 560 Project The Challenger Disaster According To The Website Referred At The
/in Uncategorized /by developerMAT 560 ProjectThe Challenger DisasterAccording to the website referred at the bottom of the page, “On January 28, 1986 the space shuttle Challenger exploded. Seven astronauts died because two large rubber O-rings leaked during takeoff. These rings had lost their resiliency because of the low temperature at the time of the flight. The air temperature was about 0 degrees Celsius, and the temperature of the O-rings about 6 degrees below that.The link between O-ring damage and ambient temperature had been established prior to the flight. The engineers at Morton Thiokol, Inc have recommended that the flight be delayed. Unfortunately their argument wasn’t persuasive enough, and the launch proceeded with disastrous consequences.The engineers had failed to display the link between ambient temperature and O-ring damage in a clear and unambiguous fashion. What was needed was a simple scatter plot. The data is given below. Draw a scatter plot from the data. Based on this graphic, what recommendation would you have made for a flight if the forecast was for below 0 degrees Celsius?”Data from Previous FlightsTemperature (C)Damage Index1211144144172190190190190190200214210214210210220230244240240260260270 Project1. Make a scatter plot.2. Find and draw the LSRL (regression line) to predict the damage index.3. Interpret the coefficient of correlation.4. Interpret the coefficient of determination.5. Interpret the slope.6. Interpret the y-intercept.7. Predict the damage index when the temperature is -2 degrees Celsius.8. Find the residual when the temperature is 12 degree Celsius.9. If the temperature dropped below zero degrees Celsius, would you have delayed the flight? Explain (be concise).10. What percentage can be explained by this regression model?11. Conduct a test to see if there is a relationship between temperature and damage index.Presentation MUST be neat. Show ALL work!! Answers w/o support will receive NO CREDIT.USE GRAPHING PAPER ONLY! http://explodingdata.cqu.edu.au/ws_scartr.htm
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Mat540 Homework Week 1 Page 1 Of 3 Mat540 Week 1 Homework Chapter 1 1 The Retrea
/in Uncategorized /by developerChapter 11. The Retread Tire Company recaps tires. The fixed annual cost of the recapping operation is$65,000. The variable cost of recapping a tire is $7.5. The company charges$25 to recap a tire.a. For an annual volume of 15, 000 tire, determine the total cost, total revenue, and profit.b. Determine the annual break-even volume for the Retread Tire Company operation.2. Evergreen Fertilizer Company produces fertilizer. The company’s fixed monthly cost is $25,000,and its variable cost per pound of fertilizer is $0.20. Evergreen sells the fertilizer for $0.45 perpound. Determine the monthly break-even volume for the company.3. If Evergreen Fertilizer Company in problem 2 changes the price of its fertilizer from $0.45 perpound to $0.55 per pound, what effect will the change have on the break-even volume?4. If Evergreen Fertilizer Company increases its advertising expenditure by $10,000 per year, whateffect will the increase have on the break-even volume computed in problem 2?5. Annie McCoy, a student at Tech, plans to open a hot dog stand inside Tech’s football stadiumduring home games. There are 6 home games scheduled for the upcoming season. She must pay theTech athletic department a vendor’s fee of $3,000 for the season. Her stand and other equipmentwill cost her $3,500 for the season. She estimates that each hot dog she sells will cost her $0.40. shehas talked to friends at other universities who sell hot dogs at games. Based on their informationand the athletic department’s forecast that each game will sell out, she anticipates that she will sellapproximately 1,500 hot dogs during each game.a. What price should she charge for a hot dog in order to break even?b. What factors might occur during the season that would alter the volume sold and thus thebreak-even price Annie might charge?6. The college of business at Kerouac University is planning to begin an online MBA program. Theinitial start-up cost for computing equipment, facilities, course development and staff recruitmentand development is $400,000. The college plans to charge tuition of $20,000 per student per year.However, the university administration will charge the college $10,000 per student for the first 100students enrolled each year for administrative costs and its share of the tuition payments.a. How many students does the college need to enroll in the first year to break-even?b. If the college can enroll 80 students the first year, how much profit will it make?
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Match Each Description Or Function With The Correct Form Of Fiber The Type Of Fi
/in Uncategorized /by developerMatch each description or function with the correct form of fiber.
The type of fiber thought to have cholesterol-lowering properties.
(Soluble Fiber or Insoluble Fiber)
The thickening agent used in making jams and jellies.
(Soluble Fiber or Insoluble Fiber)
The fibrous non-carbohydrate found in whole grains and wheat bran.
(Soluble Fiber or Insoluble Fiber)
The type of fiber that is responsible for bowel regularity and preventing constipation.
(Soluble Fiber or Insoluble Fiber)
The type of fiber found in brown rice and whole-wheat bread.
(Soluble Fiber or Insoluble Fiber)
The type of fiber found in apples and oatmeal.
(Soluble Fiber or Insoluble Fiber)
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