Mass Balance Company is manufacturing a new digitalscale for use by a large chemical company. The order isfor 40 units. The first scale took 60 hours of direct labor.The second unit took 48 hours to complete.a. What is the learning rate?b. What is the estimated time for the 40th unit?c. What is the estimated total time for producing all40 units?d. What is the average time per unit for producing thelast 10 units (#31–#40)?Please show all work and explain why each answer was chosen.

Learning Curves Find coefficient DataObservation 1Observation 2 Unit number12 Time6048 Given DataGiven Data a. What is the learning rate? Learning Rate =Learning Rate = Time for…

 

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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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Can 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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Mastery Objectives 

• Develop one mastery concept and 5 mastery objectives for your grade and subject. 
  • Map these objectives to the corresponding state objective and/or CCSS. 
• Respond to at least one of your classmates. 
  • Describe at least 2 types of assessments that could be used to test one or more mastery objectives.  
  • Only one assessment can be a formal test.  
• Peer Response

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

• Define the main idea.
• Explain the main idea of an informative text.
• Define the main character of the text.
• Explain the plot of the story.
• Lit strategies used to find the main idea of a story.

 

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