A company produces bag, each of which could be sold for\$150. It has a fixed monthly cost of \$13,000 and a variable cost of \$20 per bag produced. A. Determine the company monthly total cost function B. determine the company’s monthly revenue function C determine the company’s monthly total profit function D how many bag must the company produce to break even E how many bags must the company produce to generate \$26,000 in profit? Compute A log 100 B log 1000 C log2 8 D log5. 25 E log 0.01 F log 1 G loga a

## A company produces bag, each of which could be sold for\$150. It has a fixed monthly cost of \$13,000 and a variable cost of \$20 per bag produced. A. Determine the company monthly total cost function B. determine the company’s monthly revenue function C determine the company’s monthly total profit function D how many bag must the company produce to break even E how many bags must the company produce to generate \$26,000 in profit? Compute A log 100 B log 1000 C log2 8 D log5. 25 E log 0.01 F log 1 G loga a

Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

## Project 1: Particle Trajectory in Pleated Filters Due: 12:30 pm, Dec. 1, 2015, submission through blackboard Course: Numerical Methods Instructor: Dr. Hooman V. Tafreshi Most aerosol filters are made of pleated fibrous media. This is to accommodate as much filtration media as possible in a limited space available to an air filtration unit (e.g., the engine of a car). A variety of parameters contribute to the performance of a pleated filter. These parameters include, but are not limited to, geometry of the pleat (e.g., pleat height, width, and count), microscale properties of the fibrous media (e.g., fiber diameters, fiber orientation, and solid volume fraction), aerodynamic and thermal conditions of the flow (e.g., flow velocity, temperature, and operating pressure), and particle properties (e.g., diameter, density, and shape). Figure 1: Examples of pleated air filters [1‐2]. In this project you are asked to calculate the trajectory of aerosol particles as they travel inside a rectangular pleat channel. Due to the symmetry of the pleat geometry, you only need to simulate one half of the channel (see Figure 2). Figure 2: The simulation domain and boundary conditions (the figure’s aspect ratio is altered for illustration purposes). Trajectory of the aerosol particles can be calculated in a 2‐D domain by solving the Newton’s 2nd law written for the particles in the x‐ and y‐directions, v(h) inlet velocity fibrous media v(y) y tm l h x Ui u(l) u(x) 2 2 p 1 p 1 ( , ) d x dx u x y dt  dt    2 2 p 1 p 1 ( , ) d y dy v x y dt  dt    where 2 1/18 p p   d    is the particle relaxation time, 10 μm p d  is the particle diameter, 1000 kg/m3 p   is the particle density, and   1.85105 Pa.s is the air viscosity. Also, u(x, y) and v(x, y) represent the components of the air velocity in the x and y directions inside the pleat channel, respectively. The x and y positions of the particles are denoted by xp and yp, respectively. You may use the following expressions for u(x, y) and v(x, y) .     2 3 1 2 u x, y u x y h                  sin 2 v x,y v h π y h        where   i 1 u x U x l h          is the average air velocity inside the pleat channel in the x‐direction and Ui is the velocity at the pleat entrance (assume 1 m/s for this project). l = 0.0275 m and h =0.0011 m are the pleat length and height, respectively. Writing the conservation of mass for the air flowing into the channel, you can also obtain that   i v h U h l h         . These 2nd order ODEs can easily be solved using a 4th order Rung‐Kutta method. In order to obtain realistic particle trajectories, you also need to consider proper initial conditions for the velocity of the particles: x(t  0)  0 , ( 0) i p p y t   y , p ( 0) cos i i dx t U dt    , p ( 0) sin i i dy t U dt     . where i  is the angle with respect to the axial direction by which a particle enters the pleat channel (see Figure 3). The inlet angle can be obtained from the following equation: 2 75 0.78 +0.16 1.61St i i p p i y y e h h                    where   2 St 18 2 ρPdPUi μ h  is the particles Stokes number. Figure 3: An illustration of the required particle trajectory calculation inside a rectangular pleated filter. You are asked to calculate and plot the trajectories of particles released from the vertical positions of ?? ? ? 0.05?, ?? ? ? 0.25?, ?? ? ? 0.5?, ?? ? ? 0.75? , and ?? ? ? 0.95? in one single figure. To do so, you need to track the trajectories until they reach one of the channel walls (i.e., stop when xp  l or p y  h ). Use a time step of 0.00001 sec. For more information see Ref. [3]. For additional background information see Ref. [4] and references there. In submitting your project please stick to following guidelines: 1‐ In blackboard, submit all the Matlab files and report in one single zip file. For naming your zip file, adhere to the format as: Lastname_firstname_project1.zip For instance: Einstein_albert_project1.zip 2‐ The report should be in pdf format only with the name as Project1.pdf (NO word documents .docx or .doc will be graded). 3‐ Your zip file can contain as many Matlab files as you want to submit. Also please submit the main code which TA’s should run with the name as: Project1.m (You can name the function files as you desire). Summary of what you should submit: 1‐ Runge–Kutta 4th order implementation in MATLAB. 2‐ Plot 5 particle trajectories in one graph. 3‐ Report your output (the x‐y positions of the five particles at each time step) in the form of a table with 11 columns (one for time and two for the x and y of each particle). Make sure the units are second for time and meter for the x and y. 4‐ Write a short, but yet clean and professional report describing your work. Up to 25% of your grade will be based solely on the style and formatting of your report. Use proper heading for each section of your report. Be consistent in your font size. Use Times New Roman only. Make sure that figures have proper self‐explanatory captions and are cited in the body of the report. Make sure that your figures have legends as well as x and y labels with proper and consistent fonts. Don’t forget that any number presented in the report or on the figures has to have a proper unit. Equations and pages in your report should be numbered. Embed your figures in the text. Make sure they do not have unnecessary frames around them or are not plotted on a grey background (default setting of some software programs!). inlet angle Particle trajectory i p y i 0 p x  Important Note: It is possible to solve the above ODEs using built‐in solvers such as ode45 in MATLAB, and you are encouraged to consider that for validating your MATLAB program. However, the results that you submit for this project MUST be obtained from your own implementation of the 4th order Runge‐Kutta method. You will not receive full credit if your MATALB program does not work, even if your results are absolutely correct! References: 1. http://www.airexco.net/custom‐manufacturedbr12‐inch‐pleated‐filter‐c‐108_113_114/custommadebr12‐ inch‐pleated‐filter‐p‐786.html 2. http://www.ebay.com/itm/Air‐Compressor‐Air‐Filter‐Element‐CFE‐275‐Round‐Pleated‐Filter‐ /251081172328 3. A.M. Saleh and H.V. Tafreshi, A Simple Semi‐Analytical Model for Designing Pleated Air Filters under Loading, Separation and Purification Technology 137, 94 (2014) 4. A.M. Saleh, S. Fotovati, H.V. Tafreshi, and B. Pourdeyhimi, Modeling Service Life of Pleated Filters Exposed to Poly‐Dispersed Aerosols, Powder Technology 266, 79 (2014)

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Perception checking – 1000 words Apply the perception checking process to at least 3 different individuals Write a paper including each of the following in some way: (They need not be in this order) A brief description or outline of the basic steps in the perception checking process A detailed description of your experience in at least 1 of the applications of the process A brief mention of the other applications A summary of how it worked for you–what you learned and how you think it might apply in your life As with all writing assignments in this class, Write using the active voice wherever possible Develop a good structure with opening and closing statements and supporting material Pay attention to spelling, grammar, sentence and paragraph structure Write in the most interesting way you can

## Perception checking – 1000 words Apply the perception checking process to at least 3 different individuals Write a paper including each of the following in some way: (They need not be in this order) A brief description or outline of the basic steps in the perception checking process A detailed description of your experience in at least 1 of the applications of the process A brief mention of the other applications A summary of how it worked for you–what you learned and how you think it might apply in your life As with all writing assignments in this class, Write using the active voice wherever possible Develop a good structure with opening and closing statements and supporting material Pay attention to spelling, grammar, sentence and paragraph structure Write in the most interesting way you can

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ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

## ield ENGL 2110-01 Midterm You must write an essay for each of the following prompts. Part I: Write a 1500 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Many of the readings that we have covered up to this point in the class have considered the native population that explorers encountered when they came to the “New World.” For this essay, you should examine the readings from any two of the explorers that we have encountered to this point to compare and contrast the similarities and differences between the ways that these two explorers interacted with the indigenous peoples. The thesis for this essay should make an argumentative claim as to which approach was/is more effective, and the writer should use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument the writer is making. Please note that you should avoid summarizing the texts. Instead, your focus should be on making an argument about the ways that these explorers deal with the indigenous populations. Part II: Write a 1000 word essay (you may go over this word count, but you should not fall short of this word count) on the following prompt: Now that you have considered how the explorers interacted with the indigenous populations that they encountered, it then becomes necessary to examine how the native population viewed the explorers. Choose one of the readings that we covered in the creation/emergence accounts from Native American authors. You will then make an argumentative claim for your thesis statement about the way that this writer presents the relationship between the indigenous peoples and the European explorers. Is this a positive relationship, according to this writer? Does the writer think this is a negative relationship? You should also use quotations in each body paragraph (formatted correctly according to MLA style guidelines, with attributive tags to introduce the quotations and in-text citations following each quotation) to support the argument you are making. Please note that you should only discuss one text, and that you should avoid summarizing the text and instead focus on building and supporting an argument about the way that the author views the effect that the explorers have had or will have on the native population. Due: A typed Midterm Exam is due at the beginning of class on Wednesday, September 30th. Format: The exam should be formatted according to MLA guidelines, and it should be stapled in the upper left hand corner. It has to be from the book: The Concise Health Anthology of American Literature!!!!!!

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Mary works in a factory that produces 1,000 telephones each day. When 30 telephones were sampled, it was found that 9 were defective. Estimate how many telephones are defective each day.

## Mary works in a factory that produces 1,000 telephones each day. When 30 telephones were sampled, it was found that 9 were defective. Estimate how many telephones are defective each day.

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ELEC153 Circuit Theory II M2A4 Lab: AC Parallel Circuits Introduction In this experiment we work with AC parallel circuits. As we did in the AC series circuits lab, the results obtained through Transient Analysis in MultiSim will be verified by manual calculations. Procedure 1. Figure 1 is the circuit we want to analyze.The voltage source is 24 volts peak at 1000 Hz. Figure 1: AC parallel circuit used for analysis using MultiSim Unlike the series circuit, there is no resistor in series with the voltage source that allows us to plot the current by taking advantage of its in-phase relationship. So, in order to measure the current produced by the source (total current) add a 1 Ohm resistor in series with the source. This small resistor will not affect the calculations. Figure 2: Arrangement for analyzing the current waveforms 2. Run the simulations and with the oscilloscope measure both the source voltage and the voltage across the resistor. You should get a plot similar to the following graph: Figure 3: Source voltage (red) and source current (blue) waveforms 3. From the resulting analysis plot, determine the peak current. Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5. Calculate the phase-shift. Using the method presented in the last lab, measure the time difference at the zero-crossing of the two signals. Record it here. Time difference 6. From the resulting calculation, determine the phase shift by using the following formula Record it here. Measured Phase Shift 7. Determine the phase shift by calculation. Record it here. Does it match the measured phase shift? Explain. Calculated Phase Shift 8. Change the frequency of the voltage source to 5000 Hz. Re-simulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 9. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift 10. Replace the capacitor with a 0.8 H inductor. Set the source frequency back to 1000 Hz. Perform Transient Analysis and measure the current amplitude and phase shift. Record them here: Measured Current Measured Phase Shift 11. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? Calculated Current Calculated Phase Shift 12. Change the frequency of the voltage source to 5000 Hz. Re-simulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 13. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Write-up and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

## ELEC153 Circuit Theory II M2A4 Lab: AC Parallel Circuits Introduction In this experiment we work with AC parallel circuits. As we did in the AC series circuits lab, the results obtained through Transient Analysis in MultiSim will be verified by manual calculations. Procedure 1. Figure 1 is the circuit we want to analyze.The voltage source is 24 volts peak at 1000 Hz. Figure 1: AC parallel circuit used for analysis using MultiSim Unlike the series circuit, there is no resistor in series with the voltage source that allows us to plot the current by taking advantage of its in-phase relationship. So, in order to measure the current produced by the source (total current) add a 1 Ohm resistor in series with the source. This small resistor will not affect the calculations. Figure 2: Arrangement for analyzing the current waveforms 2. Run the simulations and with the oscilloscope measure both the source voltage and the voltage across the resistor. You should get a plot similar to the following graph: Figure 3: Source voltage (red) and source current (blue) waveforms 3. From the resulting analysis plot, determine the peak current. Record it here. Measured Peak Current 4. Determine the peak current by calculation. Record it here. Does it match the measured peak current? Explain. Calculated Peak Current 5. Calculate the phase-shift. Using the method presented in the last lab, measure the time difference at the zero-crossing of the two signals. Record it here. Time difference 6. From the resulting calculation, determine the phase shift by using the following formula Record it here. Measured Phase Shift 7. Determine the phase shift by calculation. Record it here. Does it match the measured phase shift? Explain. Calculated Phase Shift 8. Change the frequency of the voltage source to 5000 Hz. Re-simulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 9. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift 10. Replace the capacitor with a 0.8 H inductor. Set the source frequency back to 1000 Hz. Perform Transient Analysis and measure the current amplitude and phase shift. Record them here: Measured Current Measured Phase Shift 11. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? Calculated Current Calculated Phase Shift 12. Change the frequency of the voltage source to 5000 Hz. Re-simulate and perform a Transient Analysis to find the new circuit current and phase angle. Measure them and record them here: Measured Current Measured Phase Shift 13. Perform the manual calculations needed to find the circuit current and phase shift. Record the calculated values here. Do they match the measured values within reason? What has happened to the circuit with an increase in frequency? Calculated Current Calculated Phase Shift Write-up and Submission In general, for each lab you do, you will be asked to setup certain circuits, simulate them, record the results, verify the results are correct by hand, and then discuss the solution. Your lab write-up should contain a one page, single spaced discussion of the lab experiment, what went right for you, what you had difficulty with, what you learned from the experiment, how it applies to our coursework, and any other comment you can think of. In addition, you should include screen shots from the MultiSim software and any other figure, table, or diagram as necessary.

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