ENGR 1120 – PROGRAMMING FOR ENGINEERS (MATLAB) Homework Program #2 Objectives: Demonstrate knowledge of data files, vector variables, intrinsic functions, subscript manipulation, for loops, and plotting in MATLAB. You have been given a set of ASCII data files that contain directions for laying out patterns in a field. The data files contain in the first column a distance to travel and in the second column a direction heading. Unfortunately, the person who created the data did not have a good understanding of orienteering and the direction headings are given as referenced to a clock face. The pattern begins at the origin of a Cartesian coordinate system with the person facing 12 o’clock, see the figure below. The figure shows an example of the first step in the pattern being a distance of 1.5 feet in the direction of 7 o’clock. All direction headings are given in terms of this clock orientation. The distance values given are in feet. There are 5 data files provided online for testing of the program. Write a script file that will allow the user to input from the keyboard the filename of the file that they wish to analyze. Load only that ONE data file and plot the resulting pattern. Once each point forming the pattern has been located, find and designate on the plot which of the resulting nodes was the farthest away from the origin. Also find and designate the center of the pattern as defined to occur at the coordinate location corresponding to (average x, average y). When plotting the resulting pattern on the Cartesian coordinate system, set the axes limits to appropriate values. HINT: Correlate the direction headings provided in the data files to a Cartesian coordinate system by using the following vector in your script file. This requires subscript manipulation. angle = [60; 30; 0; 330; 300; 270; 240; 210; 180; 150; 120; 90] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 7 8 9 10 11 12 you are here

## ENGR 1120 – PROGRAMMING FOR ENGINEERS (MATLAB) Homework Program #2 Objectives: Demonstrate knowledge of data files, vector variables, intrinsic functions, subscript manipulation, for loops, and plotting in MATLAB. You have been given a set of ASCII data files that contain directions for laying out patterns in a field. The data files contain in the first column a distance to travel and in the second column a direction heading. Unfortunately, the person who created the data did not have a good understanding of orienteering and the direction headings are given as referenced to a clock face. The pattern begins at the origin of a Cartesian coordinate system with the person facing 12 o’clock, see the figure below. The figure shows an example of the first step in the pattern being a distance of 1.5 feet in the direction of 7 o’clock. All direction headings are given in terms of this clock orientation. The distance values given are in feet. There are 5 data files provided online for testing of the program. Write a script file that will allow the user to input from the keyboard the filename of the file that they wish to analyze. Load only that ONE data file and plot the resulting pattern. Once each point forming the pattern has been located, find and designate on the plot which of the resulting nodes was the farthest away from the origin. Also find and designate the center of the pattern as defined to occur at the coordinate location corresponding to (average x, average y). When plotting the resulting pattern on the Cartesian coordinate system, set the axes limits to appropriate values. HINT: Correlate the direction headings provided in the data files to a Cartesian coordinate system by using the following vector in your script file. This requires subscript manipulation. angle = [60; 30; 0; 330; 300; 270; 240; 210; 180; 150; 120; 90] -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 7 8 9 10 11 12 you are here

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Lab Assignment-09 Note: Create and save m-files for each problem individually. Copy all the m-files into a ‘single’ folder and upload the folder to D2L. Read chapters 2 and chapter 3.1-3.3 of the textbook (Introduction to MATLAB 7 for Engineers), solve the following problems in MATLAB. Given A= [■(3&-2&1@6&8&-5@7&9&10)] ; B= [■(6&9&-4@7&5&3@-8&2&1)] ; C= [■(-7&-5&2@10&6&1@3&-9&8)] ; Find the following A+B+C Verify the associative law (A+B)+C=A+ (B+C) D=Transpose(AB) E=A4 + B2 – C3 Find F, given that F = E-1 * D-1 – (AT) -1 Use MATLAB to solve the following set of equations 5x+7y + 9z = 12 7x- 4y + 8z = 86 15x- 9y – 6z = -57 Write a function that accepts temperature in degrees F and computes the corresponding value in degree C. The relation between the two is Aluminum alloys are made by adding other elements to aluminum to improve its properties, such as hardness or tensile strength. The following table shows the composition of five commonly used alloys, which are known by their alloy numbers ( 2024, 6061, and so on) [Kutz, 1999]. Obtain a matrix algorithm to compute the amounts of raw materials needed to produce a given amount of each alloy. Use MATLAB to determine how much raw material each type is needed to produce 1000tons of each alloy. Composition of aluminum alloys Alloy % Cu % Mg % Mn % Si % Zn 2024 4.4 1.5 0.6 0 0 6061 0 1 0 0.6 0 7005 0 1.4 0 0 4.5 7075 1.6 2.5 0 0 5.6 356.0 0 0.3 0 7 0

## Lab Assignment-09 Note: Create and save m-files for each problem individually. Copy all the m-files into a ‘single’ folder and upload the folder to D2L. Read chapters 2 and chapter 3.1-3.3 of the textbook (Introduction to MATLAB 7 for Engineers), solve the following problems in MATLAB. Given A= [■(3&-2&1@6&8&-5@7&9&10)] ; B= [■(6&9&-4@7&5&3@-8&2&1)] ; C= [■(-7&-5&2@10&6&1@3&-9&8)] ; Find the following A+B+C Verify the associative law (A+B)+C=A+ (B+C) D=Transpose(AB) E=A4 + B2 – C3 Find F, given that F = E-1 * D-1 – (AT) -1 Use MATLAB to solve the following set of equations 5x+7y + 9z = 12 7x- 4y + 8z = 86 15x- 9y – 6z = -57 Write a function that accepts temperature in degrees F and computes the corresponding value in degree C. The relation between the two is Aluminum alloys are made by adding other elements to aluminum to improve its properties, such as hardness or tensile strength. The following table shows the composition of five commonly used alloys, which are known by their alloy numbers ( 2024, 6061, and so on) [Kutz, 1999]. Obtain a matrix algorithm to compute the amounts of raw materials needed to produce a given amount of each alloy. Use MATLAB to determine how much raw material each type is needed to produce 1000tons of each alloy. Composition of aluminum alloys Alloy % Cu % Mg % Mn % Si % Zn 2024 4.4 1.5 0.6 0 0 6061 0 1 0 0.6 0 7005 0 1.4 0 0 4.5 7075 1.6 2.5 0 0 5.6 356.0 0 0.3 0 7 0

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Question 1 In order to properly manage expenses, the company investigates the amount of money spent by its sales office. The below numbers are related to six randomly selected receipts provided by the staff. \$147 \$124 \$93 \$158 \$164 \$171 a) Calculate ̅ , s2 and s for the expense data. b) Assume that the distribution of expenses is approximately normally distributed. Calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all expenses by the sales office. c) If a member of the sales office submits a receipt with the amount of \$190, should this expense be considered unusually high? Explain your answer. d) Compute and interpret the z-score for each of the six expenses. Question 2 A survey presents the results of a concept study for the taste of new food. Three hundred consumers between 18 and 49 years old were randomly selected. After sampling the new cuisine, each was asked to rate the quality of food. The rating was made on a scale from 1 to 5, with 5 representing “extremely agree with the quality” and with 1 representing “not at all agree with the new food.” The results obtained are given in Table 1. Estimate the probability that a randomly selected 18- to 49-year-old consumer a) Would give the phrase a rating of 4. b) Would give the phrase a rating of 3 or higher. c) Is in the 18–26 age group; the 27–35 age group; the 36–49 age group. d) Is a male who gives the phrase a rating of 5. e) Is a 36- to 49-year-old who gives the phrase a rating of 2. f) Estimate the probability that a randomly selected 18- to 49-year-old consumer is a 27- to 49-year-old who gives the phrase a rating of 3. g) Estimate the probability that a randomly selected 18- to 49-year-old consumer would 1) give the phrase a rating of 2 or 4 given that the consumer is male; 2) give the phrase a rating of 4 or 5 given that the consumer is female. Based on the results of parts 1 and 2, is the appeal of the phrase among males much different from the appeal of the phrase among females? Explain. h) Give the phrase a rating of 4 or 5, 1) given that the consumer is in the 18–26 age group; 2) given that the consumer is in the 27–35 age group; 3) given that the consumer is in the 36–49 age group. Table 1. Gender Age Group Rating Total Male Female 18-26 27-35 36-49 Extremely Appealing (5) 151 68 83 48 66 37 (4) 91 51 40 36 36 19 (3) 36 21 15 9 12 15 (2) 13 7 6 4 6 3 Not at all appealing(1) 9 3 6 4 3 2 Question 3 Based on the reports provided by the brokers, it is concluded that the annual returns on common stocks are approximately normally distributed with a mean of 17.8 percent and a standard deviation of 29.3 percent. On the other hand, the company reports that the annual returns on tax-free municipal bonds are approximately normally distributed with a mean return of 4.7 percent and a standard deviation of 10.2 percent. Find the probability that a randomly selected a) Common stock will give a positive yearly return. b) Tax-free municipal bond will give a positive yearly return. c) Common stock will give more than a 13 percent return. d) Tax-free municipal bond will give more than a 11.5 percent return. e) Common stock will give a loss of at least 7 percent. f) Tax-free municipal bond will give a loss of at least 10 percent. Question 4 Based on a sample of 176 workers, it is estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. It is also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. We randomly select a sample of 100 workers. a) What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? Assume σ equals 1.3 days. b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 workers will exceed 1.5 days? Assume σ equals 1.8 days. c) A sample of 100 workers is randomly selected. Suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.0 day? Explain. Assume σ still equals 1.8 days.

## Question 1 In order to properly manage expenses, the company investigates the amount of money spent by its sales office. The below numbers are related to six randomly selected receipts provided by the staff. \$147 \$124 \$93 \$158 \$164 \$171 a) Calculate ̅ , s2 and s for the expense data. b) Assume that the distribution of expenses is approximately normally distributed. Calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all expenses by the sales office. c) If a member of the sales office submits a receipt with the amount of \$190, should this expense be considered unusually high? Explain your answer. d) Compute and interpret the z-score for each of the six expenses. Question 2 A survey presents the results of a concept study for the taste of new food. Three hundred consumers between 18 and 49 years old were randomly selected. After sampling the new cuisine, each was asked to rate the quality of food. The rating was made on a scale from 1 to 5, with 5 representing “extremely agree with the quality” and with 1 representing “not at all agree with the new food.” The results obtained are given in Table 1. Estimate the probability that a randomly selected 18- to 49-year-old consumer a) Would give the phrase a rating of 4. b) Would give the phrase a rating of 3 or higher. c) Is in the 18–26 age group; the 27–35 age group; the 36–49 age group. d) Is a male who gives the phrase a rating of 5. e) Is a 36- to 49-year-old who gives the phrase a rating of 2. f) Estimate the probability that a randomly selected 18- to 49-year-old consumer is a 27- to 49-year-old who gives the phrase a rating of 3. g) Estimate the probability that a randomly selected 18- to 49-year-old consumer would 1) give the phrase a rating of 2 or 4 given that the consumer is male; 2) give the phrase a rating of 4 or 5 given that the consumer is female. Based on the results of parts 1 and 2, is the appeal of the phrase among males much different from the appeal of the phrase among females? Explain. h) Give the phrase a rating of 4 or 5, 1) given that the consumer is in the 18–26 age group; 2) given that the consumer is in the 27–35 age group; 3) given that the consumer is in the 36–49 age group. Table 1. Gender Age Group Rating Total Male Female 18-26 27-35 36-49 Extremely Appealing (5) 151 68 83 48 66 37 (4) 91 51 40 36 36 19 (3) 36 21 15 9 12 15 (2) 13 7 6 4 6 3 Not at all appealing(1) 9 3 6 4 3 2 Question 3 Based on the reports provided by the brokers, it is concluded that the annual returns on common stocks are approximately normally distributed with a mean of 17.8 percent and a standard deviation of 29.3 percent. On the other hand, the company reports that the annual returns on tax-free municipal bonds are approximately normally distributed with a mean return of 4.7 percent and a standard deviation of 10.2 percent. Find the probability that a randomly selected a) Common stock will give a positive yearly return. b) Tax-free municipal bond will give a positive yearly return. c) Common stock will give more than a 13 percent return. d) Tax-free municipal bond will give more than a 11.5 percent return. e) Common stock will give a loss of at least 7 percent. f) Tax-free municipal bond will give a loss of at least 10 percent. Question 4 Based on a sample of 176 workers, it is estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. It is also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. We randomly select a sample of 100 workers. a) What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? Assume σ equals 1.3 days. b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 workers will exceed 1.5 days? Assume σ equals 1.8 days. c) A sample of 100 workers is randomly selected. Suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.0 day? Explain. Assume σ still equals 1.8 days.

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Question 1, chap 33, sect 3. part 1 of 2 10 points The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between 7.5 × 1014 Hz and 1.0 × 1015 Hz. The speed of light is 3 × 108 m/s. What is the largest wavelength to which these frequencies correspond? Question 3, chap 33, sect 3. part 1 of 3 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 4, chap 33, sect 3. part 2 of 3 10 points Find the period of the wave. Question 2, chap 33, sect 3. part 2 of 2 10 points What is the smallest wavelength? Question 5, chap 33, sect 3. part 3 of 3 10 points At some point and some instant, the electric field has has a value of 998 N/C. Calculate the magnitude of the magnetic field at this point and this instant. Question 6, chap 33, sect 3. part 1 of 2 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 8, chap 33, sect 3. part 1 of 1 10 points The magnetic field amplitude of an electromagnetic wave is 9.9 × 10−6 T. The speed of light is 2.99792 × 108 m/s . Calculate the amplitude of the electric field if the wave is traveling in free space. Question 7, chap 33, sect 3. part 2 of 2 10 points At some point and some instant, the electric field has has a value of 998 V/m. Calculate the magnitude of the magnetic field at this point and this instant. Question 9, chap 33, sect 5. part 1 of 1 10 points The cable is carrying the current I(t). at the surface of a long transmission cable of resistivity ρ, length ℓ and radius a, using the expression ~S = 1 μ0 ~E × ~B . Question 10, chap 33, sect 5. part 1 of 1 10 points In 1965 Penzias and Wilson discovered the cosmic microwave radiation left over from the Big Bang expansion of the universe. The energy density of this radiation is 7.64 × 10−14 J/m3. The speed of light 2.99792 × 108 m/s and the permeability of free space is 4π × 10−7 N/A2. Determine the corresponding electric field amplQuestion 11, chap 33, sect 5. part 1 of 5 10 points Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 998 V/m in the positive y-direction. The wave is traveling in the positive x-direction. x y z E wave propagation The speed of light is 2.99792×108 m/s, the permeability of free space is 4π×10−7 T ・ N/A and the permittivity of free space 8.85419 × 10−12 C2/N ・ m2. Compute the instantaneous magnitude of the magnetic field at the same point and time.itude. Question 12, chap 33, sect 5. part 2 of 5 10 points What is the instantaneous magnitude of the Poynting vector at the same point and time? Question 13, chap 33, sect 5. part 3 of 5 10 points What are the directions of the instantaneous magnetic field and theQuestion 14, chap 33, sect 5. part 4 of 5 10 points What is the instantaneous value of the energy density of the electric field? Question 16, chap 33, sect 6. part 1 of 4 10 points Consider an electromagnetic plane wave with time average intensity 104 W/m2 . The speed of light is 2.99792 × 108 m/s and the permeability of free space is 4 π × 10−7 T・m/A. What is its maximum electric field? What is the instantaneous value of the energy density of the magnetic field? Question 17, chap 33, sect 6. part 2 of 4 10 points What is the the maximum magnetic field? Question 19, chap 33, sect 6. part 4 of 4 10 points Consider an electromagnetic wave pattern as shown in the figure below. Question 18, chap 33, sect 6. part 3 of 4 10 points What is the pressure on a surface which is perpendicular to the beam and is totally reflective? Question 20, chap 33, sect 8. part 1 of 1 10 points A coin is at the bottom of a beaker. The beaker is filled with 1.6 cm of water (n1 = 1.33) covered by 2.1 cm of liquid (n2 = 1.4) floating on the water. How deep does the coin appear to be from the upper surface of the liquid (near the top of the beaker)? An cylindrical opaque drinking glass has a diameter 3 cm and height h, as shown in the figure. An observer’s eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.4 . θi h d θr eye Calculate the angle θr . Question 22, chap 33, sect 8. part 2 of 2 10 points Calculate the height h of the glass.

## Question 1, chap 33, sect 3. part 1 of 2 10 points The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, particularly light with frequencies between 7.5 × 1014 Hz and 1.0 × 1015 Hz. The speed of light is 3 × 108 m/s. What is the largest wavelength to which these frequencies correspond? Question 3, chap 33, sect 3. part 1 of 3 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 4, chap 33, sect 3. part 2 of 3 10 points Find the period of the wave. Question 2, chap 33, sect 3. part 2 of 2 10 points What is the smallest wavelength? Question 5, chap 33, sect 3. part 3 of 3 10 points At some point and some instant, the electric field has has a value of 998 N/C. Calculate the magnitude of the magnetic field at this point and this instant. Question 6, chap 33, sect 3. part 1 of 2 10 points A plane electromagnetic sinusoidal wave of frequency 10.7 MHz travels in free space. The speed of light is 2.99792 × 108 m/s. Determine the wavelength of the wave. Question 8, chap 33, sect 3. part 1 of 1 10 points The magnetic field amplitude of an electromagnetic wave is 9.9 × 10−6 T. The speed of light is 2.99792 × 108 m/s . Calculate the amplitude of the electric field if the wave is traveling in free space. Question 7, chap 33, sect 3. part 2 of 2 10 points At some point and some instant, the electric field has has a value of 998 V/m. Calculate the magnitude of the magnetic field at this point and this instant. Question 9, chap 33, sect 5. part 1 of 1 10 points The cable is carrying the current I(t). at the surface of a long transmission cable of resistivity ρ, length ℓ and radius a, using the expression ~S = 1 μ0 ~E × ~B . Question 10, chap 33, sect 5. part 1 of 1 10 points In 1965 Penzias and Wilson discovered the cosmic microwave radiation left over from the Big Bang expansion of the universe. The energy density of this radiation is 7.64 × 10−14 J/m3. The speed of light 2.99792 × 108 m/s and the permeability of free space is 4π × 10−7 N/A2. Determine the corresponding electric field amplQuestion 11, chap 33, sect 5. part 1 of 5 10 points Consider a monochromatic electromagnetic plane wave propagating in the x direction. At a particular point in space, the magnitude of the electric field has an instantaneous value of 998 V/m in the positive y-direction. The wave is traveling in the positive x-direction. x y z E wave propagation The speed of light is 2.99792×108 m/s, the permeability of free space is 4π×10−7 T ・ N/A and the permittivity of free space 8.85419 × 10−12 C2/N ・ m2. Compute the instantaneous magnitude of the magnetic field at the same point and time.itude. Question 12, chap 33, sect 5. part 2 of 5 10 points What is the instantaneous magnitude of the Poynting vector at the same point and time? Question 13, chap 33, sect 5. part 3 of 5 10 points What are the directions of the instantaneous magnetic field and theQuestion 14, chap 33, sect 5. part 4 of 5 10 points What is the instantaneous value of the energy density of the electric field? Question 16, chap 33, sect 6. part 1 of 4 10 points Consider an electromagnetic plane wave with time average intensity 104 W/m2 . The speed of light is 2.99792 × 108 m/s and the permeability of free space is 4 π × 10−7 T・m/A. What is its maximum electric field? What is the instantaneous value of the energy density of the magnetic field? Question 17, chap 33, sect 6. part 2 of 4 10 points What is the the maximum magnetic field? Question 19, chap 33, sect 6. part 4 of 4 10 points Consider an electromagnetic wave pattern as shown in the figure below. Question 18, chap 33, sect 6. part 3 of 4 10 points What is the pressure on a surface which is perpendicular to the beam and is totally reflective? Question 20, chap 33, sect 8. part 1 of 1 10 points A coin is at the bottom of a beaker. The beaker is filled with 1.6 cm of water (n1 = 1.33) covered by 2.1 cm of liquid (n2 = 1.4) floating on the water. How deep does the coin appear to be from the upper surface of the liquid (near the top of the beaker)? An cylindrical opaque drinking glass has a diameter 3 cm and height h, as shown in the figure. An observer’s eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled to the brim with a transparent liquid, the observer can just barely see the center of the bottom of the glass. The liquid in the drinking glass has an index of refraction of 1.4 . θi h d θr eye Calculate the angle θr . Question 22, chap 33, sect 8. part 2 of 2 10 points Calculate the height h of the glass.

Find the magnification.

## Find the magnification.

Find the COM for a rod of uniform linear density, λ, and length l.

## Find the COM for a rod of uniform linear density, λ, and length l.

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Find Io in the network in Fig. P5.86 using source transformer.

## Find Io in the network in Fig. P5.86 using source transformer.

This week serves an opportunity for you to serve as a public relations strategist! Go to any respectable media outlet (online, tv, print, etc). Find a story that provides an example of a public relations problem or opportunity. It can be local, state, regional, national or international in nature. (Note: no fair citing the obvious; try to be creative in your story choice). 1) list the story link so we can refer to it when we are responding in the forum 2) provide a brief recap of the situation. (This should serve as about 1/2 of your posting) 3) provide a brief recommendation/suggestion of how the company/organization/celebrity, etc. should handle it from a public relations perspective. REMEMBER: it doesn’t have to be negative! (This should serve as the other 1/2 of your posting) 4) provide a question for your colleagues to ponder/respond to in the forum.

## This week serves an opportunity for you to serve as a public relations strategist! Go to any respectable media outlet (online, tv, print, etc). Find a story that provides an example of a public relations problem or opportunity. It can be local, state, regional, national or international in nature. (Note: no fair citing the obvious; try to be creative in your story choice). 1) list the story link so we can refer to it when we are responding in the forum 2) provide a brief recap of the situation. (This should serve as about 1/2 of your posting) 3) provide a brief recommendation/suggestion of how the company/organization/celebrity, etc. should handle it from a public relations perspective. REMEMBER: it doesn’t have to be negative! (This should serve as the other 1/2 of your posting) 4) provide a question for your colleagues to ponder/respond to in the forum.

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