An approximation for the boundary-layer shape in the formula where U is stream velocity far from the wall and s is the boundary layer thickness, if the fluid is helium at 20c I atm, and if u=10.8 m/s and s =3 mm, use the formula to (a) estimate the wall shear stress in pa ; and (b) find the position in boundary layer where is one half

## An approximation for the boundary-layer shape in the formula where U is stream velocity far from the wall and s is the boundary layer thickness, if the fluid is helium at 20c I atm, and if u=10.8 m/s and s =3 mm, use the formula to (a) estimate the wall shear stress in pa ; and (b) find the position in boundary layer where is one half

MAE 214 – Fall 2015 Homework 3 Due: October 1, 2015 – Thursday by 1:00 p.m. Total Problems: 4 (including Extra Credit), Total Points: 105 1. Make a solid works part model from the given figure below. All dimensions are in millimeters. All sketches must be fully defined. Also create a drawing sheet and dimension it as shown. You can use a hole call out option under annotation to dimension a counter bore hole. (30 points) Save your part files as follows: My Documents/Homework 3 Folder/Prob1_LastName.SLDPRT My Documents/ Homework 3 Folder/Prob1_LastName.SLDDRW 2. Make a solid works part of the given figure below and also make a drawing sheet – front, top and right side views using 3rd angle projection method. Dimension the views with appropriate dimension technique. All dimensions are in mm. (30 points) Save your part file and drawing sheet as follows: Documents/Homework 3 folder/Problem 2_Last Name.SLDPRT Documents/Homework 3 folder/Problem 2_Last Name.SLDDRW 3. Make a solid works part file for the given figure below. All sketches must be fully defined. Your design tree menu must have advanced features i.e. plane, mirror, and fillet. The spot facing (SF) must be defined in a problem. The inclined cut must be created with an offset sketch and extrude cut or a suitable sketch that uses “up to surface” option. (40 points) Your part model must stick to the isometric view as it is shown here. Save your part file into: My documents/Homework 3 Folder/Problem3_Last Name.SLDPRT Given: A = 76 B = 127 Unit: MMGS ALL ROUNDS (FILLET) EQUAL 6 MM 4. (Extra Credit) Make a solid works part from the given figure below. All sketches must be fully defined. Save your part file to Documents/Homework3 Folder/Prob#4_Last Name.SLDPRT All dimensions are in millimeters. (5 points)

## MAE 214 – Fall 2015 Homework 3 Due: October 1, 2015 – Thursday by 1:00 p.m. Total Problems: 4 (including Extra Credit), Total Points: 105 1. Make a solid works part model from the given figure below. All dimensions are in millimeters. All sketches must be fully defined. Also create a drawing sheet and dimension it as shown. You can use a hole call out option under annotation to dimension a counter bore hole. (30 points) Save your part files as follows: My Documents/Homework 3 Folder/Prob1_LastName.SLDPRT My Documents/ Homework 3 Folder/Prob1_LastName.SLDDRW 2. Make a solid works part of the given figure below and also make a drawing sheet – front, top and right side views using 3rd angle projection method. Dimension the views with appropriate dimension technique. All dimensions are in mm. (30 points) Save your part file and drawing sheet as follows: Documents/Homework 3 folder/Problem 2_Last Name.SLDPRT Documents/Homework 3 folder/Problem 2_Last Name.SLDDRW 3. Make a solid works part file for the given figure below. All sketches must be fully defined. Your design tree menu must have advanced features i.e. plane, mirror, and fillet. The spot facing (SF) must be defined in a problem. The inclined cut must be created with an offset sketch and extrude cut or a suitable sketch that uses “up to surface” option. (40 points) Your part model must stick to the isometric view as it is shown here. Save your part file into: My documents/Homework 3 Folder/Problem3_Last Name.SLDPRT Given: A = 76 B = 127 Unit: MMGS ALL ROUNDS (FILLET) EQUAL 6 MM 4. (Extra Credit) Make a solid works part from the given figure below. All sketches must be fully defined. Save your part file to Documents/Homework3 Folder/Prob#4_Last Name.SLDPRT All dimensions are in millimeters. (5 points)

What is the concentration (M) of 3 CH OH in a solution prepared by dissolving 11.7 g of 3 CH OH in sufficient water to give exactly 230 mL of solution? A) 11.9 B) -3 1.59× 10 C) 0.0841 D) 1.59 E) -3 11.9 ×10

## What is the concentration (M) of 3 CH OH in a solution prepared by dissolving 11.7 g of 3 CH OH in sufficient water to give exactly 230 mL of solution? A) 11.9 B) -3 1.59× 10 C) 0.0841 D) 1.59 E) -3 11.9 ×10

D) 1.59
Question 3 (1 point) Historically, alternative medicine has been well accepted and integrated by the mainstream medical community. Question 3 options: True False

## Question 3 (1 point) Historically, alternative medicine has been well accepted and integrated by the mainstream medical community. Question 3 options: True False

Question 3 (1 point)   Historically, alternative medicine has been … Read More...
Two wires #1 carries a current I, toward the top of the page and is held rigidly in place. wire #2 carries a current I to the left and is free to move. wire # 2 will experience a magnatic force which cause it to; 1) move down , 2) move up , 3) rotate clockwise , 4) rotate counterclockwise, 5) move right.

## Two wires #1 carries a current I, toward the top of the page and is held rigidly in place. wire #2 carries a current I to the left and is free to move. wire # 2 will experience a magnatic force which cause it to; 1) move down , 2) move up , 3) rotate clockwise , 4) rotate counterclockwise, 5) move right.

FSE 100 Extra Credit (20 points) Instructions: Read the description below and work through the design process to build an automated waste sorting system. Turn in the following deliverables in one document, typed: 1. Problem Statement – 1 point 2. Technical System Requirements (at least 3 complete sentences using “shall”) – 3 points 3. Judging Criteria (at least 3, explain why you chose them) – 2 points 4. AHP – 2 points 5. Summaries of your 3 design options (paragraph minimum for each option) – 3 points 6. Design Decision Matrix – 3 points 7. Orthographic Drawing of your final design (3 projections required) – 3 points 8. Activity Diagram of how your sorter functions – 3 points Description: The city of Tempe waste management has notified ASU that due to the exceptional effort the Sundevil students have made in the sustainability area, ASU has been contributing three times the amount of recyclable materials than what was predicted on a monthly basis. Unfortunately, due to the immense amount of materials being delivered, the city of Tempe waste management has asked for assistance from ASU prior to picking up the recyclable waste. They have requested that ASU implement an automated waste sorting system that would pre-filter all the materials so the city of Tempe can collect the materials based on one of three types and process the waste much faster. ASU has hired you to design an automated sorter, but due to the unexpected nature of this request, ASU prefers that this design be as simple and inexpensive to build as possible. The city of Tempe would like to have the waste categorized as either glass, plastic, or metal. Paper will not be considered in this design. Any glass that is sorted in your device needs to stay intact, and not break. Very few people will be able to monitor this device as it sorts, so it must be able to sort the items with no input from a user, as quickly as possible. This design cannot exceed 2m in length, width, or height, but the weight is unlimited. ASU is not giving any guidance as to the materials you can use, so you are free to shop for whatever you’d like, but keep in mind, the final cost of this device must be as inexpensive as possible. Submit through Blackboard or print out your document and turn it in to me no later than the date shown on Blackboard.

## FSE 100 Extra Credit (20 points) Instructions: Read the description below and work through the design process to build an automated waste sorting system. Turn in the following deliverables in one document, typed: 1. Problem Statement – 1 point 2. Technical System Requirements (at least 3 complete sentences using “shall”) – 3 points 3. Judging Criteria (at least 3, explain why you chose them) – 2 points 4. AHP – 2 points 5. Summaries of your 3 design options (paragraph minimum for each option) – 3 points 6. Design Decision Matrix – 3 points 7. Orthographic Drawing of your final design (3 projections required) – 3 points 8. Activity Diagram of how your sorter functions – 3 points Description: The city of Tempe waste management has notified ASU that due to the exceptional effort the Sundevil students have made in the sustainability area, ASU has been contributing three times the amount of recyclable materials than what was predicted on a monthly basis. Unfortunately, due to the immense amount of materials being delivered, the city of Tempe waste management has asked for assistance from ASU prior to picking up the recyclable waste. They have requested that ASU implement an automated waste sorting system that would pre-filter all the materials so the city of Tempe can collect the materials based on one of three types and process the waste much faster. ASU has hired you to design an automated sorter, but due to the unexpected nature of this request, ASU prefers that this design be as simple and inexpensive to build as possible. The city of Tempe would like to have the waste categorized as either glass, plastic, or metal. Paper will not be considered in this design. Any glass that is sorted in your device needs to stay intact, and not break. Very few people will be able to monitor this device as it sorts, so it must be able to sort the items with no input from a user, as quickly as possible. This design cannot exceed 2m in length, width, or height, but the weight is unlimited. ASU is not giving any guidance as to the materials you can use, so you are free to shop for whatever you’d like, but keep in mind, the final cost of this device must be as inexpensive as possible. Submit through Blackboard or print out your document and turn it in to me no later than the date shown on Blackboard.

Problem statement      ASU has been contributing three … Read More...
Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

## Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

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