QUESTION 1 1. Convert 30 degrees 2 minutes to decimal degrees. Give this answer to 6 decimal places. Do not provide units. You know those are decimal degrees. 5 points QUESTION 2 1. Convert 342 degrees 6 minutes and 41 seconds to decimal degrees. Show your answers to only 6 decimal places. Do not give units. 5 points QUESTION 3 1. COMPUTE the sin of 52 degrees. Give the answer to 6 decimal places. 5 points QUESTION 4 1. What is the sine of 277 degrees and 16 minutes? Give your answer to 6 decimal places. Pay attention to rounding. 5 points QUESTION 5 1. This is a right triangle problem. Angle A is 90 degrees. Draw the triangle and label it as we did in lecture. If angle B is 24 degrees 43 minutes and side c is 395.82 feet, what is the distance in feet of side b? Give your answer to two decimal places. Do not provide units. Those are in feet – right? 10 points QUESTION 6 1. This is a right triangle problem with angle A being the 90 degree angle. It should look like the one from lecture. If angle B is 25 degrees 18 minutes and side c is 206.1 feet, what is the distance to two decimal places of side a? Give your answer to two decimal places. Do not provide units – those are in feet. 10 points QUESTION 7 1. You are given a right triangle with angle A being the 90 degree angle – just like in lecture. If angle C is 42 degrees 9 minutes and side a is 401.73 feet, what is the length of side c? Give your answer to two decimal places. The units are feet – don’t list those. 10 points QUESTION 8 Ad by Browse Safe | Close 1. It is desired to determine the height of a flagpole. Assuming that the ground is level, an instrument is set up 227.59 feet from the flagpole with its telescope centered 5.31 feet above the ground. The telescope is sighted horizontally to a point 5.31 feet from the bottom of the flagpole and then the angle at the instrument looking to the top of the pole is measured. That angle is 26 degrees 51 minutes. How tall is the flagpole from its base? Give your answer to two decimal places with NO units. 10 points QUESTION 9 1. You are hiking in the mountains. For every 100.00 feet you would be walking horizontally, you have increased your elevation by 4 feet. At what grade are you climbing? Give your answer to three decimal places. Hint: Your units will be in ft/ft. 5 points QUESTION 10 1. A grade of -0.9 percent is being considered for a mountain roadway. The elevation at the initial point is 2,848.25 feet and a horizontal distance of 4,377.51 needs to be covered. What is the elevation at the end of the grade? 10 points QUESTION 11 1. A slope distance was measured between two points (A and T) and determined to be 4,788.68 feet. At point A the elevation is 857.23 feet and at point T the elevation is 877.96 feet. What is the horizontal distance between A and T?

QUESTION 1 1. Convert 30 degrees 2 minutes to decimal degrees. Give this answer to 6 decimal places. Do not provide units. You know those are decimal degrees. 5 points QUESTION 2 1. Convert 342 degrees 6 minutes and 41 seconds to decimal degrees. Show your answers to only 6 decimal places. Do not give units. 5 points QUESTION 3 1. COMPUTE the sin of 52 degrees. Give the answer to 6 decimal places. 5 points QUESTION 4 1. What is the sine of 277 degrees and 16 minutes? Give your answer to 6 decimal places. Pay attention to rounding. 5 points QUESTION 5 1. This is a right triangle problem. Angle A is 90 degrees. Draw the triangle and label it as we did in lecture. If angle B is 24 degrees 43 minutes and side c is 395.82 feet, what is the distance in feet of side b? Give your answer to two decimal places. Do not provide units. Those are in feet – right? 10 points QUESTION 6 1. This is a right triangle problem with angle A being the 90 degree angle. It should look like the one from lecture. If angle B is 25 degrees 18 minutes and side c is 206.1 feet, what is the distance to two decimal places of side a? Give your answer to two decimal places. Do not provide units – those are in feet. 10 points QUESTION 7 1. You are given a right triangle with angle A being the 90 degree angle – just like in lecture. If angle C is 42 degrees 9 minutes and side a is 401.73 feet, what is the length of side c? Give your answer to two decimal places. The units are feet – don’t list those. 10 points QUESTION 8 Ad by Browse Safe | Close 1. It is desired to determine the height of a flagpole. Assuming that the ground is level, an instrument is set up 227.59 feet from the flagpole with its telescope centered 5.31 feet above the ground. The telescope is sighted horizontally to a point 5.31 feet from the bottom of the flagpole and then the angle at the instrument looking to the top of the pole is measured. That angle is 26 degrees 51 minutes. How tall is the flagpole from its base? Give your answer to two decimal places with NO units. 10 points QUESTION 9 1. You are hiking in the mountains. For every 100.00 feet you would be walking horizontally, you have increased your elevation by 4 feet. At what grade are you climbing? Give your answer to three decimal places. Hint: Your units will be in ft/ft. 5 points QUESTION 10 1. A grade of -0.9 percent is being considered for a mountain roadway. The elevation at the initial point is 2,848.25 feet and a horizontal distance of 4,377.51 needs to be covered. What is the elevation at the end of the grade? 10 points QUESTION 11 1. A slope distance was measured between two points (A and T) and determined to be 4,788.68 feet. At point A the elevation is 857.23 feet and at point T the elevation is 877.96 feet. What is the horizontal distance between A and T?

Question no Assignment 2 1 30.0333333 degrees 2 342.111389 degrees … Read More...
Project Part 1 Objective Our objective, in this Part 1 of our Project, is to practise solving a problem by composing and testing a Python program using all that we have learnt so far and discovering new things, such as lists of lists, on the way. Project – Hunting worms in our garden! No more turtles! In this project, we shall move on to worms. Indeed, our project is a game in which the player hunts for worms in our garden. Once our garden has been displayed, the player tries to guess where the worms are located by entering the coordinates of a cell in our garden. When the player has located all the worms, the game is over! Of course there are ways of making this game more exciting (hence complicated), but considering that we have 2 weeks for Part 1 and 2 weeks for Part 2, keeping it simple will be our goal. We will implement our game in two parts. In Part 1, we write code that constructs and tests our data structures i.e., our variables. In Part 2, we write code that allows the player to play a complete “worm hunting” game! ? Project – Part 1 – Description Data Structures (variables): As stated above, in Part 1, we write code that constructs our data structures i.e., our variables. In our game program, we will need data structures (variables) to represent: 1. Our garden that is displayed to the player (suggestion: list of lists), 2. The garden that contains all the worms (suggestion: another list of lists), Garden: Our garden in Part 1 of our Project will have a width and a height of 10. Warning: The width and the height of our garden may change in Part 2 of our Project. So, it may be a good idea to create 2 variables and assign the width and the height of our garden to these 2 variables. 3. Our worms and their information. For each worm, we may want to keep the following information: a. worm number, b. the location of the worm, for example, either the coordinates of the cells containing the worm OR the coordinate of the first cell containing the worm, its length and whether the worm is laying horizontally or vertically. Worms: We will create 6 worms of length 3. 4. And other variables as needed. Testing our data structures: ? Suggestion: as we create a data structure (the “displayed” garden, the garden containing the worms, each worm, etc…), print it with a “debug print statement”. Once we are certain the data structure is well constructed, comment out the “debug print statement”. Code: In Part 1, the code we write must include functions and it must include the main section of our program. In other words, in Part 1, the code we write must be a complete program. In terms of functions, here is a list of suggestions. We may have functions that … ? creates a garden (i.e., a garden data structure), ? creates the worms (i.e., the worm data structure), ? places a worm in the garden that is to hold the worms (i.e., another garden data structure), ? displays the garden on the screen for the player to see, ? displays a worm in the displayed garden, ? etc… ? Finally, in Part 1, the code we write must implement the following algorithm: Algorithm: Here is the algorithm for the main section of our game program: ? Welcome the player ? Create an empty “displayed” garden, (“displayed” because this is the garden we display to the player) ? Create the worms (worms’ information) ? Create an empty “hidden” garden Note 1: “hidden” because one can keep track of the worms in this “hidden” garden, which we do not show to the player. This is why it is called “hidden”. Note 2: One can keep track of worm’s locations using a different mechanism or data structure. It does not have to be a list of lists representing a “hidden” garden. We are free to choose how we want to keep track of where our worms are located in our garden. ? Place each worm in the “hidden” garden (or whatever mechanism or data structure we decide to use) ? Display the “displayed” garden on the screen for the player to see ? While the player wants to play, ask the player for a worm number (1 to 6), read this worm number and display this worm on the “displayed” garden. This is not the game. Remember, we shall implement the game itself in Part 2. Here, in this step, we make sure our code works properly, i.e., it can retrieve worm information and display worms properly. Displaying worms properly: Note that when we create worms and display them, it may be the case that worms overlap with other worms and that worms wrap around the garden. These 2 situations are illustrated in the 3 Sample Runs discussed below. At this point, we are ready for Part 2 of our Project. Sample Runs: In order to illustrate the explanations given above of what we are to do in this Part 1 of our Project, 3 sample runs have been posted below the description of this Part 1 of our Project on our course web site. Have a look at these 3 sample runs. The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs. Of course, the position of our worms will be different but everything else should be the same. What we see in each of these 3 sample runs is 1 execution of the code we are to create for this Part 1 of our Project. Note about Sample Run 1: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 2 wraps around: it starts at (row 7, column B), (row 7, column A) then wraps around to (row 7, column J). Worm 6 also wraps around: it starts at (row 2, column E), (row 1, column E) then wraps around to (row 10, column E). Overlap: There are some overlapping worms: worms 5 and 6 overlap at (row 1, column E). Note about Sample Run 2: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 3 wraps around: it starts at (row 1, column B) then wraps around to (row 10, column B) and (row 9, column B). Worm 6 also wraps around: it starts at (row 1, column D) then wraps around to (row 10, column D) and (row 9, column D). Overlap: There are some overlapping worms: worms 2 and 4 overlap at (row 3, column H), worms 1 and 2 overlap at (row 3, column G) and worms 2 and 5 overlap at (row 3, column E). Note about Sample Run 3: In this Sample Run, the player enters the numbers in the following sequence: 3, 2, 6, 4, 5, 1, 7, 8. Wrap around: Worm 3 wraps around: it starts at (row 2, column C), (row 1, column C) then wraps around to (row 10, column C). Worm 1 also wraps around: it starts at (row 2, column B), (row 2, column A) then wraps around to (row 2, column J). Overlap: There are some overlapping worms: worms 6 and 3 overlap at (row 1, column C) and (row 2, column C). Other Requirements: Here are a few more requirements the code we are to create for this Part 1 of our Project must satisfy. 1. The location of each worm in the garden must be determined randomly. 2. Whether a worm is lying horizontally or vertically must also be determined randomly. 3. It is acceptable in Part 1 of our Project if worms overlap each other (see Sample Runs) 4. When placing a worm in a garden, the worm must “wrap around” the garden. See Sample Runs for examples of what “wrapping around” signifies. How will we implement this wrapping around? Hint: wrapping around can be achieved using an arithmetic operator we have already seen. 5. We must make use of docstring when we implement our functions (have a look at our textbook for an explanation and an example). 6. Every time we encounter the word must in this description of Part 1 of our Project, we shall look upon that sentence as another requirement. For example, the sentence “The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs.”, even though it is not listed below the Other Requirements heading, is also a requirement because of its must.

Project Part 1 Objective Our objective, in this Part 1 of our Project, is to practise solving a problem by composing and testing a Python program using all that we have learnt so far and discovering new things, such as lists of lists, on the way. Project – Hunting worms in our garden! No more turtles! In this project, we shall move on to worms. Indeed, our project is a game in which the player hunts for worms in our garden. Once our garden has been displayed, the player tries to guess where the worms are located by entering the coordinates of a cell in our garden. When the player has located all the worms, the game is over! Of course there are ways of making this game more exciting (hence complicated), but considering that we have 2 weeks for Part 1 and 2 weeks for Part 2, keeping it simple will be our goal. We will implement our game in two parts. In Part 1, we write code that constructs and tests our data structures i.e., our variables. In Part 2, we write code that allows the player to play a complete “worm hunting” game! ? Project – Part 1 – Description Data Structures (variables): As stated above, in Part 1, we write code that constructs our data structures i.e., our variables. In our game program, we will need data structures (variables) to represent: 1. Our garden that is displayed to the player (suggestion: list of lists), 2. The garden that contains all the worms (suggestion: another list of lists), Garden: Our garden in Part 1 of our Project will have a width and a height of 10. Warning: The width and the height of our garden may change in Part 2 of our Project. So, it may be a good idea to create 2 variables and assign the width and the height of our garden to these 2 variables. 3. Our worms and their information. For each worm, we may want to keep the following information: a. worm number, b. the location of the worm, for example, either the coordinates of the cells containing the worm OR the coordinate of the first cell containing the worm, its length and whether the worm is laying horizontally or vertically. Worms: We will create 6 worms of length 3. 4. And other variables as needed. Testing our data structures: ? Suggestion: as we create a data structure (the “displayed” garden, the garden containing the worms, each worm, etc…), print it with a “debug print statement”. Once we are certain the data structure is well constructed, comment out the “debug print statement”. Code: In Part 1, the code we write must include functions and it must include the main section of our program. In other words, in Part 1, the code we write must be a complete program. In terms of functions, here is a list of suggestions. We may have functions that … ? creates a garden (i.e., a garden data structure), ? creates the worms (i.e., the worm data structure), ? places a worm in the garden that is to hold the worms (i.e., another garden data structure), ? displays the garden on the screen for the player to see, ? displays a worm in the displayed garden, ? etc… ? Finally, in Part 1, the code we write must implement the following algorithm: Algorithm: Here is the algorithm for the main section of our game program: ? Welcome the player ? Create an empty “displayed” garden, (“displayed” because this is the garden we display to the player) ? Create the worms (worms’ information) ? Create an empty “hidden” garden Note 1: “hidden” because one can keep track of the worms in this “hidden” garden, which we do not show to the player. This is why it is called “hidden”. Note 2: One can keep track of worm’s locations using a different mechanism or data structure. It does not have to be a list of lists representing a “hidden” garden. We are free to choose how we want to keep track of where our worms are located in our garden. ? Place each worm in the “hidden” garden (or whatever mechanism or data structure we decide to use) ? Display the “displayed” garden on the screen for the player to see ? While the player wants to play, ask the player for a worm number (1 to 6), read this worm number and display this worm on the “displayed” garden. This is not the game. Remember, we shall implement the game itself in Part 2. Here, in this step, we make sure our code works properly, i.e., it can retrieve worm information and display worms properly. Displaying worms properly: Note that when we create worms and display them, it may be the case that worms overlap with other worms and that worms wrap around the garden. These 2 situations are illustrated in the 3 Sample Runs discussed below. At this point, we are ready for Part 2 of our Project. Sample Runs: In order to illustrate the explanations given above of what we are to do in this Part 1 of our Project, 3 sample runs have been posted below the description of this Part 1 of our Project on our course web site. Have a look at these 3 sample runs. The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs. Of course, the position of our worms will be different but everything else should be the same. What we see in each of these 3 sample runs is 1 execution of the code we are to create for this Part 1 of our Project. Note about Sample Run 1: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 2 wraps around: it starts at (row 7, column B), (row 7, column A) then wraps around to (row 7, column J). Worm 6 also wraps around: it starts at (row 2, column E), (row 1, column E) then wraps around to (row 10, column E). Overlap: There are some overlapping worms: worms 5 and 6 overlap at (row 1, column E). Note about Sample Run 2: In this Sample Run, the player enters the numbers 1 to 8 sequentially. Wrap around: Worm 3 wraps around: it starts at (row 1, column B) then wraps around to (row 10, column B) and (row 9, column B). Worm 6 also wraps around: it starts at (row 1, column D) then wraps around to (row 10, column D) and (row 9, column D). Overlap: There are some overlapping worms: worms 2 and 4 overlap at (row 3, column H), worms 1 and 2 overlap at (row 3, column G) and worms 2 and 5 overlap at (row 3, column E). Note about Sample Run 3: In this Sample Run, the player enters the numbers in the following sequence: 3, 2, 6, 4, 5, 1, 7, 8. Wrap around: Worm 3 wraps around: it starts at (row 2, column C), (row 1, column C) then wraps around to (row 10, column C). Worm 1 also wraps around: it starts at (row 2, column B), (row 2, column A) then wraps around to (row 2, column J). Overlap: There are some overlapping worms: worms 6 and 3 overlap at (row 1, column C) and (row 2, column C). Other Requirements: Here are a few more requirements the code we are to create for this Part 1 of our Project must satisfy. 1. The location of each worm in the garden must be determined randomly. 2. Whether a worm is lying horizontally or vertically must also be determined randomly. 3. It is acceptable in Part 1 of our Project if worms overlap each other (see Sample Runs) 4. When placing a worm in a garden, the worm must “wrap around” the garden. See Sample Runs for examples of what “wrapping around” signifies. How will we implement this wrapping around? Hint: wrapping around can be achieved using an arithmetic operator we have already seen. 5. We must make use of docstring when we implement our functions (have a look at our textbook for an explanation and an example). 6. Every time we encounter the word must in this description of Part 1 of our Project, we shall look upon that sentence as another requirement. For example, the sentence “The code we create for this Part 1 of our Project must produce exactly the same output as the one shown in these 3 sample runs.”, even though it is not listed below the Other Requirements heading, is also a requirement because of its must.

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A company purchased $1,800 of merchandise on December 5. On December 7, it returned $200 worth of merchandise. On December 8, it paid the balance in full, taking a 2% discount. The amount of the cash paid on December 8 equals:

A company purchased $1,800 of merchandise on December 5. On December 7, it returned $200 worth of merchandise. On December 8, it paid the balance in full, taking a 2% discount. The amount of the cash paid on December 8 equals:

Question 19   A company purchased $1,800 of merchandise on … 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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(20 pts total) Continuous Probability Density a) (4 pts) Graph f when the density f(x) = k where k is a constant if −4≤?≤4 and 0 elsewhere b) (4 pts) What is the value of k? c) (4 pts) Graph F for the same functions d) (4 pts) What is the ?(0≤?≤4)? e) (4 pts) Find the interval ?(−?≤?≤?) where the probability is 95% 7) (20 pts total) Find the mean and variance of the random variable X with probability function f(x) a) (10 ???) ?(0)=0.512,?(1)=0.384,?(2)=0.096,?(3)=0.008 b) (10 ???) ?(?)=2? (0≤?≤1) 8) (20 pts total) Let X be normal with a mean of 80 and a variance of 9. Find: a) (5 pts) P(X>83) b) (5 pts) P(X<81) c) (5 pts) P(X<80) d) (5 pts) P(78<X<82)

(20 pts total) Continuous Probability Density a) (4 pts) Graph f when the density f(x) = k where k is a constant if −4≤?≤4 and 0 elsewhere b) (4 pts) What is the value of k? c) (4 pts) Graph F for the same functions d) (4 pts) What is the ?(0≤?≤4)? e) (4 pts) Find the interval ?(−?≤?≤?) where the probability is 95% 7) (20 pts total) Find the mean and variance of the random variable X with probability function f(x) a) (10 ???) ?(0)=0.512,?(1)=0.384,?(2)=0.096,?(3)=0.008 b) (10 ???) ?(?)=2? (0≤?≤1) 8) (20 pts total) Let X be normal with a mean of 80 and a variance of 9. Find: a) (5 pts) P(X>83) b) (5 pts) P(X<81) c) (5 pts) P(X<80) d) (5 pts) P(78

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The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155

The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155

D) 10,155
People v. Glover 233 Cal. App. 3d 1476 (1991) Deadline is 12 hours from posting time. There is no page minimum as long as every question in the following instructions is answered thoroughly and completely. Instructions: Complete a case brief on People v. Glover 233 Cal. App. 3d 1476 (1991) and answer the following 11 questions… 1. name of case 2. legal citation and year case decided 3. character of action (how the case was brought before the appellate court) 4. facts of the case 5. legal issues in the case 6. decision of the appellate court 7. majority opinion 8. concurring opinion(s) 9. dissenting opinion 10. comment by the student 11. principle of the case (what the case stands for)

People v. Glover 233 Cal. App. 3d 1476 (1991) Deadline is 12 hours from posting time. There is no page minimum as long as every question in the following instructions is answered thoroughly and completely. Instructions: Complete a case brief on People v. Glover 233 Cal. App. 3d 1476 (1991) and answer the following 11 questions… 1. name of case 2. legal citation and year case decided 3. character of action (how the case was brought before the appellate court) 4. facts of the case 5. legal issues in the case 6. decision of the appellate court 7. majority opinion 8. concurring opinion(s) 9. dissenting opinion 10. comment by the student 11. principle of the case (what the case stands for)

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Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 57 5/9/2014 8:02 PM Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 57 5/9/2014 8:02 PM Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? = = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 57 5/9/2014 8:02 PM Hint 1. What is the general quadratic equation? The general quadratic equation is , where , , and are constants. Depending on the value of the discriminant, , the equation may have two real valued 1. solutions if , 2. one real valued solution if , or 3. two complex valued solutions if . In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. No; there is no chance he is going to get aboard. Yes; he will get a second chance Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 57 5/9/2014 8:02 PM ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: C and E E and F A and F C and D B and D C and D A and F E and F A and B E and D Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 57 5/9/2014 8:02 PM Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 2. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. ANSWER: A and F A and E D and B C and D E and F Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 57 5/9/2014 8:02 PM Correct Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. = 5 positive negative Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 57 5/9/2014 8:02 PM ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth’s gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, , is constant. 1. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by , is equal to 9.80 near the surface of the earth. Hence, the y component of its velocity, , changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time corresponds to the moment just after the ball is launched from position and . Its launch velocity, also called the initial velocity, is . Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time with velocity . Its position at this moment is denoted by or since it is at its maximum height. The other point, at time with velocity , corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is , also known as ( since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence . Part A , = -2,-5 , Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 57 5/9/2014 8:02 PM How do the speeds , , and (at times ,

Extra Credit Due: 11:59pm on Thursday, May 15, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A Man Running to Catch a Bus A man is running at speed (much less than the speed of light) to catch a bus already at a stop. At , when he is a distance from the door to the bus, the bus starts moving with the positive acceleration . Use a coordinate system with at the door of the stopped bus. Part A What is , the position of the man as a function of time? Answer symbolically in terms of the variables , , and . Hint 1. Which equation should you use for the man’s speed? Because the man’s speed is constant, you may use . ANSWER: Correct Part B What is , the position of the bus as a function of time? Answer symbolically in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 1 of 57 5/9/2014 8:02 PM Hint 1. Which equation should you use for the bus’s acceleration? Because the bus has constant acceleration, you may use . Recall that . ANSWER: Correct Part C What condition is necessary for the man to catch the bus? Assume he catches it at time . Hint 1. How to approach this problem If the man is to catch the bus, then at some moment in time , the man must arrive at the position of the door of the bus. How would you express this condition mathematically? ANSWER: Correct Part D Inserting the formulas you found for and into the condition , you obtain the following: , or . Intuitively, the man will not catch the bus unless he is running fast enough. In mathematical terms, there is a constraint on the man’s speed so that the equation above gives a solution for that is a real positive number. Find , the minimum value of for which the man will catch the bus. Express the minimum value for the man’s speed in terms of and . = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 2 of 57 5/9/2014 8:02 PM Hint 1. Consider the discriminant Use the quadratic equation to solve: . What is the discriminant (the part under the radical) of the solution for ? Hint 1. The quadratic formula Recall: If then ANSWER: Hint 2. What is the constraint? To get a real value for , the discriminant must be greater then or equal to zero. This condition yields a constraint that exceed . ANSWER: Correct Part E Assume that the man misses getting aboard when he first meets up with the bus. Does he get a second chance if he continues to run at the constant speed ? = = Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 3 of 57 5/9/2014 8:02 PM Hint 1. What is the general quadratic equation? The general quadratic equation is , where , , and are constants. Depending on the value of the discriminant, , the equation may have two real valued 1. solutions if , 2. one real valued solution if , or 3. two complex valued solutions if . In this case, every real valued solution corresponds to a time at which the man is at the same position as the door of the bus. ANSWER: Correct Adding and Subtracting Vectors Conceptual Question Six vectors (A to F) have the magnitudes and directions indicated in the figure. Part A Which two vectors, when added, will have the largest (positive) x component? Hint 1. Largest x component The two vectors with the largest x components will, when combined, give the resultant with the largest x component. Keep in mind that positive x components are larger than negative x components. No; there is no chance he is going to get aboard. Yes; he will get a second chance Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 4 of 57 5/9/2014 8:02 PM ANSWER: Correct Part B Which two vectors, when added, will have the largest (positive) y component? Hint 1. Largest y component The two vectors with the largest y components will, when combined, give the resultant with the largest y component. Keep in mind that positive y components are larger than negative y components. ANSWER: Correct Part C Which two vectors, when subtracted (i.e., when one vector is subtracted from the other), will have the largest magnitude? Hint 1. Subtracting vectors To subtract two vectors, add a vector with the same magnitude but opposite direction of one of the vectors to the other vector. ANSWER: C and E E and F A and F C and D B and D C and D A and F E and F A and B E and D Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 5 of 57 5/9/2014 8:02 PM Correct Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 2. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. ANSWER: A and F A and E D and B C and D E and F Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 6 of 57 5/9/2014 8:02 PM Correct Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. Express your answers, separated by a comma, in meters to one significant figure. = 5 positive negative Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 7 of 57 5/9/2014 8:02 PM ANSWER: Correct Conceptual Problem about Projectile Motion Learning Goal: To understand projectile motion by considering horizontal constant velocity motion and vertical constant acceleration motion independently. Projectile motion refers to the motion of unpowered objects (called projectiles) such as balls or stones moving near the surface of the earth under the influence of the earth’s gravity alone. In this analysis we assume that air resistance can be neglected. An object undergoing projectile motion near the surface of the earth obeys the following rules: An object undergoing projectile motion travels horizontally at a constant rate. That is, the x component of its velocity, , is constant. 1. An object undergoing projectile motion moves vertically with a constant downward acceleration whose magnitude, denoted by , is equal to 9.80 near the surface of the earth. Hence, the y component of its velocity, , changes continuously. 2. An object undergoing projectile motion will undergo the horizontal and vertical motions described above from the instant it is launched until the instant it strikes the ground again. Even though the horizontal and vertical motions can be treated independently, they are related by the fact that they occur for exactly the same amount of time, namely the time the projectile is in the air. 3. The figure shows the trajectory (i.e., the path) of a ball undergoing projectile motion over level ground. The time corresponds to the moment just after the ball is launched from position and . Its launch velocity, also called the initial velocity, is . Two other points along the trajectory are indicated in the figure. One is the moment the ball reaches the peak of its trajectory, at time with velocity . Its position at this moment is denoted by or since it is at its maximum height. The other point, at time with velocity , corresponds to the moment just before the ball strikes the ground on the way back down. At this time its position is , also known as ( since it is at its maximum horizontal range. Projectile motion is symmetric about the peak, provided the object lands at the same vertical height from which is was launched, as is the case here. Hence . Part A , = -2,-5 , Extra Credit http://session.masteringphysics.com/myct/assignmentPrintView?displayM… 8 of 57 5/9/2014 8:02 PM How do the speeds , , and (at times ,

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Race and Ethnic Relations in the United States Sociology 215, Section 003 Assignment 4 (Points: 25) 1. How the people of mixed race or multiracial descends were historically defined in America? Please describe the four different types of identities that presently characterize the biracial Americans with examples. (Use specific references from the textbook chapter 5 to answer this question) (6 points) 2. “Whereas African Americans had been exploited for their labor, Native Americans were exploited for their land.” Explain this statement with at least 3 specific reference to the legislative policies and how did those impact Native Americans. (Use specific references from the textbook Chapter 6 to answer this question)? (6 points) 3. Discuss the evolution of federal policies on immigration from Mexico over the course of the twentieth century. What were the major policies? When and why did they change? (Use specific references from the textbook Chapter 7 to answer this question) (6 points) 4. How accurate do you think is the portrait of “model minority” for the Asian American groups in the US? Please describe the contact situations with the Chinese and Japanese Americans in the US. How did it affect the development of their relations with the larger society? (Use specific references from the textbook Chapter 8 to answer this question) (7 points)

Race and Ethnic Relations in the United States Sociology 215, Section 003 Assignment 4 (Points: 25) 1. How the people of mixed race or multiracial descends were historically defined in America? Please describe the four different types of identities that presently characterize the biracial Americans with examples. (Use specific references from the textbook chapter 5 to answer this question) (6 points) 2. “Whereas African Americans had been exploited for their labor, Native Americans were exploited for their land.” Explain this statement with at least 3 specific reference to the legislative policies and how did those impact Native Americans. (Use specific references from the textbook Chapter 6 to answer this question)? (6 points) 3. Discuss the evolution of federal policies on immigration from Mexico over the course of the twentieth century. What were the major policies? When and why did they change? (Use specific references from the textbook Chapter 7 to answer this question) (6 points) 4. How accurate do you think is the portrait of “model minority” for the Asian American groups in the US? Please describe the contact situations with the Chinese and Japanese Americans in the US. How did it affect the development of their relations with the larger society? (Use specific references from the textbook Chapter 8 to answer this question) (7 points)

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