Evaluate how effectively did LTG Natonski utilize the mission command approach

2nd Battle of Fallujah (Phantom Fury) Iraq War LTG Natonski    (USA)
     

 

Students will analyze a commander’s performance from a selected historical battle.   This analysis will be 6-8 pages in length, and will evaluate how effectively the commander executed the Mission Command Approach and the Command and Control Warfighting Function during the battle.  Specifically, students will examine how he utilized the mission command principles. Students must address at least four of the seven principles in their analysis, and suggest how the commander’s utilization of those principles ultimately affected the battle’s outcome.  The student must determine by their research if the selected commander executed good or bad mission command during the battle.​

Citation Format : Chicago/Turabian 

MISSION COMMAND Never tell people how to do things. Tell them what to do and they will surprise you with their ingenuity. General George S. Patton, Jr. 1-13. Army operations doctrine emphasizes shattering an enemy force’s ability and will to resist, and destroying the coherence of enemy operations. Army forces accomplish these things by controlling the nature, scope, and tempo of an operation and striking simultaneously throughout the area of operations to control, neutralize, and destroy enemy forces and other objectives. The Army’s command and control doctrine supports its operations doctrine. It balances coordination, personal leadership, and tactical flexibility. It stresses rapid decision making and execution, including rapid response to changing situations. It emphasizes mutual trust and shared understanding among superiors and subordinates. 1-14. Mission command is the Army’s approach to command and control that empowers subordinate decision making and decentralized execution appropriate to the situation. Mission command supports the Army’s operational concept of unified land operations and its emphasis on seizing, retaining, and exploiting the initiative. 1-15. The mission command approach to command and control is based on the Army’s view that war is inherently chaotic and uncertain. No plan can account for every possibility, and most plans must change rapidly during execution to account for changes in the situation. No single person is ever sufficiently informed to make every important decision, nor can a single person keep up with the number of decisions that need to be made during combat. Subordinate leaders often have a better understanding of what is happening during a battle, and are more likely to respond effectively to threats and fleeting opportunities if allowed to make Chapter 1 1-4 ADP 6-0 31 July 2019 decisions and act based on changing situations and unforeseen events not addressed in the initial plan in order to achieve their commander’s intent. Enemy forces may behave differently than expected, a route may become impassable, or units could consume supplies at unexpected rates. Friction and unforeseeable combinations of variables impose uncertainty in all operations and require an approach to command and control that does not attempt to impose perfect order, but rather accepts uncertainty and makes allowances for unpredictability. 1-16. Mission command helps commanders capitalize on subordinate ingenuity, innovation, and decision making to achieve the commander’s intent when conditions change or current orders are no longer relevant. It requires subordinates who seek opportunities and commanders who accept risk for subordinates trying to meet their intent. Subordinate decision making and decentralized execution appropriate to the situation help manage uncertainty and enable necessary tempo at each echelon during operations. Employing the mission command approach during all garrison activities and training events is essential to creating the cultural foundation for its employment in high-risk environments.

 

THE COMMAND AND CONTROL WARFIGHTING FUNCTION 1-95. A warfighting function is a group of tasks and systems united by a common purpose that commanders use to accomplish missions and training objectives (ADP 3-0). Warfighting functions are the physical means that tactical commanders use to execute operations and accomplish missions assigned by higher level commanders. The purpose of warfighting functions is to provide an intellectual organization for common critical capabilities available to commanders and staffs at all echelons. 1-96. Operations executed through simultaneous offensive, defensive, stability, or defense support of civil authorities operations require the continuous generation and application of combat power. Combat power is the total means of destructive, constructive, and information capabilities that a military unit or formation can apply at one time (ADP 3-0). Combat power includes all capabilities provided by unified action partners that are integrated and synchronized with the commander’s objectives to achieve unity of effort in sustained operations. 1-97. Combat power has eight elements: leadership, information, command and control, movement and maneuver, intelligence, fires, sustainment, and protection. The elements facilitate Army forces accessing joint and multinational fires and assets. The Army collectively describes the last six elements as warfighting functions. Commanders apply combat power through the warfighting functions using leadership and information. Leadership is a multiplying and unifying element of combat power. Information enables commanders at all levels to make informed decisions about the application of combat power and achieve definitive results. 1-98. The command and control warfighting function is the related tasks and a system that enable commanders to synchronize and converge all elements of combat power (ADP 3-0). The primary purpose of the command and control warfighting function is to assist commanders in integrating the other elements of combat power (movement and maneuver, intelligence, fires, sustainment, protection, information and leadership) to achieve objectives and accomplish missions. The command and control warfighting function consists of the command and control warfighting function tasks and the command and control system

module 1 algebra assignment

Solve the problems contained in the documents below. You can type directly into the DOCX file or you can do handwritten work on the PDF. If you prefer, you can also do a screencast or video recording of your verbal solutions and submit the media here on Canvas.

Posted in Uncategorized

module 1 discussion

Module 1 Algebra 

Please read the following article by Usiskin — lead author of the University of Chicago School Mathematics Project secondary math curriculum — about conceptions of algebra, which is from the 1980s but is still relevant today (not much has changed in school algebra, really).

Then respond to the following prompts in a discussion post

  • What examples can you think of where algebra seems to be treated as generalized arithmetic? Or what questions do you have about this conception?
  • What examples can you think of where algebra seems to be treated as procedures for solving certain problems? Or what questions do you have about this conception?
  • What examples can you think of where algebra seems to be treated as studying relationships among quantities? Or what questions do you have about this conception?
Posted in Uncategorized

MCR3U Worksheet – Trigonometric Equations & CAS

MCR3U Worksheet – Trigonometric Equations & CAST Rule Date: ______________

Trig Identities worksheet 3.3 name: Prove each identity:

1. cscθ =

cotθ cosθ

2.

1 sec2 x

+ 1

csc2 x = 1

3. csc 2 y tan2 y − 1 = tan2 y 4.

 

secθ cosθ

− tanθ cotθ

= 1

5. csc 4 x − cot4 x = csc2 x + cot2 x 6. sec

4 y − tan4 y = tan2 y + sec2 y

7. 1 − tanθ( )2 = sec2 θ − 2tanθ 8.

1 − sin2 x( ) 1 + tan2 x( ) = 1

Trig Identities worksheet 3.3

 

 

9.

cotw cosw

+ sec w cot w

= sec2 wcsc w 10. 2sin 2 y − 1 = 1 − 2cos2 y

11. sec y − tany sin y = cos y 12. 1 − cos2 θ( ) cot2 θ + 1( ) = 1

13.

1 − sin2 θ 1 + tan2θ

= cos4 θ 14.

sin t csc t

+ cos t sec t

= 1

15.

sin y + tan y 1 + sec y

= sin y 16.

1 − tan2 w 1 + tan2 w

= 2cos2 w − 1

Trig Identities worksheet 3.3

 

 

MCR 3U Worksheet – Transformations of Sinusoidal Functions Dec 3, 2019

Graph each function. The parent function, y=sin x or y=cos x , is shown as a dotted line.

(a) vertical stretch or compression sketch y= 2sin x

(b) horizontal stretch or compression sketch y=cos (3 x)

(c) vertical translation (or shift) sketch y=sin (x )+ 2

(d) horizontal translation (or phase shift) sketch one cycle of y=cos (x+ 90 ̊ )

(e) vertical reflection (about the x-axis) sketch y=−cos x

(f) horizontal reflection (about the y-axis) sketch one cycle of y=sin (−x )

Page 1 of 2.

 

 

(g) combination of transformations sketch y=2sin (12 x)−1

(h) combination of transformations sketch y= 1

2 cos (2 x )−1.5

Blank graphs for student practice y=sin x y=cos x

Unit 6: Periodic Functions Page 2 of 2.

MCR3U Determining Trigonometric Equations from Graphs May 27, 2019

A)

B)

C) D)

E) F)

rev. 18. May. 2011

 

  • MCR3U Trig 08 WS Solving Trig Equations & CAST Rule
  • WS – Trig Identities
  • MCR3U – Periodic 03 – WS – Graphing Transformations
  • MCR3U – Periodic 05 – WS – Equations from Graphs

culminating task 1

ame: ________________________

MCR3U – WS – Transformations & Graphing of Exponential Functions

Write each of the following using x-y notation (i.e., y  a b  k x  p

    q)

1. y  h x  5   3, given h x   2x

2. y  3g x  5   1, given g x   4x

3. y  f 1 3

x  5  



  5, given f x   4x

4. y  h 1 4

x  3  



  3, given h x   5x

5. y  f  x  2    

    5, given f x   4

x

6. y  1 4 g

1 3

x  4  



  3, given g x   5x

7. y  3h 1 2

x 



  5, given h x   5x

8. y  f 1 3

x  2  



  4, given f x   5x

9. y  3h 1 2

x  4  



  1, given h x   2x

Identify the transformations and write using function notation (i.e., y  af k x  p   

  

    q ). Be sure to specify the

parent function, f x   bx .

10. y  5 2  1

3 x  4 

 4

11. y  2 3  1 2

x  3   1

12. y  2 2  1 2

x  1   2

13. y  5 2  1

2 x  3 

 1

14. y  3 2  1 2

x  3 

15. y  3 2  1 5

x  3   4

Graph the following using transformations (if possible using integer values). Sketch otherwise.

16. y  1 5

g 4 x  3    

    3, given g x   2

x

17. y  h 1 4

x  4  



  5, given h x   2x

18. y  2g  x  2    

    2, given g x   2

x

19. y  3g 3 x  2    

    4, given g x   2

x

20. y  h x  1   4, given h x   2x

21. y  2h 1 5

x  3  



  4, given h x   2x

22. y  1 4

g 2 x  1    

    3, given g x   2

x

23. y  3f 3 x  4    

    4, given f x   2

x

 

 

Name: _______________ WS – Rational Functions – Order of Operations Mar 25, 2019

Simplify and state and restrictions:

1. 3 x+ 1 2 x– 3

+ x

x 2−9

2. 3 x

x 2+ 3 x+ 2

− 4 x

x 2+ 5 x+ 6

+ 5 x

x 2+ 4 x+ 3

3. 3 x

6 x 2 – x−2

+ 2 x

10 x 2 – x−3

4. x+ 1

2 x 2 – 7 x+ 6

− x –3

2 x 2 – x−3

5. 3 x

6 x 2+ 13 x– 5

+ 2 x+ 1

6 x 2 + 7 x−3

6. x– 2

6 x 2 – 7 x– 5

÷ 2 x

3 x 2 –5 x

− 3 x+ 2

2 x 2+ 11 x+ 5

Name: _______________ WS – Rational Functions – Order of Operations Mar 25, 2019

Simplify and state and restrictions:

1. 3 x+ 1 2 x– 3

+ x

x 2−9

2. 3 x

x 2+ 3 x+ 2

− 4 x

x 2+ 5 x+ 6

+ 5 x

x 2+ 4 x+ 3

3. 3 x

6 x 2 – x−2

+ 2 x

10 x 2 – x−3

4. x+ 1

2 x 2 – 7 x+ 6

− x –3

2 x 2 – x−3

5. 3 x

6 x 2+ 13 x– 5

+ 2 x+ 1

6 x 2 + 7 x−3

6. x– 2

6 x 2 – 7 x– 5

÷ 2 x

3 x 2 –5 x

− 3 x+ 2

2 x 2+ 11 x+ 5

 

 

Name: ________________________ Date: ______________________

Ver: A # Pages: 1

MPM2D – Worksheet – Factoring Complex Trinomials (with Common Factors)

1. 3x 2

+ 25x + 8

2. 5x 2

+ 46x + 9

3. 2x 2

+ 15x + 22

4. 3x 2

+ 14x + 15

5. 8x 2

+ 22x + 5

6. 2x 2

+ 7x + 3

7. 5x 2

+ 61x + 12

8. 8x 2

+ 46x + 11

9. 6x 2

+ 11x + 3

10. 8x 2

+ 38x + 9

11. −4x 2

+ 2x + 72

12. 12x 2

− 117x − 30

13. 20x 2

− 42x + 16

14. 12x 2

+ 69x − 105

15. 50x 2

+ 140x + 80

16. −20x 2

− 230x + 120

17. 15x 2

− 70x − 25

18. 6x 2

− 22x − 84

19. 18x 2

+ 87x − 66

20. 100x 2

− 170x − 110

21. −6x 2

− 44x + 160

22. −3x 2

− 4x + 20

23. 4x 2

+ 17x + 18

24. 24x 2

+ 20x − 100

25. 20x 2

+ 29x + 5

26. 75x 2

− 170x − 385

27. 30x 2

− 129x − 198

28. 2x 2

+ 13x + 20

29. 5x 2

+ 14x + 8

30. 20x 2

− 150x + 280

31. 10x 2

+ 106x − 44

32. 20x 2

+ 13x + 2

33. 4x 2

+ 15x + 14

34. 2x 2

+ 11x + 9

35. 25x 2

− 70x + 40

36. 5x 2

+ 11x + 6

37. 5x 2

+ 13x + 8

38. 20x 2

+ 88x − 192

39. −8x 2

− 66x − 70

 

 

MCR 3U Function Notation Date:

Fill in the table. Simplify the functions f(x) = x and f(x) = x2 so that they are in the form y=mx+ b and y=a(x–h)2+ k . Do your rough work (where necessary) on a separate page.

f (x) x x2 √x 1 x

1. 5 f (a)

2. – f (a)

3. f (a)+ 4

4. f (a)– 6

5. f (a+ 2)

6. f (a –1)

7. f (3a)

8. f (–a)

9. f (– 2a)

10. f ( a2) 11. f [ 3(a– 1)]

12. f (– 3a)+ 6

13. – 2 f (a– 6)+ 4

14. 5 f [ 4(a –1)]– 3

15. 3a– 6

16. 3a2 – 4

17. −√3−a

18. 1 a+ 2

−1

19. –5(a– 2)2+7

20. 3√4a−8−2

21. −3 a−5

+2

Answers from #15-21 may vary.

 

 

MCR3U Worksheet – Graphs of Parent Functions Feb 27, 2019

The Quadratic Function: y=x2 The Absolute Value Function: y=∣x∣

x y

-3

-2

-1

0

1

2

3

x

y x y

-3

-2

-1

0

1

2

3

x

y

Domain: Domain:

Range: Range:

Max/Min (if any): Max/Min (if any):

The Radical Function: y=x The Reciprocal Function: y= 1 x

x y

-1

0

1

4

9

x

y x y

-2

-1

-0.5

0

0.5

1

2

x

y

Domain: Domain:

Range: Range:

Max/Min (if any): Max/Min (if any):

Asymptotes (if any): Asymptotes (if any):

rev 24. Sep. 2012 Text: McGraw-HIll Ryerson Mathematics 11 (2001)

 

 

Name: ________________________ Class/Period: __________ Attempt # _____ Date: 01/31/2012 ID: A

y = ax 2

+ bx + c y = a(x − r)(x − s) y = a(x − h) 2

+ k x = −b ± b

2 − 4ac

2a D = b

2 − 4ac

Proficiency Demonstrated: Perfect ���� Sufficient ���� Insufficient (Repeat Evaluation) ����

MPM2D – Essential Skills Proficiency Assessment # 3 – Quadratic Properties, Expanding, and Factoring

1. Determine the key features of the provided graph and record them in the table.

Direction of Opening

Number of Zeroes

Location of Zeroes

y-intercept

Axis of Symmetry

Max/Min Value

Vertex

2. Expand and simplify (x + 4)(5x − 4)

3. Fully factor x 2

− 3x − 18

4. Determine the y-intercept, zeroes, equation of the

axis of symmetry, and the vertex of:

y = (x + 10)(x − 12)

 

 

Name: ________________________ Class: ___________________ Date: __________ ID: A

1

Practice – Rational Expressions

1. x + 5

x 2

+ 5x + 4 −

x + 4

x 2

+ 13x + 36

2. x + 3

x 2

+ 3x − 28 +

x − 6

x 2

+ x − 20

3. x + 5

x 2

− 11x + 30 +

x + 6

x 2

− 12x + 35

4. x + 3

x 2

− 2x − 35 −

x − 4

x 2

− 14x + 49

5. x + 2

x 2

− 7x + 6 −

x + 7

x 2

− 6x + 5

6. x − 7

x 2

− 4 −

x − 9

x 2

− 5x − 14

7. x + 2

x 2

− 16x + 63 +

x + 7

x 2

− 7x − 18

8. x − 8

x 2

− 3x − 28 −

x − 8

x 2

− 49

9. x + 5

x 2

− x − 56 +

x − 6

x 2

− 4x − 32

10. x − 5

x 2

− 3x − 54 +

x − 1

x 2

+ 8x + 12

11. x + 7

x 2

+ 6x + 5 −

x + 5

x 2

− 3x − 4

12. x − 5

x 2

+ x − 42 −

x − 8

x 2

− x − 56

13. x + 8

x 2

− 8x + 16 −

x − 2

x 2

− 3x − 4

14. x − 3

x 2

+ x − 12 −

x + 7

x 2

− 16

15. x − 9

x 2

+ 7x + 12 +

x − 6

x 2

+ 6x + 8

16. x − 2

x 2

− 13x + 36 −

x + 5

x 2

− x − 72

17. x

2 + x − 20

x 2

+ 2x − 35 ÷

x 2

− 3x − 4

x 2

− 14x + 45

18. x

2 + 2x − 48

x 2

+ 8x − 9 ÷

x 2

+ 2x − 48

x 2

+ 7x − 18

19. x

2 + 15x + 54

x 2

− x − 12 ×

x 2

+ 3x − 28

x 2

+ 15x + 54

20. x

2 − x − 56

x 2

+ 2x − 3 ×

x 2

− 4x + 3

x 2

+ 6x − 7

21. x

2 − 7x + 12

x 2

+ 8x + 15 ÷

x 2

− 11x + 24

x 2

+ x − 6

22. 6x

2 − 2x − 48

3x 2

+ 5x − 28 ×

x 2

+ 6x + 8

4x 2

− 18x + 18

23. 5x

2 + 34x − 7

4x 2

− 24x ×

12x 2

+ 24x

3x 2

+ 15x − 42

24. x

2 + 6x + 8

x 2

+ 8x + 15 ÷

4x 2

+ 13x + 10

2x 2

+ 2x − 40

25. x

2 − 36

9x 2

+ 3x ×

3x 2

+ 25x + 8

4x 2

− 26x + 12

26. x

2 + 7x − 8

8x 2

− 16x + 6 ÷

x 2

− 64

20x 2

+ 10x − 10

27. 4x

2 − 24x − 64

3x 2

+ 21x + 30 ÷

4x 2

+ 16x + 16

9x 2

+ 30x + 24

28. 8x

2 + 36x

15x 2

− 4x − 4 ×

25x 2

+ 35x + 10

12x 2

+ 28x

29. 2x

2 − 8x − 24

6x 2

− 5x − 56 ÷

x 2

− 5x − 6

2x 2

+ 11x − 63

30. 12x

2 + 53x + 56

x 2

+ 4x − 45 ÷

3x 2

+ 17x + 24

x 2

− 5x

31. x

2 + x − 42

x 2

− 2x − 35 ×

4x 2

+ 24x + 20

5x 2

+ 34x − 7

 

 

Name: ________________________ Date: 10/21/2013 ID: A

COMMUNICATION No Level 0 1 2 3 4 5 6 7 8 9 10

Page 1 of 1Conventions & Terminology No level assigned based on content of this page

Unacceptable Few Major / Many Minor Errors Few Minor Errors No Errors

Expression & Organization Significant Improvements Required Few Improvements Required No Improvements Required

MCR3U – WS – Radicals

1. Write each as a mixed radical (a b ) in simplest

form:

a) −4 18 b) 7 125

2. Write each as a mixed radical (a b ) in simplest

form:

a) 112 b) −9 50

3. Write each as a mixed radical (a b ) in simplest

form:

a) 5 12 b) 32

4. Write each as a mixed radical (a b ) in simplest

form:

a) 6 48 b) −4 8

5. Write each as a mixed radical (a b ) in simplest

form:

a) 4 27 b) −8 72

6. Write each as an entire radical ( a ):

a) 8 3 b) −7 2

7. Write each as an entire radical ( a ):

a) 6 2 b) −6 3

8. Write each as an entire radical ( a ):

a) −4 7 b) 12 3

9. Write each as an entire radical ( a ):

a) 10 2 b) −9 3

10. Simplify:

6 128 + 6 108 + 10 75 − 5 50

11. Simplify:

−7 125 + 8 112 + 9 63 − 7 20

12. Simplify:

8 18 − 10 48 − 6 12 + 3 50

13. Simplify:

2 12 + 6 80 − 7 20 − 2 108

14. Simplify:

6 72 − 3 12 − 48 − 5 128

15. Simplify:

2 128 − 7 45 − 2 20 − 8

16. Simplify 8

175

17. Simplify 98

245

18. Simplify 125

20

19. Simplify 343

27

20. Simplify 2 7 − 2 2

4 35 − 5 10

21. Simplify 2 21 − 14

−4 21 − 3 14

22. Simplify − 7

− 7 − 5

23. Simplify − 10 − 5 15

4 2 − 3 3

 

 

Name: ________________________ 10/30/2019 ID: A

MCR3U – WS – Transformations & Graphing of Exponential Functions

Determine the exponential equation given:

1. (a) common ratio 2. (b) horizontal asymptote at y  7. (c) y-intercept of –2.

2. (a) common ratio 1

3 .

(b) horizontal asymptote at y  3. (c) y-intercept of –7.

3. (a) common ratio 2. (b) horizontal asymptote at y  6. (c) y-intercept of –3.

4. (a) common ratio 1

5 .

(b) horizontal asymptote at y  17. (c) y-intercept of 21.

Determine the exponential equation for each of the following graphs:

5.

6.

7.

8.

 

 

ID: A

9.

10.

11.

12.

Rewrite the following using only vertical transformations (i.e., in the form y  a b  x  q).

13. y  2 4  3 x  2   4

14. y  4 32  1 5

x  1   4

15. y  2 9  1 2

x  4   1

16. y  5 625  1

4 x  5 

 3

Determine the equation of the exponential function corresponding to the following points.

17. (–2, 169), (–3, 49), (–4, 29), (–5, 77 3

)

18. (–11,  31 6

), (–7,  67 6

), (–3,  79 6

), (1,  83 6

)

19. (20,  19 2

), (15,  7 2

), (10,  1 2

), (5, 1)

20. (5, 14), (3, 16), (1, 21), (–1, 131 6

)

discussion post

Respond to the following in a minimum of 175 words:

  • This week we began to examine relationships between quantities. Some ways we can compare quantities are by using percentages, ratios, rates, and unit labels. In your life, there are likely many situations that require you to compare quantities, understand the meaning of those comparisons, and make decisions based on those comparisons. What is an example of a situation from your professional or personal life that requires you to compare, understand, and make decisions based on quantitative comparison? Be sure to describe the types of quantitative comparisons you had to make, what decisions you made, and why. Would your decision be different if you had the benefit of learning this week’s concepts? Why or why not?

PHY 1001 Unit Five –Momentum

PHY 1001

Unit Five –Momentum

Mathematical Assignment

1. Calculate the momentum of a 265 kg motorcycle traveling at 25 m/s.

Key Idea  Stock of Data and

Solution

Sanity Check

2. A rubber ball (1 kg) falls from a height of 10 m and collides elastically with the floor.  What is the velocity of the ball as it rebounds from the floor?

Key Idea  Stock of Data and

Solution

Sanity Check

3. Two clay balls collide and stick. Ball 1 has a mass of 10 kg and an initial velocity of 10 m/s in the positive x direction. Ball 2 has a mass of 20 kg and an initial velocity of 5 m/s in the negative x direction.   What is the final velocity of the combined mass?

Key Idea  Stock of Data and

Solution

Sanity Check

4. Two clay balls collide and stick. Ball 1 has a mass of 10 kg and an initial velocity of 5 m/s in the positive x direction. Ball 2 has a mass of 20 kg and an initial velocity of 5 m/s in the negative x direction.   What is the final velocity of the combined mass?

Key Idea  Stock of Data and

Solution

Sanity Check

5. Two rubber balls undergo an elastic collision. Ball 1 has a mass of 10 kg and an initial velocity of 5 m/s in the positive x direction. Ball 2 has a mass of 10 kg and is stationary.   What is the final velocity of the two balls, v1f, and v2f?

Key Idea  Stock of Data and

Solution

Sanity Check

6. A ceiling fan turns at a rate of 20 RPM what is its speed in radians per second, and the speed of a tip of a 50 cm fan blade in m/s?

Key Idea  Stock of Data and

Solution

Sanity Check

7. Calculate the angular momentum of a 265 kg motorcycle traveling at 25 m/s. traveling around a circular curve 500 m in radius

Key Idea  Stock of Data and

Solution

Sanity Check

8. A ceiling fan turns at a rate of 20 RPM.  A 1 gram bug hangs on to the end of a 50 cm fan blade.  What is the magnitude of the frictional force between the bug’s feet and the blade?

Key Idea  Stock of Data and

Solution

Sanity Check

9. A wrench 30 cm long is attached to a nut and bolt.  You exert a 15 N force on the wrench.  What is the maximum torque you can exert under these conditions?

Key Idea  Stock of Data and

Solution

Sanity Check

10. A uniform beam of length 10 m and mass 100 kg is supported by pylons on either end.  A 200 kg box is centered at 5 m from the left end of the beam.  What is the downward force on the left most pylon?

Key Idea  Stock of Data and

Solution

Sanity Check

MFM1P0- Culminating Activity

MFM1P0- Culminating Activity

You are a city planner, trying to get the bid for a new city space. This task requires a series of steps and the application of knowledge from the course. We will be working on this activity throughout the entirety of the course, and at the end you will present your proposal to the Mayor (Ms. Pell). There will be one task related to each unit of study. Each task will be assigned at the end of the unit, instead of a unit test. At the end of the course you will incorporate feedback from the design phase and finalize your project. You may make changes from the design phase to the final product (just as many city planners do!) You will present your findings in any way you prefer (a video presentation, an interview with the mayor, a powerpoint, a poster, or any other approved method. Be creative!) You will need to complete a full report with total costs of your design in order for it to be approved by the city. Use the following questions to organize your ideas and show your work. Use proper mathematical communication to ensure your findings are clear and easy to understand. Unit 1: Geometry Unit 2: Algebra Unit 3: Proportions and Ratios Unit 4: Plane Geometry Unit 5: Linear Systems

Unit 1: Summative Task Your community space must consist of a pool. The pool can be any shape you desire, but keep in mind you will need to be able to calculate the area of the base as well as the volume of the shape. Your pool is required to have a deep end and a shallow end. The deep end and the shallow end must be composed of two different shapes (ex. Semicylinder and a rectangular based prism). To adhere to city guidelines the shallow end of the pool must be 0.5m deep. The deep end of the pool can be between 1.5m deep to 2.5m deep, you can decide what depth you would like it to be. 1. Draw your pool. Be sure to label all dimensions. [3A] 2. You must put a non-slip border around your pool. Calculate how many meters of non slip border you will be required to purchase. [4A] 3. The non-slip border costs $8.75/m. How much will it cost to purchase? [2T]

4. Your pool will need a cover. Determine how much area (hint: this area of the base) you will need to cover your pool. [5A] 5. If the material for a pool cover costs $5.00/m​2​, how much will it cost to cover your pool? [2T] 6. You will need to fill up the pool with water. How many liters of water will your pool hold? [6A] (hint: 1m​3​ = 1000L of water) [2T]

Self Assessment Checklist Use this little checklist to ensure you have meet the expectations!

Have I answer each question

Have I used formulas, and shown all of my work

Do my solutions have units

Have I reviewed material if questions were challenging

 

Have I included therefore statements for each questions

 

Have I double checked my calculations

maths

Please answer all questions asked in your initial post using detail and complete thoughts.

  • Scientific notation is used all around us, though it is generally hidden in metric prefixes. In the grocery store we might see it as a label saying there are 6060 milligrams of sodium in a product. This means 60×10−360×10−3 or 6×10−26×10−2 grams. What is an example of scientific notation you see in everyday use and what is one you might encounter in your major?

Problem Sheet 1 Mathematics for AI

Problem Sheet 1 Mathematics for AI

Problem Sheet 1 Week 2

This problem sheet consists of two questions. Each question contains three parts.

• Parts a), worth 40% of the marks in each question, test your knowledge of the core

material, and you should aim to provide good answers to this part of all questions.

• Parts b), worth 30% of the marks in each question, involve taking the concepts you have

been taught, but applying them in ways you may not have directly been shown. You

should attempt all the parts b), but you can still get a good mark without completing

all of them.

• Parts c), worth 30% of the marks in each question, are difficult questions which will test your understanding of the concepts taught in unfamiliar situations.

Question 1 (50%):

a) Translate the following sentences into propositional logic. Your formalizations should

be as detailed as possible.

i) Alice will go to the cinema or the theatre.

ii) Two is a prime number and not an odd number.

iii) If the speed limit is 30mph and I am driving at 25mph, then I am not breaking the

law.

iv) If Bob is not sleeping then he is working, eating, or relaxing.

v) Carlos will go to the park only if it is not raining.

Translate the following sentences into predicate logic. Your formalizations should be as

detailed as possible.

vi) Everyone is mortal.

vii) Unicorns do not exist.

viii) Every professional tennis player could beat any amateur tennis player.

ix) Everyone has either a father or a mother.

x) Somebody has visited every country that currently exists.

b) Consider the following formula of propositional logic:

P = ((A∧B)∨(¬A∧¬B)) →C

i) Suppose A = “I will go to the shops”, B = “I will go out for lunch” , C = “My

partner will be unhappy”. Translate P into an English sentence.

 

 

Problem Sheet 1 Mathematics for AI

ii) Suppose A is true, B is false and C is true. Is P true or false? Briefly explain

why.

iii) Which truth values for A , B and C result in P being false?

c) Consider the sentence “There is an animal in the zoo such that, if that animal is sleeping,

then every animal in the zoo is sleeping.”, formalised in predicate logic by the sentence

Q = ∃x(P x →∀yP y)

i) Suppose the zoo contains two animals, and both are sleeping. Is Q true or false?

ii) Now suppose one animal is sleeping, and one is awake. Is Q true or false?

iii) Now suppose we still know that the zoo contains two animals, but we do not know

how many are sleeping or awake. Can we know if Q is true or false?

iv) Now suppose we don’t know how many animals the zoo contains, except that there

is at least one animal, and we don’t know how many are awake or asleep. Can we

know if Q is true or false?

Question 2 (50%):

a) Identify which of these relations are reflexive, which are symmetric, which are transitive,

and which are equivalence relations. You do not need to show any working.

i) A is the set of all animals, R1 = {(a,b) |a is the same species as b}⊆A×A

ii) R2 = {(m,n) |m2 ≤n2}⊆Z×Z

iii) R3 = {(x,y) |x + y < 1}⊆R×R

iv) B = {0,1,2} , R4 = {(0,0),(0,1),(1,0),(1,1),(2,2)}⊆B×B

v) B = {0,1,2} , R5 = {(0,1),(1,2),(2,0)}⊆B×B

b) We define a function f : N→Z such that:

f (x) =

 x 2 if x is even

−x+12 if x is odd

i) Prove that f is an injection.

ii) Prove that f is a bijection.

iii) Given that f is a bijection, find the inverse function f −1 : Z→N

iv) Given the previous parts, what can we say about the cardinality of N and Z ?

c) In this problem sheet, we will call a relation R geometric if ∀x,y,z(xRy∧xRz →yRz)

i) Prove that if a relation is geometric and reflexive, then it is also symmetric.

 

 

Problem Sheet 1 Mathematics for AI

ii) Using the previous part, prove that if a relation is geometric and reflexive, then it

is an equivalence relation.

iii) Let f : A→B be a function. We define the relation

R⊆A×A, R = {(x,y) | f (x) = f (y)}

By showing that it is geometric and reflexive, show that R is an equivalence

relation. What are the equivalence classes of R ?