;
!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root Entry
FMicrosoft Word-Dokument
MSWordDocWord.Document.89qDyKyKhttp://www2.ed.gov/about/offices/list/ocr/docs/qa-201404-title-ix.pdfDI
[hhNormald1$*$A$/B*OJQJCJmH sH PJnHtH^JaJ_H<<Default Paragraph Font.. WW8Num1z0OJQJ^J.. WW8Num1z2OJQJ^J.!. WW8Num1z3OJQJ^J"1" WW8Num2z0"A" WW8Num2z1"Q" WW8Num2z2"a" WW8Num2z3"q" WW8Num2z4"" WW8Num2z5"" WW8Num2z6"" WW8Num2z7"" WW8Num2z8"" WW8Num3z0"" WW8Num3z1"" WW8Num3z2"" WW8Num3z3"" WW8Num3z4"" WW8Num3z5"!" WW8Num3z6"1" WW8Num3z7"A" WW8Num3z8"Q" WW8Num4z0"a" WW8Num4z1"q" WW8Num4z2"" WW8Num4z3"" WW8Num4z4"" WW8Num4z5"" WW8Num4z6"" WW8Num4z7"" WW8Num4z8"" WW8Num5z0"" WW8Num5z1"" WW8Num5z2"" WW8Num5z3"!" WW8Num5z4"1" WW8Num5z5"A" WW8Num5z6"Q" WW8Num5z7"a" WW8Num5z8.q. WW8Num6z0OJQJ^J.. WW8Num6z1OJQJ^J.. WW8Num6z2OJQJ^JBBWW-Default Paragraph FontFFBalloon Text CharOJQJCJ^JaJ::apple-converted-space6U6
Internet LinkB*ph>*FFHeading
>x$OJ QJ CJPJ
^JaJ4B4 Text Body?d / List@^J@"@Caption
Axx$CJ6^JaJ]&"&IndexB$^J2Colorful Shading - Accent 31Cd^]`m$OJQJCJPJ^JaJ|B|Light Grid - Accent 31%Dd$a$^]`m$OJQJCJPJ^JaJNRNBalloon TextEdOJQJCJ^JaJ^b^
No SpacingF1$*$/B*OJQJCJmH sH PJnHtH^JaJ_H4r4Table ContentsG$>q>
Table HeadingH$a$$5\N|<<2udDhT`j$ABCDEFl?F\HIKzLM6OOQQTUfVVWjXYYJZZx[t\"]]^^,__b``a.bbccrddZeeeehhijhkkplmmdnFoppqx&GHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~vyf<XXX8@0(
T
0@<<P
GTimes New Roman5Symbol3&ArialiLiberation SerifTimes New Roman5Tahoma7Calibri5Symbol?Courier New;WingdingsS&Liberation SansArialODroid Sans Fallback9FreeSans7CambriaBhRHgSHgRHgG 9G 900IvanaDerek MartinezyKyKthttps://policy.unm.edu/university-policies/2000/2740.htmlDyKyK<http://www.registrar.unm.edu/Oh+'0
px
IvanaNormal.dotmDerek Martinez4@F#@°*@°*@p E՜.+,D՜.+,\M 0&Caolan80 <AG::::D~4V
:&bP
MATH 153: Pre-calculus and Trigonometry
University of New Mexico, Fall 2016
Instructor:
E-mail:
Office:
Office Hours:Prerequisite: MATH 121 or placement test
Course Description: This course is a combination of math 123 and Math 150. Students who complete this course may go directly into math 162.
Topics covered: Algebraic expressions, algebraic equations, inequalities, functions, graphing. Exponential, logarithmic, and trigonometric functions. Complex numbers and vectors. Limits
Textbook: Precalculus Mathematics, Steward 7E
Calculator: Scientific calculator may be necessary. No calculators will be allowed on any of the exams (including the final).
Homework: Your daily homework is your most important effort in this course. It is imperative that you do all of the assigned problems, especially the hard ones, because this is how you actually learn the material. Expect 2-3 hours of homework for every hour of class meeting time (on average 6-9 hours per week). The HW you turn in should be neat, organized and your papers must be stapled to receive credit (do not put your work together at the last minute!).
WebAssign: is the electronic support that is crucial for your success in this class. It includes practice problems, quizzes, and tutorials. To register, go to http://www.webassign.com A registration code comes with your new textbook. Your instructor will have your course code. If you do not register within the first two weeks of class you may be dropped from the course.
Quizzes: Quizzes will be given throughout the term. Your two lowest quiz grades will be dropped. No make-up quizzes will be given.
Exams: There will be three in-class exams, 100 points each. No notes or calculators will be allowed on exams, including the final. You have to show all your work and use proper mathematical notation to receive full credit. A correct answer without work will receive 0 points. If you must miss an exam, you must contact your instructor on or before the day of the exam in order to discuss a make-up test. Make-up tests will be given solely at your instructor's discretion. If you do not contact your instructor immediately, you may be dropped from the course.
Final Exam: Core final exam, worth 200 points. The final exam will be on Monday, Dec 12th, 10 am-12 pm, room TBA.
Exam dates are set by either the syllabus or your instructor, examdates are not negotiable. No early final exam will be given; we willadhere to the final exam schedule published by the Registrar's Office.
Grading: To get full credit on graded work students must address all mathematical components presented by the problem, showing all steps and calculations. The use of proper notation, well structured procedures, and legibility will be taken into account when assigning points.
Your grade will be determined based on your performance on the following:
Webassign: 50 points Quizzes/Assignments: 150 points Exams: 400 points
Exams: 400 points Final Exam: 200 points Total: 800 points
Attendance: Attendance is mandatory. If a student has more than three unexcused absences he/she may be dropped from the course. Tardiness or early departure may be regarded as absence. Please note that it is the student s responsibility to drop the course if he/she stops attending. A failing grade of F may be assigned if the student stops attending and does not drop.
Student Behavior: According to the Code of Conduct as stated in the Policies and Regulations for UNM, student activities that interfere with the rights of others to pursue their education or to conduct their University duties and responsibilities will lead to disciplinary action. This includes any activities that are disruptive to the class and any acts of academic dishonesty. Students are expected to behave in a courteous and respectful manner toward the instructor and their fellow students. Students may be dropped for inappropriate behavior. The use of cell phones, headphones, etc. is not permitted during class or exams.
In an effort to meet obligations under Title IX, UNM faculty, Teaching Assistants, and Graduate Assistants are considered responsible employees by the Department of Education (see pg 15 - HYPERLINK "http://www2.ed.gov/about/offices/list/ocr/docs/qa-201404-title-ix.pdf" \n _blankhttp://www2.ed.gov/about/offices/list/ocr/docs/qa-201404-title-ix.pdf). This designation requires that any report of gender discrimination which includes sexual harassment, sexual misconduct and sexual violence made to a faculty member, TA, or GA must be reported to the Title IX Coordinator at the Office of Equal Opportunity (oeo.unm.edu). For more information on the campus policy regarding sexual misconduct, see: HYPERLINK "https://policy.unm.edu/university-policies/2000/2740.html" \n _blankhttps://policy.unm.edu/university-policies/2000/2740.html
Cheating: Cheating of any kind will not be tolerated. Examples are: looking at a neighbor s exam, plagiarizing, using a calculator when not permitted, using the book and/or a cheat sheet, modifying an exam after it is graded, etc. The instructor may warn an offending student, the score of the exam may be reduced, the score may be set to zero, the student may get dropped from the class, the student may get a grade of F for the class, and in most cases the incident will be reported to the Dean of Students.
Deadlines: The Department of Mathematics and Statistics will adhere to all of the registration deadlines published by the Office of the Registrar in the schedule of classes.
Grading: To get full credit on graded work students must address all mathematical components presented by the problem, showing all steps and calculations. The use of proper notation, well structured procedures, and legibility will be taken into account when assigning points.
Grade mode and Withdrawals: You must select your grade mode (Letter Grade, CR/NC, or Audit) within the first 2 weeks of the semester. We will not give permission to change the grade mode after the deadline.
Students who are in the regular grade mode and who withdraw after the end of week 3 will receive a grade of W . If you do not withdraw (but stop attending), you will receive a letter grade of A, B, C, D, or F (not a W).
Students who are in the CR/NC grade mode and who withdraw after the end of week 3 will receive a grade of W . If you do not withdraw (but stop attending), you will receive a letter grade of NC (not a W).
See the list of all deadlines: HYPERLINK "http://www.registrar.unm.edu/"www.registrar.unm.edu
Accessibility Statement: We will accommodate students with documented disabilities (through ARC). During the first two weeks of the semester, those students should inform the instructor of their particular needs.
Extra Help: In addition to your instructor's office hours, there is extra help available at:
- The Algebra Tutoring Table, staffed by algebra instructors 9 - 3 every day. It is located in front of the elevators on the second floor of DSH and behind room #224.
- CAPS: Center for Academic Program Support. Located on the 3rd floor of Zimmerman Library, 277-4560
- MEP Engineering Annex, room 210, or call the study group at 277-8795
- CATS: Counseling and Therapy Services, Student Health Center, 277-4537. (For test anxiety, etc.)
Registration, Drop, and Grade Change Deadlines: The Department of Mathematics and Statistics will adhere to ALL registration deadlines published by the Office of the Registrar in the schedule of classes. For full term classes in the fall 2015 term the deadlines are:
September 2nd Add a course, change sections, or change grade mode in MyUnm
September 9th Last day to drop without a grade
November 11th Last day to withdraw without the Dean s permission (grade of W assigned)
December 9th Last day to withdraw with the Dean s Permission
Note: The instructor reserves the right to change the syllabus at any point of time during the semester.
Schedule of Topics:
Week (of)Topics1 (8/22) 2.2 and 2.4 Graphs of Functions and Rates of Change; 2.6 Transformations; 2.7 Combining Functions2 (8/29)3.1 Quadratic Functions/Models (two days); 3.2 Polynomial Functions; 3.6 Rational Functions (day 1)3 (9/5)No Class Monday; 3.6 Rational Functions (day 2); 1.8 Inequalities; Review4 (9/12)Exam 1; 2.8 Inverse Functions; 4.1 and 4.2 Exponential Functions5 (9/19)4.3-4.6 Logarithms, equations and models6 (9/26)11.2 and 11.3; Ellipses/Hyperbolas (one day); 10.8 Nonlinear Systems (include linear systems, ellipses, hyperbolas); Review; Exam 27 (10/3)5.1 Unit Circle; 5.2 Trig Functions; 5.3 and 5.4 Trig Graphs8 (10/10) 5.5 Inverse Trig Functions; 6.1 Angle Measure; 6.2 Applications; No Class Thurs/Fri (Holiday)9 (10/17)6.2 Applications; 6.3 Trig Functions of Angles; 6.4 Inverse Functions and Right Triangles; 6.5 Law of Sines10 (10/24)6.6 Law of Cosines; Review; Exam 3; 11 (10/31)7.1 Identities; 7.2 and 7.3 Special Formulas; 7.4 Trig Equations12 (11/7)7.5 More Trig Equations; 8.4 Parametric Equations; 8.1 Polar Coordinates; 1.6 Complex Numbers13 (11/14)8.3 Polar Form of Complex Numbers; 9.1 and 9.2 Vectors/Dot Product; Review14 (11/21)13.1 and 13.2 Limits; No Class Thurs/Fri (Holiday)15 (11/28) 13.3 and 13.4 Limits (limit of DQ to get tangent slope/line); Review; Exam 416 (12/5)Review Week17 (12/12)Final Exam on Monday Dec 12th: 10am-12pm; Room TBA
Textbook Suggested HW: This is a fairly comprehensive list of practice problems to do from the book. These are not collected for a grade, but are where you ll get the majority of practice for tests, quizzes, etc. Skip any parts of problems asking you to use a graphing calculator. Do only the odd problems, unless otherwise specified.2.2 Graphs of Functions11,19,25,35-41,49,53,56,61,632.4 Average Rate of Change9-24all,29-352.6 Transformations of Functions7-17,29-37,41-51,63-67,71,73,83-892.7 Combining Functions17,19,27-37,49-55,59,63,65,77-813.1 Quadratic Functions/Models15,19,23-33,39-43,47,51-65 3.2 Polynomial Functions/Graphs5-433.6 Rational Functions15,17,21-25,31-37,43,49,55,57,63,69-731.8 Inequalities21,23,35,43,53,55,57,61,69,75-85 2.8 One-to-One, Inverse Functions15,17,25,43-47,53,55,59-68,71,73,87,93,974.1 Exponential Functions21-27all,27-414.2 Natural Exponential Function7-13,23,25,29,33,354.3 Logarithmic Functions9-23,27,29,33,35,39,53,55,61-69,73-774.4 Laws of Logarithms9-19,25,37,41,43,47,51-57,614.5 Exp. /Log. Equations15,21,29,35,37,39,45,61,65,67,89-974.6 Modeling with Exp./Log. 3-2711.2 Ellipses(no foci, graph using intercepts) 5-25,45,51,6911.3 Hyperbolas(no foci, graph using intercepts/asymptotes) 5-25,29,41-4510.8 Systems of Nonlinear Equations3,9,15,17,21,23,27,31,41,455.1 Unit Circle1-19, 41-515.2 Trig Functions of Real Numbers5-21,37-43,53-67,71,735.3 Trig Graphs5,9,13,17,21,25,27,35,39,40,41,43,47-53,83,855.4 Trig Graphs 3-13,17,19,25,27,35-47,53-595.5 Inverse Trig Functions3-11,17,23,25,31,456.1 Angle Measure5, 9, 13-17,23,29,31,41,49,53-69,77,79,85-916.2 Trig of Acute Angles/Applications3-7,15,19-23,37,41,53-656.3 Trig Functions of Angles7-17,23,27,31,37,53,65,67a6.4 Inverse Trig and Right Triangles1-19,23-37,41,436.5 Law of Sines3-9, 17-21, 31,396.6 Law of Cosines7-15, 25, 39-43, 49, 517.1 Identities7,9,13,19-23,31-43,45,55,63,65,73,77,85,89-937.2 Special Formulas21-35,47,49,63,657.3 Special Formulas5-13, 25, 29-33, 37, 41, 55, 57, 73, 74, 757.4 Trig Equations5-9, 13, 17, 19, 25, 31, 37, 41-537.5 More Trig Equations3, 9, 11, 17-27, 35b, 37b, 38b, 39-43,478.4 Parametric Equations 3-7, 13-19,25,33-37,598.1 Polar Coordinates7-15,25-33,39-631.6 Complex Numbers19-518.3 Polar Form of Complex Numbers5-17,21-53,57-619.1 Vectors in 2D5-21, 33-51, 53-59, 679.2 Dot Product9-2313.1 Limits5-9,11-15 (table only), 17, 19, 29, 3113.2 Limits9-4313.4 Limits5-17,23-3313.3 DQ/Derivative3-9, 11-17
Graded HW: This is a more concise list problems from the book. These ARE collected for a grade, unless your instructor is using graded worksheets instead. Ask your instructor for due dates.
1.8: 42, 46, 58, 66, 682.2: 36, 38, 42, 46, 502.4: 14, 16, 20, 22, 24, 322.6: 46, 48, 50, 52, 682.7: 49, 55, 56, 64, 66
3.1: (lecture 1) 18, 20, 28, 33, 37
3.1: (lecture 2) 53, 55, 56, 58, 63, 64
3.2: 7, 16,18, 30, 36, 43
3.6: (lecture 1) 14, 16, 26, 34, 36,
3.6: (lecture 2) 48, 52, 60, 69, 72, 76, 92
2.8: 18, 46, 48, 50, 58, 62, 74
4.1: 8, 12, 14, 22
4.2: 8, 10 ,12, 14, 26,, 27
4.3: 12, 18, 24, 34, 42, 44, 60, 64, 784.4: 20, 22, 46, 54, 58, 744.5: 22, 36, 46, 51,90, 95, 96, 10010.8: 4, 10, 16, 20, 46
11.2: 10, 16, 27, 46
11.3: 10, 24, 386.1: 8, 16, 18, 24, 48, 54, 55
6.2: 16, 24, 38, 42, 48, 58, 68
6.3: 26, 34, 38, 48, 59, 70
6.4: 8, 12,18, 40, 42
6.5: 14, 16, 20, 32, 34
6.6: 16, 20, 26, 40, 44, 485.1: 24, 26, 38, 42, 465.2: 6, 8, 10, 12, 18, 265.3: 5,6, 12, 18, 20, 34, 46, 485.4: 10, 12, 18, 36, 625.5: 4, 8, 10, 14, 24, 26, 40, 467.1: 16, 20, 28, 38, 48, 66, 109
7.2: 4, 16, 26, 28, 40, 44, 48, 52, 627.3: 8, 10, 32, 46, 48, 74, 114
7.4
7.5: 8, 14, 20, 25, 32, 40, 66
8.1: 6, 8, 12, 18, 28,30, 36, 44, 58, 64
8.3: 14, 16, 18, 54, 56, 62, 728.4: 4, 8, 10, 14, 3213.1: 10, 20, 29, 3213.2: 3, 15, 31, 4213.3: 3, 6, 13, 1713.4: 6, 10, 11, 14, 17, 39
Math 153: Trigonometry and Precalculus Student Learning Outcomes
By the end of the semester, students should be able to
(SLO#1) Use Correct Mathematical Notation and Terminology
(SLO#2) Graph and Interpret Functions: Sketch and interpret graphs in context of applications; apply appropriate transformations for the following: polynomial functions (linear, quadratic, followed by those with degree three and higher), trigonometric functions, exponential and logarithmic functions, rational functions, parametric equations, and conic sections. Be able to create and graph piece-wise functions from all of the above. Create graphs to model situations.
(SLO#3) Perform Operations on Functions: Be able to use function notation to evaluate expressions and perform operations on functions such as addition, subtraction, multiplication, division, composition and difference quotients of functions. Be able to find the domain and range of functions as well as their inverses (if they exist).
(SLO#4) Analyze the Behavior of Functions: Be able to determine the end behavior and intercepts of functions. Be able to determine extreme values of functions and intervals where functions increase or decrease. Apply this analysis to interpreting an applied problem.
(SLO#5) Solve Equations: Be able to solve exponential, logarithmic, trigonometric, quadratic, radical, and rational equations. Also be able to solve linear and non-linear systems of equations. Be able to interpret solutions in context of applications.
(SLO#6) Solve Applied Problems: Be able to set up models from word problems using appropriate functions or laws.
(SLO#7) Perform Operations with Complex Numbers and Vectors: Be able to determine the trigonometric and polar form of a complex number. Be able to add vectors in two dimensions, project vectors onto one another, and determine the angles between vectors. Use vectors and complex numbers to solve applied problems. N H r d
4L0
D
z,4fjr~&>
j
aJ5aJ)B*ph!!!CJPJnH tH ^JaJOJQJ:B*ph!!!CJfHq
PJnH tH ^JaJOJQJH*CJ5aJCJ>*5aJCJ6aJCJ65aJ56]CJaJCJ5aJ9""('B'p'(()))4*6*,,---
...$.2$2j3|355::::";$;&;P;R;;<====??????h@n@v@.AADC\C`CCCCLDdDH*CJaJCJ6aJCJaJCJ5aJ0J=jU5jU!0J=fHq
^JOJQJjUU&B*ph!!!fHq
^JOJQJ>*5\>dDhDDDEEEREZEEEXFFFFFFF|GGGXH\HjHHII$IIIIIIJ
KKK*KKKK@LxL|LLfMjM~MMMMMbNfNxN4O8OLOOOO(P`PdPzPQQQ*QBQFQZQQQQQQQdThTCJ5^JaJOJQJH*CJ5aJCJ5aJCJaJCJ5aJCJaJH*CJaJOhTTTT
U&U*UjUUUU$V(VdVVVVVVWfWjWWWWXhXlXXXXY(Y,Y^YYYYZZHZZZZZZZ8[T[X[v[[[[8\p\t\\\\\ ]$]B]]]]]^4^\^`^^^^*_\_`____`<`@`````CJ^JaJOJQJCJ5^JaJOJQJ5^JOJQJ^JOJQJV`````Xa\aaaaa,b0bTbbbbc"cRcccccccddNdpdtddddddd
eXe\ere|eeeeeeeeeeeeetgxgzgggggghhhBhNhrhvhhhhiiFiJiiiiii0j4jXjjjj^JPJ^J5^JOJQJCJ5PJ^JaJOJQJ^JOJQJVjjkfkjkkkkkkkk*l.lllplrlllll
mmmFmvmmmmnbnfnnnn:oBoFoHooooop pJptppppppqqqqqrhrzrrv*vlvxxyzz{||}}}*~$CJPJ^JaJOJQJCJ5PJ^JaJOJQJPJ^J^JLPJ f
62
(l
d*$$a$
$a$m$l"r'..2l35878:T;<=?
^]`m$m$^h]`^h]`^h]`^h]`^h]`^h]`^h]`^h]`^h]`^h]`^h]`??j@0AFCCNDEEZFFFFFFzP$$If0* p44l44l4f4
$If$Ifd1$*$A$m$
^]`m$F~GGGZH\H/P$$If0* p44l44l4f4$Ifd1$*$A$
$IfP$$If0* p44l44l4f4$Ifd1$*$A$\HlHIIII$Ifd1$*$A$P$$If0* p44l44l4f4$Ifd1$*$A$
$IfIIIIIJKSA$Ifd1$*$A$P$$If0* p44l44l4f4
$IfP$$If0* p44l44l4f4KK,KKKKzLSA$Ifd1$*$A$P$$If0* p44l44l4f4
$IfP$$If0* p44l44l4f4zL|LLhMjMMMSA$Ifd1$*$A$P$$If0* p44l44l4f4
$IfP$$If0* p44l44l4f4MMMdNfNzN6OSA$Ifd1$*$A$P$$If0* p44l44l4f4
$IfP$$If0* p44l44l4f46O8ONOOOOAP$$If0* p44l44l4f4
$If$Ifd1$*$A$P$$If0* p44l44l4f4ObPdP|PQQ/P$$If0* p44l44l4f4$Ifd1$*$A$
$IfP$$If0* p44l44l4f4$Ifd1$*$A$Q,QDQFQ\QQQQA?P$$If0* p44l44l4f4$Ifd1$*$A$P$$If0* p44l44l4f4
$IfQQfThTTTTDT$$If0Y* p44l44l4f4T$If$a$G$$IfG$>$$If*
p
44l44l4f4T
$IfTU(U*UlUUt$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$UUU&V(VfV:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4TfVVVVV$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$VVWhWjWW:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4TWWWXjX$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$jXlXXXXY:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4TY*Y,Y`YY$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$YYYZZJZ:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4TJZZZZZ$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$ZZZV[X[x[:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Tx[[[:\r\t\.T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$IfG$t\\\\\"]t$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$"]$]D]]]]:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4T]]^6^^^$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$^^`^^^^,_:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4T,_^_`___$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$__`>`@`b`:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Tb`````$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$```Za\aa:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Taaaa.b$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$.b0bVbbbb:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Tb c"cTcc$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$cccccc:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Tc
ddPdrd$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$rdtddddd:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4TdddeZe$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$Ze\ete~eee:.$IfG$T$$If0Y* p44l44l4f4T$If$a$G$$IfG$T$$If0Y* p44l44l4f4Teeeee$If$a$G$$IfG$T$$If0Y* p44l44l4f4T$If$a$G$eeeeeee=;9T$$If0O* p44l44l4f4T$IfG$$IfG$T$$If0Y* p44l44l4f4Teevgxgzgggh<$$If$
p
44q44l4f4
$Ifd$IfdhhDhthvhhh$If
$Ifdh$$IfF$P p44q44l4f4hhiiHiJiii
$Ifd$Ifh$$IfF$P p44q44l4f4iiii2j4jZjjj
$Ifd$Ifh$$IfF$P p44q44l4f4jjj khk
$Ifdh$$IfF$ p44q44l4f4hkjkkkkkkwqw$If
$Ifd$IfG$
$Ifh$$IfF$ p44q44l4f4kkk,l.lnlpl$If
$Ifdh$$IfF$P p44q44l4f4plrlllllmm
$Ifd$Ifh$$IfF$P p44q44l4f4mmHmxmm
$Ifd
$Ifh$$IfF$P p44q44l4f4mmm ndn
$Ifh$$IfF$P p44q44l4f4dnfnnnn