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NMSU - ASTR - 110G
we find that 1 light-year we can convert:100,000 light years * = 9.46 * 1017 km9.461012 km, soPlanet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune PlutoDriving Time 66 years 123 years 170 years 259 years 888 years 1,630 years 3,300 years 5,1
NMSU - ASTR - 110G
Chapter 2 Discovering the Universe for Yourself2.1 Patterns in the Night Sky Our goals for learning: What does the universe look like from Earth? Why do stars rise and set? Why do the constellations we see depend on latitude and time of year?What does
NMSU - ASTR - 110G
Chapter 3 The Science of Astronomy3.1 The Ancient Roots of Science Our goals for learning: In what ways do all humans employ scientific thinking? How did astronomical observations benefit ancient societies? What did ancient civilizations achieve in astr
NMSU - ASTR - 110G
Chapter 4 Making Sense of the UniverseUnderstanding Motion, Energy, and Gravity4.1 Describing Motion: Examples from Everyday LifeOur goals for learning: How do we describe motion? How is mass different from weight?How do we describe motion?Precise de
NMSU - ASTR - 110G
semimajor axis is 28,000 light-years. We need to convert these to seconds and meters respectively:230,000,000 yr * 365 days 24 hr * 1 year 1 day 60 min 60 s * * = 7.25 * 1015 s 1 hr 1 minMgalaxy =4p2 m3 a 6.67 * 10-11 b A 7.25 * 1015 s B 2 kg * s2 * A
NMSU - ASTR - 110G
Chapter 6 Formation of Planetary Systems Our Solar System and Beyond6.1 A Brief Tour of the Solar SystemOur goals for learning: What does the solar system look like?The solar system exhibits clear patterns of composition and motion. These patterns are
UCSD - ECON - 100B
Name: Economics 100B Microeconomics Spring 2010 James RauchPRACTICE FINAL EXAMThis exam is worth 240 points. Do all four problems. (50 points) 1. Suppose that the supply curve for gasoline is linear and upward-sloping with a positive intercept, the dema
UCSD - ECON - 100B
Due May 25, 2010Economics 100B Microeconomics Spring 2010 James RauchPROBLEM SET 5: General Equilibrium and Economic Welfare with two marketsConsider an economy populated by a representative consumer with preferences given by U(X,Y) = X2Y and endowment
UCSD - ECON - 100B
ECON 100B Spring 2009 Professor RauchAnswer Key for Problem Set 512
UCSD - ECON - 100B
Due June 1, 2010Economics 100B Microeconomics Spring 2010 James RauchPROBLEM SET 6: General Equilibrium and Economic Welfare with Three MarketsConsider an economy populated by a representative consumer with preferences given by U(X,Y) = XY and labor en
UCSD - ECON - 100B
M RS =XD YDY X=Px Py=1 (Px /PY )Cx = w Lx = w X/2 M Cx = w/2 = Px M Cy = w/4 = Py =XD YD X Y Px PyCy = w Ly = w Y /4 =4 2=2 =1 2= =1 (Px /Py ) 1 2Py = M Cy = Py = w/4 = w/Py = 4 M = w L/Py = 4 300 = 12002Y = 1200 = Y = 600; X = 300 L = x L
UCSD - ECON - 100B
Due June 1, 2010Economics 100B Microeconomics Spring 2010 James RauchPROBLEM SET 7: General Competitive Equilibrium with four markets Consider an economy with the following technology for producing X and Y: each unit of X requires 6 units of capital inp
UCSD - PHYS - 2cl
Final exam: Wednesday June 2 Location: CENTR 1018:00 - 8:50 pmAn 8 x 11 cheat sheet (both sides) will be allowed, recommended, and you can use your calculator during the exam. Exam will consist of 4 problems. 1 optics problem and 3 statistics problems.
University of Toronto - MANG - mgtb09
UNIVERSITY OF TORONTO at Scarborough Management MGTC09 (Intermediate Finance) Mid term Exam Date: March 6, 2009 Total Marks: 100 Time: 3-5 p.m. Rooms: HW216, SW309, SW319 Prof. Syed W. Ahmed TAs: David Chen & Evan Huang Number of Pages includin
American College of Gastroenterology - MGMT - MG2034
Introduction to the Field of Organizational BehaviorMcGraw-Hill/Irwin McShane/Von Glinow OB 5eCopyright 2010 by The McGraw-Hill Companies, Inc. All rights reserved.Pixar Animation StudiosOB practices have helped Pixar Animation Studios to become the w
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper A Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper B Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper C Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper D Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper E Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper F Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper G Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper H Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper I Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper J Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper K Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper L Time: 1 hour 30 minutesInstructions and InformationCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and / or integration.
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper BMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper CMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper DMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper EMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper FMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper GMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper HMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper IMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper JMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper KMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - c3
FOR EDEXCELGCE Examinations Advanced SubsidiaryCore Mathematics C4Paper LMARKING GUIDEThis guide is intended to be as helpful as possible to teachers by providing concise solutions and indicating how marks could be awarded. There are obviously altern
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper A Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper B Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper C Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper D Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper E Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper F Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper G Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper H Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper I Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper J Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper K Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Core Mathematics C4 Advanced LevelPaper L Time: 1 hour 30 minutesInstructions and InformationFor EdexcelCandidates may use any calculator EXCEPT those with the facility for symbolic algebra, differentiation and/or integration. Full marks may be obtain
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper A1 2 3x = + (a) (x - 1)(x + 2) x-1 x+233.(a)dy = ex - 3 dx at M ex = 3 x = ln 3ln 3 ln3 3 (ex - 3x)dx = ex - x 2 2 01.(using `cover up' rule)(3)(2)(b)22 1 + dx = ln(x - 1) + 2 ln(x + 2) x-1 x+2 5 4 25 = ln 2
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper B1. (a) xy - 2y + 5x - 10 = 12 x dy dy + y.1 - 2 +5=0 dx dx (b) - 3. 1 1 - 1 2 2 (a) 1 + (8x) + 2 2 1 1 3 - - 2 2 2 (8x)2 + 3.2 (8x)3 + . . . (3) (1)= 1 + 4x - 8x 2 + 32x 3 1 1 <x< 8 8dy (x - 2) = -(y + 5) dx dy y+5 =
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper C1. (a) 5x + 7 2 3 = + (x + 1)(x + 2) x+1 x+2 y = 2(x + 1)-1 + 3(x + 2)-1 dy = -2(x + 1)-2 - 3(x + 2)-2 dx d2 y dx 2 = 4(x + 1)-3 + 6(x + 2)-3 d2 y dx 2 4 6 13 = 3 + 3 = 18 2 3 (3) 4. (3) (b) valid for - 1 1 <x< 2 2 (1)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper D1. (a)y3.GivendS dr = 640 cm2 s-1 . To find . dt dtS = 4r 2 dS = 8r dr2 xdS dr dS = dt dr dt when r = 5, (2) 640 = 8 5 640 dr = dt 40 = 16 cm s-1 (4) dr dt22 2(b) volume = y 2 dx = (9 - x 2 )dx0 02 1 8 = 9x
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper E3. 1. (a) when y = 1, 4x 2 + 3 = 12 x2 = 9 4 3 2 dy 8x 4x =- =- dx 6y 3y (2) 1 2 cos 2 cos 2 dy 2 = =- (a) dx - sin sin 1 cos 3 = - 2 = -1 at = , gradient = - 1 6 sin 6 2 3 1 1 (b) at = , x = cos = and y = sin = 3. 6 6
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper F1. dx dy = cos t, = 2 + sin t dt dt cos t dy = dr 2 + sin t dy = 0. stationary points where dx 3 , . 2 2 when t = , x = 2 - cos = ; y = 2 2 2 2 i.e. cos t = 0 t = t= 3 , 2 x =2 3 3 - cos = 3; 2 2 y = 1 + sin 3 =0 2 (5)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper G1. (a) 2 cos t dy = dx - sin t when t = , 2 gradient = 0 (2) (b) (1 + bx) 1 + 6ax + 15a 2 x 2 = 1 + 6ax + 15a 2 x 2 + bx + 6abx 2 we have 6a + b = -9 15a 2 + 6ab = 24 from equation [A] substitute in [B] Hence a = -2, .[
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper Hx 1. (a) 1 1 + e-1 -1 1 1+e 0 1 1+1 1 1 1+ 1 e e = 1 e+1 1+ e 1 2. (a) (i) differentiating implicitly, 1 = ey 1 1 dy = y = dx e x (ii) when y = 0, x = e0 = 1 dy =1 dx dy dx (2)integral 1 e 1 1 + +2 2 1+e e+1 2 (b) (4)
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper I1. (a) dy 1 dx = (- sin ), = 2 cos 2 d (1 + cos ) d dy - sin = dx (1 + cos )2 cos 2 where = , gradient = 6 1 - 1 2 =- 1 3 3 2 2 1+ 1+ 2 2 2 1 (2 - 3) =- =- = 3-2 2+ 3 (2 + 3)(2 - 3) 3. (a) 1 dy + 3x 2 - 2 = 0 y dx dy =
Cambridge College - MATH - C4
Worked Solutions Edexcel C4 Paper J1. (a) We are given that dA = 40 cm2 s-1 dt 3. (a) 3 2 + 2x - 1 x + 2 1 dy = y (using `cover up' rule) (3)(b)after 10 seconds area of circle = 400 cm2 so r 2 = 400 r= (b) A = r 2 dA = 2r dr dA dr dA = dt dr dt when r