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BU >> HUMANITIES >> HU 101-202 (Spring, 2008)
Ethical Philosophy - Together the word philosophy is formed meaning the love of wisdom 3 Major studies of philosophy - metaphysics o literally means above physics o physics is the study of physical properties- what is above that is what holds the wor...
BU >> HUMANITIES >> HU 101-202 (Spring, 2008)
Lynda Guerrero Humanities 202 Professor Sweeting \"Trader Joes: The Side Not Advertised\" March 19, 2008 Trader Joes is advertised as the neighborhood grocery store that gives you a quick exotic culinary experience without the high prices of airfare. ...
BU >> HUMANITIES >> HU 101-202 (Spring, 2008)
Humanities Lecture Monday September 24, 2007 Read the handout also Functions of Mankind - he starts looking at what makes a specific animal that animal - and what makes a living thing living o he says a living thing is able to sustain itself o it als...
BU >> HUMANITIES >> HU 101-202 (Spring, 2008)
Painters to consider: Vienna became the center for a strange form of modernism known as expressionism - it\'s a strange modernism in which things are not holding together o something is wrong o not interested in capturing reality at all - around 1900 ...
Texas State >> COMM >> 1310 (Spring, 2008)
COMMUNICATIONS STUDY GUIDE: CHP 1-6 Chapter 1: 1. Communication- the process of acting on information. Human Communication- is the process of making sense out of the world and sharing that sense with others by creating meaning through the use of verb...
SUNY Oswego >> BRC >> 350 (Spring, 2008)
Broadcasting 350 Study Sheet Women & Media 2007 Percent of Women Reports, Guests, etc. Women in Newsrooms Percent Teenage viewing of Music Videos Malamuth and Donnerstein Research on Slaher films, etc. Violence on MTV Violence Against Women in Mus...
UC Riverside >> ENGL >> 1A (Spring, 2008)
Yelba Payan English 103 One of the ideas that play a crucial role in \"The Handmaid\'s Tale\" by Margaret Atwood is a portrait on the examination of gender. In their society women are brainwashed to adapt to a society were they have to be pure. Meaning...
Vanderbilt >> POLYSCI >> 100 (Spring, 2008)
225 benson hall -Eisenhower, Dulles, and the Cold War -1950-conformity, sharply defined gender roles, non-diversified -Eisenhower -Figure who has a long career in the military -Gains support from whites and blacks against Stevenson with New Deal Plan...
Vanderbilt >> POLYSCI >> 100 (Spring, 2008)
Page 1 On Track For Success United States-Russian Relations By: Alexander Litt Quic kTim eTM and a TIFF (Unc om pressed) decom pressor are needed to see this picture. ? Page 2 Since the middle of the nineteenth century, compromises such as the U...
Vanderbilt >> POLYSCI >> 100 (Spring, 2008)
hina and US engage in trade manoeuvres.(VIEW FROM CHINA). Simon Robinson. ICIS Chemical Business (Weekly) 1.13 (April 3, 2006): p13(1). From General Business File ASAP. About this publication | How to Cite | Source Citation | Translate Subjects Full ...
Vanderbilt >> POLYSCI >> 100 (Spring, 2008)
American Foreign Policy Midterm 2 Reading Notes: \"Going Critical\" The number of people collecting social security and Medicare will double in 5 years while the number of people paying taxes will only increase by 18 percent. This will put US governme...
Vanderbilt >> POLYSCI >> 100 (Spring, 2008)
1. Is continued progress of the EU toward becoming more like a federal union in the interest of the United States? Should the US still continue to support ever higher levels of integration for the EU? a. No, the United States should limit the EU beca...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.143 For the vectors U D 6i C 2j 4k, V D 2i C 7j, and W D 3i C 2k, evaluate the following mixed triple products: (a) U V W ; (b) W V U ; (c) V W U . Solution: Use Eq. (2.36). 6 2 (a) U V W D 2 7 3 0 D 6 14 3 (b) W V U D 2 6 D3 2 (c...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.144 Use the mixed triple product to calculate the volume of the parallelepiped. y (140, 90, 30) mm (200, 0, 0) mm x z (160, 0, 100) mm Solution: We are given the coordinates of point D. From the geometry, we need to locate points A and ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.145 that By using Eqs. (2.23) and (2.34), show Uy Vy Wy Uz Vz Wz Ux U V W D Vx Wx . Solution: One strategy is to expand the determinant in terms of its components, take the dot product, and then collapse the expansion. Eq. (2.23) is an...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.146 The vectors U D i C UY j C 4k, V D 2i C j 2k, and W D 3i C j 2k are coplanar (they lie in the same plane). What is the component Uy ? Solution: Since the non-zero vectors are coplanar, the cross product of any two will produce a vector ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.157 (a) Write the position vector rAB from point A to point B in terms of scalar components. (b) The vector F has magnitude jFj D 200 N and is parallel to the line from A to B. Write F in terms of scalar components. Solution: (a) rAB D xB D...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.158 The rope exerts a force of magnitude jFj D 200 lb on the top of the pole at B. (a) (b) Determine the position vector Determine the position vector vector rAB F, where rAB is the from A to B. vector rAC F, where rAC is the from A to C....
Washington >> A A >> 210 (Spring, 2008)
Problem 2.159 The magnitude of FB is 400 N and jFA C FB j D 900 N. Determine the components of FA . FB y FA 60 30 50 40 x z Solution: jFB j D 400 N We need to write each vector in terms of its known or unknown components. From the diagram FAx D ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.160 Suppose that the forces FA and FB shown in Problem 2.159 have the same magnitude and FA FB D 600 N2 . What are FA and FB ? Solution: From Problem 2.159, the forces are: FA D jFA j i cos 40 sin 50 C j sin 40 C k cos 40 cos 50 D jFA j 0....
Washington >> A A >> 210 (Spring, 2008)
Problem 2.161 The magnitude of the force vector FB is 2 kN. Express it in terms of scalar components. y F D (4, 3, 1) m FC FB A z FA C x (6, 0, 0) m B (5, 0, 3) m Solution: The strategy is to determine the unit vector collinear with FB and then e...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.137 The force vector F points along the straight line from point A to point B. Its magnitude is jFj D 20 N. The coordinates of points A and B are xA D 6 m, yA D 8 m, zA D 4 m and xB D 8 m, yB D 1 m, zB D 2 m. (a) (b) Express the vector F in...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.138 The rope AB exerts a 50-N force T on the collar at A. Let rCA be the position vector from point C to point A. Determine the cross product rCA T. B y 0.15 m 0.4 m C T Solution: The vector from C to D is rCD D xD yC j C zD jrCD j D zC...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.135 For the points O, A, and B in Problem 2.134, use the cross product to determine the length of the shortest straight line from point B to the straight line that passes through points O and A. Solution: rOA D 6i 2j C 3k (m) 4k m (The magn...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.136 The cable BC exerts a 1000-lb force F on the hook at B. Determine rAB F. Solution: The coordinates of points A, B, and C are A (16, 0, 12), B (4, 6, 0), C (4, 0, 8). The position vectors are 6 ft rOA D 16i C 0j C 12k, rOB D 4i C 6j C 0...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.133 Use the cross product to determine the components of a unit vector e that is normal to both of the vectors U D 8i 6j C 4k and V D 3i C 7j C 9k. (Notice that there are two answers.) Solution: First, find U V D R i RDUVD 8 3 RD RD eR D s...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.134 (a) What is the cross product rOA rOB ? (b) Determine a unit vector e that is perpendicular to rOA and rOB . Solution: The two radius vectors are rOB D 4i C 4j (a) 4k, rOA D 6i 2j C 3k y B ( 4, 4, 4) m rOB O The cross product is i r...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.132 By evaluating the cross product U V, prove the identity sin 1 2 D sin 1 cos 2 cos 1 sin 2 . y U V 1 2 x Solution: Assume that both U and V lie in the x-y plane. The strategy is to use the definition of the cross product (Eq. 2.28)...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.131 The force F D 10i mine the cross product rAB F. 4j (N). Deter- y (6, 3, 0) m A rAB z x (6, 0, 4) m B F Solution: The position vector is rAB D 6 6 iC 0 3 jC 4 0 k D 0i 3j C 4k y A (6, 3, 0) The cross product: i 0 10 j k 3 4 D i 16 ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.129 The cross product of two vectors U and V is U V D 30i C 40k. The vector V D 4i 2j C 3k. Determine the components of U. Solution: We know i U V D Ux 4 j k Uy Uz 2 3 3Ux j C 2Ux 4Uy k (1) Equating components of (1) and (2), we get 3Uy C...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.130 20. (a) (b) (c) (d) The magnitudes jUj D 10 and jVj D y V U Use the definition of the cross product to determine U V. Use the definition of the cross product to determine V U. Use Eq. (2.34) to determine U V. Use Eq. (2.34) to det...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.128 Suppose that the cross product of two vectors U and V is U V D 0. If jUj 6D 0, what do you know about the vector V? Solution: Either V D 0 or VjjU c 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This mater...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.126 What is the cross product r F of the position vector r D 2i C 2j C 2k (m) and the force F D 20i 40k (N)? Solution: Use Eq. (2.34) and expand into 2 by 2 determinants. rFD i 2 20 j 2 0 k 2 Di 2 40 40 0 2 j 2 40 20 2 C k 2 0 rFD 80i C ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.127 Determine the cross product r F of 12j C 3k (m) and the force Solution: rFD i 4 16 j 12 22 k 3 10 40 j the position vector r D 4i F D 16i 22j 10k N . r F D 120 C 88 66 i C 48 192 k N-m r F D 186i C 88j C 104k N-m c 2005 Pearso...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.124 (a) Determine the cross product U V of the vectors U D 4i C 6j 10k and V D 8i C 12j C 2k. (b) Use the dot product to prove that the vector U V is perpendicular to U and perpendicular to V. Strategy: The vectors are expressed in terms ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.123 Point P is at longitude 30 W and latitude 45 N on the Atlantic Ocean between Nova Scotia and France. (See Problem 2.86.) Point Q is at longitude 60 E and latitude 20 N in the Arabian Sea. Use the dot product to determine the shortest di...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.139 The straight line L is collinear with the force vector F. Let D be the perpendicular distance from an arbitrary point P to L. Prove that DjFj D jr Fj, where r is a position vector from point P to any point on L. Solution: By definition...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.140 The bar AB is 6 m long and is perpendicular to the bars AC and AD. Use the cross product to determine the coordinates xB , yB , zB of point B. Solution: The strategy is to determine the unit vector perpendicular to both AC and AD, and t...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.141* Determine the minimum distance from point P to the plane defined by the three points A, B, and C. Solution: The strategy is to find the unit vector perpendicular to the plane. The projection of this unit vector on the vector OP: rOP e...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.142* The force vector F points along the straight line from point A to point B. Use Eqs. (2.28)(2.31) to prove that rB F D rA F. y A F rA B rB x Strategy: Let rAB be the position vector from point A to point B. Express rB in terms of of...
Washington >> CHEM E >> 260 (Spring, 2008)
12-1 Chapter 12 THERMODYNAMIC PROPERTY RELATIONS Partial Derivatives and Associated Relations 12-1C z dz (z)y (z)x x dx y dy dz = (z ) x + (z ) y y x dx x+dx dy y + dy y x 12-2C For functions that depend on one variable, they are identical. ...
Washington >> CHEM E >> 260 (Spring, 2008)
7-1 Chapter 7 ENTROPY Entropy and the Increase of Entropy Principle 7-1C No. The Q represents the net heat transfer during a cycle, which could be positive. 7-2C No. A system may produce more (or less) work than it receives during a cycle. A st...
Washington >> MATH >> 308 (Spring, 2008)
Linear Algebra 1 2 3 1 x1 x3 2 1 6 2 8 1 Jim Hefferon Notation R N C {. . . . . . } . V, W, U v, w 0, 0V B, D En = e1 , . . . , en , RepB (v) Pn Mnm [S] M N V W = h, g H, G t, s T, S RepB,D (h) hi,j |T | R(h), N (h) R (h), N (h) real numbers n...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.147 The magnitude of F is 8 kN. Express F in terms of scalar components. y (3, 7) m Solution: The unit vector collinear with the force F is developed as follows: The collinear vector is r D 7 3 i C 2 7 j D 4i 5j The magnitude: jrj D eD r D...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.148 The magnitude of the vertical force W is 600 lb, and the magnitude of the force B is 1500 lb. Given that A C B C W D 0, determine the magnitude of the force A and the angle . B 50 W A Solution: The strategy is to use the condition o...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.149 The magnitude of the vertical force vector A is 200 lb. If A C B C C D 0, what are the magnitudes of the force vectors B and C? 50 in. 70 in. 100 in. C E B A D F Solution: The strategy is to express the forces in terms of scalar ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.150 The magnitude of the horizontal force vector D in Problem 2.149 is 280 lb. If D C E C F D 0, what are the magnitudes of the force vectors E and F? Solution: The strategy is to express the force vectors in terms of scalar components, and...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.151 What are the direction cosines of F? y F = 20i + 10j 10k (lb) A (4, 4, 2) ft Refer to this diagram when solving Problems 2.1512.157. B (8, 1, 2) ft x z Solution: Use the definition of the direction cosines and the ensuing discus...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.152 Determine the scalar components of a unit vector parallel to line AB that points from A toward B. Solution: Use the definition of the unit vector, we get The position vectors are: rA D 4i C 4j C 2k, rB D 8i C 1j 2k. The 4 vector from A...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.153 What is the angle between the line AB and the force F? Solution: Use the definition of the dot product Eq. (2.18), and Eq. (2.24): cos D rAB F . jrAB jjFj From the solution to Problem 2.130, the vector parallel to AB is rAB D 4i 3j...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.154 Determine the vector component of F that is parallel to the line AB. Solution: Use the definition in Eq. (2.26): UP D e U e, where e is parallel to a line L. From Problem 2.152 the unit vector parallel to line AB is eAB D 0.6247i 0.46...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.155 Determine the vector component of F that is normal to the line AB. Solution: Use the Eq. (2.27) and the solution to Problem 2.154. FN D F FP D 20 8.78 i C 10 C 6.59 j C 1.22k (lb) 10 C 8.78 k D 11.22i C 16.59j c 2005 Pearson Education...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.156 Determine the vector rBA F, where rBA is the position vector from B to A. Solution: Use the definition in Eq. (2.34). Noting rBA D rAB , from Problem 2.155 rBA D 4i C 3j C 4k. The cross product is rBA F D j 4 3 20 10 i k 4 D 10 C D 30...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.125 C 4j. (a) (b) Two vectors U D 3i C 2j and V D 2i Solution: Use Eq. (2.34) and expand into 2 by 2 determinants. i j k UVD 3 2 0 Di 2 0 2 4 0 Ck 3 4 i j k VUD 2 4 0 Di 4 0 3 2 0 Ck 2 2 4 0 j 3 0 2 0 What is the cross product U V? What...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.119 The disk A is at the midpoint of the sloped surface. The string from A to B exerts a 0.2lb force F on the disk. If you resolve F into vector components parallel and normal to the sloped surface, what is the component normal to the surfa...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.84 The pole supporting the sign is parallel to the x axis and is 2 m long. Point A is contained in the y-z plane. Express the position vector r from the origin to the end of the pole in terms of components. y A Bedford Falls Solution: Th...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.79 Consider the structure described in Problem 2.78. After returning to the United States, an archaeologist discovers that a graduate student has erased the only data file containing the dimension b. But from recorded GPS data he is able to...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.80 Observers at A and B use theodolites to measure the direction from their positions to a rocket in flight. If the coordinates of the rocket\'s position at a given instant are (4, 4, 2) km, determine the direction cosines of the vectors rAR...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.72 Determine the components of the position vector rBD from point B to point D. Use your result to determine the distance from B to D. y D (4, 3, 1) m Solution: We have the following coordinates: A 0, 0, 0 , B 5, 0, 3 m, C 6, 0, 0 m, D 4, ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.73 What are the direction cosines of the position vector rBD from point B to point D? Solution: cos x D 1m D 3.74 m 0.267, cos y D 3m D 0.802, 3.74 m cos z D 2m D 0.535 3.74 m c 2005 Pearson Education, Inc., Upper Saddle River, NJ. All ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.60 Let r be the position vector from point C to the point that is a distance s meters from point A along the straight line between A and B. Express r in terms of scalar components. (Your answer will be in terms of s.) y B (10, 9) m s r A ...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.61 magnitude? A vector U D 3i 4j 12k. What is its Solution: Use definition given in Eq. (14). The vector magnitude is jUj D 32 C 4 2 Strategy: The magnitude of a vector is given in terms of its components by Eq. (2.14). C 12 2 D 13...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.62 The vector e D 1 i C 2 j C ez k is a unit 3 3 vector. Determine the component ez . (Notice that there are two answers.) Solution: eD Thus ez D 2 3 or ez D 2 3 1 2 i C j C ez k ) 3 3 1 3 2 C 2 3 2 C ez 2 D 1 ) e 2 D 4 9 c 2005 Pear...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.63 An engineer determines that an attachment point will be subjected to a force F D 20i C Fy j 45k kN . If the attachment point will safely support a force of 80-kN magnitude in any direction, what is the acceptable range of values for Fy ?...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.64 A vector U D Ux i C Uy j C Uz k. Its magnitude is jUj D 30. Its components are related by the equations Uy D 2Ux and Uz D 4Uy . Determine the components. (Notice that there are two answers.) Solution: Substitute the relations between the...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.166 In Problem 2.165, let rBC be the position vector from point B to point C. Determine the cross product rBC T. Solution: The vector from B to C is rBC D xC D xB i C yC yB j C zC zB k 0.35i C 0.2j 0.2k m. 120k N. The cross product of T...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.165 The rope CE exerts a 500-N force T on the hinged door. y E (0.2, 0.4, 0.1) m (a) (b) Express T in terms of components. Determine the vector component of T parallel to the line from point A to point B. C (0, 0.2, 0) m T D A (0.5, 0...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.163 The magnitude of the vertical force vector F in Problem 2.161 is 6 kN. Given that F C FA C FB C FC D 0, what are the magnitudes of FA , FB , and FC ? Solution: The strategy is to expand the forces into scalar components, and then use th...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.164 The magnitude of the vertical force W is 160 N. The direction cosines of the position vector from A to B are cos x D 0.500, cos y D 0.866, and cos z D 0, and the direction cosines of the position vector from B to C are cos x D 0.707, co...
Washington >> A A >> 210 (Spring, 2008)
Problem 2.162 The magnitude of the vertical force vector F in Problem 2.161 is 6 kN. Determine the vector components of F parallel and normal to the line from B to D. Solution: The projection of the force F onto the line from B to D is FP D F eBD eB...
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