TN Tech - MATH - Cal I- Cal

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.2 Line Integrals1. x=t and y=t , 0 tC22 , so by Formula 32y ds = =20 2t t2dx dt+dy dt2dt= t0 2 02(2t) +(1) dt 1 (17 17 1) 122204t +1 dt=1 2 3/2 (4t +1

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.5 Curl and Divergence1. (a) i curl F =2j / y 0F=/ x xyzk / z xy2=( x 0) i ( 2xy xy) j+(0 xz) k2= x i+3xy j xz k (b) div F= 2. (a) curlF = F=2 2F=x(xyz)+y(0)+z(

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.6 Parametric Surfaces and Their Areas1. r(u, v)=ucos v i+usin v j+u k , so the corresponding parametric equations for the surface are x=ucos v, y=usin v, z=u . For any point (x, y, z) on the

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.7 Surface Integrals1. Each face of the cube has surface area 2 =4 , and the points P are the points where the cubeij2*intersects the coordinate axes. Here, f (x, y, z)= x +2y +3z , so

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.8 Stokes' Theorem1. Both H and P are oriented piecewise smooth surfaces that are bounded by the simple, closed, smooth curve x +y =4 , z=0 (which we can take to be oriented positively for bo

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;16. Vector Calculus; 16.9 The Divergence Theorem1. The vectors that end near P are longer than the vectors that start near P , so the net flow is inward1 1near P and divF(P ) is negative. The vectors that end ne

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.1 Three-Dimensional Coordinate Systems1. We start at the origin, which has coordinates ( 0,0,0 ) . First we move 4 units along the positive x axis, affecting only the x coo

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.2 Vectors1. (a) The cost of a theater ticket is a scalar, because it has only magnitude. (b) The current in a river is a vector, because it has both magnitude (the speed of

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.3 The Dot Product1. (a) a b is a scalar, and the dot product is defined only for vectors, so ( a b) c has no meaning. (b) ( a b) c is a scalar multiple of a vector, so it d

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.4 The Cross Producti j k 2 0 1 0 1 2 1. a b= 1 2 0 = i j+ k 3 1 0 1 0 3 0 3 1 =(2 0) i (1 0) j+(3 0) k=2 i j+3 k Now (a b) a= 2, 1,3 1,2,0 =2 2+0=0 and (a b) b= 2, 1,3 0,3,

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.5 Equations of Lines and Planes1. (a) True; each of the first two lines has a direction vector parallel to the direction vector of the third line, so these vectors are each

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.6 Cylinders and Quadric Surfaces1. (a) In R , the equation y=x represents a parabola.22(b)In R , the equation y=x doesn't involve z , so any horizontal plane with e

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;12. Vectors and the Geometry of Space; 12.7 Cylindrical and Spherical Coordinates1. See Figure 1 and the accompanying discussion; see the paragraph accompanying Figure 3. 2. See Figure 5 and the accompanying discus

TN Tech - MATH - Cal I- Cal

Stewart Calculus ET 5e 0534393217;13. Vector Functions; 13.1 Vector Functions and Space Curves1. The component functions t , t 1 , and 5 t are all defined when t 1 0 t 5 , so the domain of r(t) is 1,5 . 2. The component functions2t1 and 5 t

FSU - HIST - 08758

Prcis 1-28-08The Chinese Exclusion Act of 1882 denied Chinese immigrants the right to obtain citizenship in America. It states that any captain of a ship facilitating Chinese immigrants into the country would be subject to criminal charges. Another

FSU - HIST - 08758

Prcis 2-11-08This passage of Harry Emerson Fosdick's "Shall the Fundamentalists Win?"(1922) shows Fosdick's distaste in the people who call themselves fundamentalists who feel there is no place for liberal Christians in the church. Evidence of this

FSU - HIST - 08758

Prcis 2-20-08The passage from Meridel Le Sueur's "Women on the Breadlines" (1932) displays how The Great Depression affected an endless number of people of any race, gender or religion. In this particular passage, Sueur describes a typical day of a

FSU - HIST - 08758

Prcis 2-22-08Franklin D Roosevelt's "First Inaugural Address (1933)", gives a glimpse on how he planned to revive the nation through his presidency by using any tactics he felt that was necessary to restore American prosperity. He shows the desire

Kansas State - PHYS - 213

1. With speed v = 11200 m/s, we findK= 1 2 1 mv = (2.9 105 ) (11200) 2 = 18 1013 J. . 2 22. (a) The change in kinetic energy for the meteorite would be1 1 K = K f - K i = - K i = - mi vi2 = - 4 106 kg 15 103 m/s 2 2()()2= -5 1014 J

FSU - HIST - 08758

Prcis 3-26-08In George F. Kennan's "The Sources of Soviet Conduct" (1947), he states, "it is easy to regard to the Soviet Union as a rival not a partner, in the political arena. It must continue to expect that Soviet policies will reflect no abstra

Kansas State - PHYS - 214

1. (a) The magnitude of the magnetic field due to the current in the wire, at a point a distance r from the wire, is given byB= 0i2r.With r = 20 ft = 6.10 m, we havec4 10 B=hb 2 b6.10 mg-7T m A 100 Ag = 3.3 10-6T = 3.3 T.(b

Kansas State - PHYS - 214

1. The amplitude of the induced emf in the loop is m = A 0 ni0 = (6.8 10-6 m 2 )(4 10 -7 T m A)(85400 / m)(1.28 A)(212 rad/s)= 1.98 10-4 V.2. (a) =d B d = 6.0t 2 + 7.0t = 12t + 7.0 = 12 2.0 + 7.0 = 31 mV. dt dtchb g(b) Appealing to

Kansas State - PHYS - 214

1. (a) All the energy in the circuit resides in the capacitor when it has its maximum charge. The current is then zero. If Q is the maximum charge on the capacitor, then the total energy is2.90 10-6 C Q2 U= = = 117 10-6 J. . -6 2C 2 3.60 10 Fc

FSU - HIST - 08758

Prcis 3-28-08The Supreme Court's decision on Brown v. Board of Education of Topeka (1954) served as a turning point and as a milestone in the start of the civil rights movement. It reviewed the "separate but equal" principle decided by the case of

FSU - HIST - 08758

Prcis 4-2-08George C. Wallace displayed his prominence among white conservatives as Governor of Alabama in a speech on" The Civil Rights Movement: Fraud, Sham, and a Hoax" (1964). In June of 1963, Wallace defiantly prevented the first black student

FSU - HIST - 08758

Prcis 4-4-08Martin Luther King's Letter from Birmingham Jail (1963)is a letter Dr. King wrote after being jailed in Birmingham Alabama after organizing a economic boycott of white businesses, using a smuggled pen and piece of paper. King's statemen

FSU - GLY - 01636

Origin of the Universe: The Big Bang: Supernova: Life elements: Leon Sinks: Karst topography: Caves, caverns: Ground water: Porosity: Permeability Water table: Springs: Sink holes: o Wet Sinks: o Dry sinks: o Sink vs. Swamp Natural Bridge: Evolution

FSU - CLA - 2123

Classics 2123: The Roman Way Lecture 1 ~ Eras of Roman History Reading: BHR 2-4.Spring 2008Roman history is traditionally divided into three phases: monarchy, republic and empire. The dates are as follows (keep in mind that the very earliest date

FSU - CLA - 2123

Classics 2123: The Roman Way Lecture 2: Roman Society and Roman Values Readings: BHR 129-131; Shelton 128, 163-4, 171, 194-5, 197Spring 2008Roman Values and Virtues Roman virtues public, not private: virtuous man acts on behalf of the state Virtu

FSU - CLA - 2123

Classics 2123: The Roman Way Notes to Virgil's Aeneid, Books I-IVSpring 2008Virgil's Aeneid, strongly modeled on Homer's Iliad and Odyssey, was considered even in antiquity the great epic of Rome. It tells the story of the Trojan Aeneas who, afte

FSU - CLA - 2123

Classics 2123: The Roman Way Notes to Virgil's Aeneid, Books V-VIIISpring 2008Book V provides a transition between the high emotion of Book IV and the sombre majesty of the descent to the underworld in Book VI. Most of the book is taken up with g

FSU - CLA - 2123

Classics 2123: The Roman Way Notes to Virgil's Aeneid, Books IX-XIISpring 2008Book IX. War finally breaks out, the full-scale battles spoken of in Book VII. The book divides into three sections: (1) Turnus and the Rutulians attack the Trojan ship

FSU - CLA - 2123

Classics 2123: The Roman Way Lecture 5. Roman Imperialism and Expansion Readings: BHR 44-67; Shelton 291-293 I. Roman Imperialism - definition of `imperialism' - older notion of `defensive imperialism': how realistic? - was Rome more warlike/aggressi

FSU - CLA - 2123

Classics 2123: The Roman Way Roman Names A Roman had three names: praenomen (first name) nomen (name of the gens or clan) cognomen (family branch) Thus for: Publius praenomen Cornelius nomen Scipio cognomenSpring 2008his given name was "Publius,"

Stevens - PEP - 111

AC CIRCUITS35.1. Model: A phasor is a vector that rotates counterclockwise around the origin at angular frequency w. Solve: (a) Refemng to the phasor in Figure Ex35.1, the phase angle isU? = 180'n rad - 30" = 150 x -= 2.618 rad180"w=2*618ra

Stevens - PEP - 111

15.1. Solve: The density of the liquid is=m 0.120 kg 0.120 kg = = = 1200 kg m 3 V 100 mL 100 10 -3 10 -3 m 3Assess: The liquid's density is more than that of water (1000 kg/m3) and is a reasonable number.15.2. Solve: The volume of the helium

Stevens - PEP - 111

16.1. Solve: The mass of lead mPb = Pb VPb = (11,300 kg m 3 )(2.0 m 3 ) = 22,600 kg . For water to have thesame mass its volume must beVwater =mwater 22,600 kg = = 22.6 m 3 water 1000 kg m 316.2. Solve: The volume of the uranium nucleus isV

Stevens - PEP - 111

17.1. Model: For a gas, the thermal energy is the total kinetic energy of the moving molecules. That is, Eth =Kmicro. Solve: The number of atoms isN=M 0.0020 kg = = 3.01 10 23 m 6.64 10 -27 kgBecause helium atoms have an atomic mass number A

Stevens - PEP - 111

18.1. Solve: We can use the ideal-gas law in the form pV = NkBT to determine the Loschmidt number (N/V):1.013 10 5 Pa N p = 2.69 10 25 m -3 = = V kB T (1.38 10 -23 J K )(273 K )()18.2. Solve: Nitrogen is a diatomic molecule, so r 1.0 10-1

Stevens - PEP - 111

19.1. Model: The heat engine follows a closed cycle, starting and ending in the original state. The cycleconsists of three individual processes. Visualize: Please refer to Figure Ex19.1. Solve: (a) The work done by the heat engine per cycle is the a

Stevens - PEP - 111

20.1. Model: This is a wave traveling at constant speed. The pulse moves 1 m to the right every second.Visualize: Please refer to Figure Ex20.1. The snapshot graph shows the wave at all points on the x-axis at t = 0 s. You can see that nothing is h

Stevens - PEP - 111

21.1. Model: The principle of superposition comes into play whenever the waves overlap.Visualize:The graph at t = 1 s differs from the graph at t = 0 s in that the left wave has moved to the right by 1 m and the right wave has moved to the left by

Stevens - PEP - 111

22.1. Visualize: Please refer to Figure Ex22.1.Solve: (a)(b) The initial light pattern is a double-slit interference pattern. It is centered behind the midpoint of the slits. The slight decrease in intensity going outward from the middle indicates

Stevens - PEP - 111

23.1. Model: Light rays travel in straight lines.Solve: (a) The time ist=x 1.0 m = = 3.33 10 -9 s = 3.33 ns c 3 10 8 m / s(b) The refractive indices for water, glass, and zircon are 1.33, 1.50, and 1.96, respectively. In a time of 3.33 ns, l

Stevens - PEP - 111

24.1. Model: Balmer's formula predicts a series of spectral lines in the hydrogen spectrum.Solve: Substituting into the formula for the Balmer series,=91.18 nm 91.18 nm = = 410.3 nm 1 1 1 1 - 2 - 2 2 22 n 2 6where n = 3, 4, 5, 6, . and wher

Stevens - PEP - 111

ELECTROMAGNETIC AND WAVES FIELDSw.1. Model: The net magnetic flux over a closed surface is zero. Visualize: Please refer to Ex34.1. Solve: Because we can't enclose a "net pole" within a surface, Q, = f B . d i = 0 . Since the magnetic field isunif

FSU - CLA - 2123

CLA 2123: The Roman Way First Exam. February 8, 2007Name _Please read all directions carefully; no credit will be given for doing more than is required in each section. Part I. Identifications (35 points). Choose FIVE of the following and identif

Stevens - PEP - 111

14.1. Solve: The frequency generated by a guitar string is 440 Hz. The period is the inverse of the frequency, henceT= 1 1 = = 2.27 10 -3 s = 2.27 ms f 440 Hz14.2. Solve: Your pulse or heart beat is 75 beats per minute. The frequency of your hear

Stevens - PEP - 111

1.1.Solve:1.2.Solve:Solve: (a) The basic idea of the particle model is that we will treat an object as if all its mass is concentrated into a single point. The size and shape of the object will not be considered. This is a reasonable approxim

Stevens - PEP - 111

2.1.Solve:Model: The car is represented by the particle model as a dot. (a) Time t (s) Position x (m) 0 1200 1 975 2 825 3 750 4 700 5 650 6 600 7 500 8 300 9 0(b)2.2. Solve:Diagram (a) (b) (c)Position Negative Negative PositiveVelocity

Stevens - PEP - 111

3.1. Solve: (a) If one component of the vector is zero, then the other component must not be zero (unless the whole vector is zero). Thus the magnitude of the vector will be the value of the other component. For example, if Ax = 0 m and Ay = 5 m, the

Stevens - PEP - 111

4.1. Solve: A force is basically a push or a pull on an object. There are five basic characteristics of forces. (i) A force has an agent that is the direct and immediate source of the push or pull. (ii) Most forces are contact forces that occur at a

Stevens - PEP - 111

5.1.Model: We can assume that the ring is a single massless particle in static equilibrium. Visualize:Solve:Written in component form, Newton's first law is( Fnet ) x = Fx = T1x + T2 x + T3 x = 0 NT1 x = - T1T1y = 0 N Using Newton's first l

Stevens - PEP - 111

6.1. Model: We will assume motion under constant-acceleration kinematics in a plane.Visualize:Instead of working with the components of position, velocity, and acceleration in the x and y directions, we will use the kinematic equations in vector f

Stevens - PEP - 111

7.1. Solve: (a) From t = 0 s to t = 1 s the particle rotates clockwise from the angular position +4 rad to -2 rad. Therefore, = -2 - ( +4 ) = -6 rad in one sec, or = -6 rad s . From t = 1 s to t = 2 s, = 0 rad/s. From t = 2 s to t = 4 s the partic

Stevens - PEP - 111

8.1. Visualize:Solve: Figure (i) shows a weightlifter (WL) holding a heavy barbell (BB) across his shoulders. He is standing on a rough surface (S) that is a part of the earth (E). We distinguish between the surface (S), which exerts a contact forc

Stevens - PEP - 111

Solve: (a) The momentum p = mv = (1500 kg)(10 m /s) = 1.5 10 4 kg m /s . (b) The momentum p = mv = (0.2 kg)( 40 m /s) = 8.0 kg m /s .9.1. Model: Model the car and the baseball as particles.9.2. Model: Model the bicycle and its rider as a particl

Stevens - PEP - 111

10.1. Model: We will use the particle model for the bullet (B) and the bowling ball (BB).Visualize:Solve:For the bullet,KB =For the bowling ball,1 1 2 mB vB = (0.01 kg)(500 m /s) 2 = 1250 J 2 2 1 1 2 mBB vBB = (10 kg)(10 m / s) 2 = 500 J 2

Stevens - PEP - 111

11.1. Visualize:r Please refer to Figure Ex11.1. rSolve: (b) (c)(a) A B = AB cos = ( 4)(5)cos 40 = 15.3. r r C D = CD cos = (2)( 4)cos120 = -4.0. r r E F = EF cos = (3)( 4)cos 90 = 0.11.2. Visualize:r Please refer to Figure Ex11.2. rSolve

Stevens - PEP - 111

12.1.Solve: (b)Model: Model the sun (s), the earth (e), and the moon (m) as spherical. (a)Fs on e =Gms me (6.67 10 -11 N m 2 / kg 2 )(1.99 10 30 kg)(5.98 10 24 kg) = 3.53 10 22 N = (1.50 1011 m ) 2 rs2 e -Fm on e =GMm Me (6.67 10 -1