Problem 1.56Compute the line integral of v=6+yz²ŷ+ (3y+z) 2 along the triangular path shown in Fig. 1.49. Check your answer using Stokes' theorem. [Answer: 8/3]
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![Problem 1.56Compute the line integral of
v=6+yz²ŷ+ (3y+z) 2
along the triangular path shown in Fig. 1.49. Check your answer using Stokes'
theorem. [Answer: 8/3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9868ebb-88e7-472b-8fc9-69f5a41cf75d%2F1b2cc34c-d2ce-4b29-92d8-d2f601b49139%2F4hany9s_processed.png&w=3840&q=75)


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- Subject: Mathematical Physics Topic: Functions of A Complex Variable-Analytic Function Answer the following functions and determine whether the following functions are Analytic. Please answer neatly and with details.1.16. Establish thermodynamically the formulae (F). V = S and v (3) ₁² V T = N. Express the pressure P of an ideal classical gas in terms of the variables μ and T, and verify the above formulae.Calculate the first derivative of the function f(x) = 2x e X at the point x=1.19. Express the answer with two decimal places.
- I need to show all the solution steps1 W:0E *Problem 1.3 Consider the gaussian distribution p(x) = Ae¬^(x-a)² %3D where A, a, and A are positive real constants. (Look up any integrals you need.) (a) Use Equation 1.16 to determine A. (b) Find (x), (x²), and ơ. (c) Sketch the graph of p(x).Question 2 |A spherical pendulum consists of a bob of mass m suspended from an inextensible string of length l. Determine the Lagrangian and the equations of motion. See Figure 1.7. Note that 0, the polar angle, is measured from the positive z axis, and ø, the azimuthal angle, is measured from the x axis in the x – y plane.? V = Figure 1.7 A spherical pendulum. Answer.
- Imagine two concentric cylinders, centered on the vertical axis, with radii R± ε, where ε is very small. A small frictionless puck of thickness 2ε is inserted between the two cylinders, so that it can be considered a point mass that can move freely at a fixed distance from the vertical axis. If we use cylindrical polar coordinates (p, op, z) for its position (Problem 1.47), then p is fixed at p = R, while op and z can vary at will. Write down and solve Newton's second law for the general motion of the puck, including the effects of gravity. Describe the puck's motion.1.16. Establish thermodynamically the formulae v (7)= = S and v (R), V = N. Express the pressure P of an ideal classical gas in terms of the variables and 7, and verify the μl above formulae.I cant seem to come to (3/2)a . I set up my integral like this: (4/a^3) ∫ r^2 e^[ (-e/a)^2 ] dr is this correct?
- You are designing an RPG (role-playing game) for a gaming console and have decided to use an open world design, where players can explore the terrain freely, encountering enemies by chance. 8. Your design team has coded this in-game world to exist on the circle x² + y? < 900 Page 3 on the xy-plane. At any point (x, y) in this world you've also associated a danger function d(x, y) that measures how likely it is to encounter an enemy at that point. Thus high values of d(x,y) correspond to dangerous points, while low values of d(x, y) correspond to safe points. If d(x, y) = e¬a²y, find the safest point(s) and most dangerous point(s) in-game.Problem 4.16 It is desired to find the equation for the shortest distance be- tween two points on a sphere. Determine the functional for this problem. (Use spherical coordinates.)The results of 5.11 are added, need help setting up and solving.