all a,b,c,d 1. Suppose C is simple closed curve in the plane given by the parametric equation and recall that the outward unit normal vector n to C is given by y(t r'(t) If g is a scalar field on...
a) A vector field F is called incompressible if div F = 0. Show that a vector field of the form F = <f(y,z),g(x,z),h(x,y)> is incompressible. b) Suppose that S is a closed surface (a boundary of a solid in three dimensional space) and that F is an incompressible vector field. Show that the flux of F through S is 0. c)Show that if f and g are defined on R3 and C is a closed curve in R3 then...
all questions are related and need help answering! rough the surface 4. o pm) What is the value of the flux of the vector field F(x,y)j+z ioriented with upward- pointing normal vector? (A) 0 (B) 2n/3 (C) π (D) 4T/3 (E) 2π Use Stokes, Theorem to evaluateⅡcurl F.dS, where F(x, y, z)-(x2 sin Theorem to evaluate Jceun F'.asS , where Fl.e)(', ») and 5. (5pts.) F,y, sin z, y', xy) and s is the part of the paraboloid : -...
(1) Let F denote the inverse square vector field (axr, y, z) F= (Note that ||F 1/r2.) The domain of F is R3\{(0, 0, 0)} where r = the chain rule (a) Verify that Hint: first show that then use (b) Show that div(F 0. (c) Suppose that S is a closed surface in R3 that does not enclose the origin. Show that the flux of F through S is zero. Hint: since the interior of S does not contain...
Consider the vector field F(x, ) (4x3y -6ry3,2rdy - 9x2y +5y*) along the curve C given by r(t)(tsin(rt), 2t +cos(xl)), -2ss 0 To show that F is conservative we need to check a) b) We wish to find a potential for F. Let r,y be that potential, then Use the first component of F to find an expression for ф(x, y)-Po(x,y) + g(y), where ф(x,y) in the form: Differentiate ф(x,y) with respect to y and determine g(y) e Using the...
Suppose a plane passes through the points O(0,0,0). B(1,2,2) and C(-1,-1,2) and u -OB and v-OC. (See figure below.) The vector equation of the plane is:x-sutv Choose... s=0, t=0 s-1, t-1 (5,8,2) s--3, t--1.5 (2,5,8) s 3, t-1 s-3, t--2 What values of s and t correspond to point O? What values of s and t correspond to point D? What values of s and t correspond to point B? what values of s and t correspond to point C?...
Consider IS-LM Model: Real Sector: Y=C+I+G C=a+b (1-t) Y I=d-ei G=GO t-income tax rate i- rate of interest Money Market: Ma=M Ma=ky-li M = Mo Mo - exogenous stock of money 1) Setup the system of solutions in general form, with variables vector in the following order: Y, C, I, i; (6 points) 2) Now, suppose we have the following values of parameters: a= 10; b = 0.7; t = 0.2; d = 25; k = 0.25; 1 = 0.04;...