F = 2xy + 4y + 5k is the velocitly field of a fuld flowing through a region in space. Find the flow along the given curve r(t)t +fPj+k, Osts in the direction of increasing t. The flow is (Type a simplified fraction.)
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(t) = (-2 cost, 2 sin t, 2t) 0 < t < 2π (3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83,...
Find the work done by F over the curve in the direction of increasing t F = 4xyi + 2yj – 2yzk r(t) = ti + t'j-tk Osts 1 Type an integer or a simplified fraction
:) IS (x+y+z)ds X-1 (b): Find the work done by F over the curve in the direction of increasing t, where F =< x² + y, y2 + 1, ze >, r(t) =< cost, sint,t/27 >, Osts 27. y-2=2-3 =+ C) -1-2 I-3
Find the length of the curve given in parametric form by x = f(t) = sin(t) and y = g(t) = In( V1 – t) for t e [0,1/2).
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in the xy plane defined parametrically as x(t) = 2cos(t), y(t) = sin(t) a. Find z'(t). Imagine you are walking directly above the curve C in the direction of increasing t. Find the values of t for which you are walking uphill. Hint:Graph z'(t). Graph f(x, y) for -7 < x < 7 and -7 < y < 7. (You will have to find software...
Find the center of mass of a thin wire lying along the curve r(t) = 3+1 + 3tj + قN | ل قت نہ k, Osts 2 if the density is 8 =518+t. (X.4.2) = (0) (Type exact answers, using radicals as needed.)
Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) , Evaluate the line integral f F dr for the vector field F(x, y, z) curve C parametrised by Vf (x, y, z) along the with tE [0, 2 r() -(Vt sin(2πt), t cos (2πi), ?) ,
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
please help 13) Graph the parametric curve for all real values of x, and indicate the direction moved by a particale along the path (interpreting t as time), and the direction of motion. x = 2 sin t, y = 5 cos t, Osts 27 2+ 1+ + -5 -4 -3 -2 1 2 - 1 -1+ 3 4 5% 2+ -3+ + Describe the graph of the polar equation sin 20 = 22