Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos...
Determine the potential for the field: } = (-6 cos (2y), 12x sin (2y), 5 cos (1z) – 5z sin (1z)) Do not put the constant "+c" for the potential in your answer below. f(x, y, z) = Submit Answer Tries 0/8 Now calculate 18.di where C is the path ř (t) = (4 cos t, 4 sin t, 3t) for 0 <tsa. The line integral equals
Determine the potential for the field: F = (2y2 + 20e4x-2y, 4xy + 5 - 10e4x-2y) Do not put the constant "+c" for the potential in your answer below. f (x, y) = Submit Answer Tries 0/8 Now calculate Si F. dr where C is the path ř (t) = (2t, 4t) for 0 <t<1 The line integral equals
(1 point) Determine whether the vector field is conservative and, if so, find the general potential function. F = (cos z, 2y!}, -x sin z) Q= +c Note: if the vector field is not conservative, write "DNE". (1 point) Show F(x, y) = (8xy + 4)i + (12x+y2 + 2e2y)j is conservative by finding a potential function f for F, and use f to compute SF F. dr, where is the curve given by r(t) = (2 sinº 1)i +...
Homework set 6: Problem 9 Previous Problem Problem List Next Problem (1 point) Evaluate the line integral JF d r where F (-sin z, 4 cos y, 10zz) and C is the path given by r(t) (-3t3,362,-3t) for 0 ts 1 Preview My Answers Submit Answers
Homework set 6: Problem 9 Previous Problem Problem List Next Problem (1 point) Evaluate the line integral JF d r where F (-sin z, 4 cos y, 10zz) and C is the path given...
QUESTION 4 Suppose a fourth field and path: F= <cos(z), sin(z), xy > and r= <sin(t), cos(t), t-> when Osts 21 What does this field look like? What does the path look like? Find ff. dr (use a calculator), what does it represent? Explain.
Consider the spiral given parametrically by z(t) = 6e 0.4 sin (2) y(t) = 6e 0.4t cos (2) on the interval 0<t< 5. -3 -2 -1 0 1 2 3 4 5 Fill in the expression which would complete the integral determining the arc length of this spiral on 0 <t<5. dt Submit Answer Tries 0/8 Determine the arc length of the given spiral on 0<t<5. Submit Answer Incorrect. Tries 1/8 Previous Tries Now determine the arc length of the...
(4) Evaluate the line integral F dr where C is the epicycloid with parametrization given by r(t) 5 cos t - gradient of the function f(x, y) = 3 sin(ry) + cos(y2) cos 5t and y(t) = 5 sin t - sin 5t for 0 < t < 2« and F is the (5) EvaluateF dr where F(x, y) with counterclockwise orientation (2y, xy2and C is the ellipse 4r2 9y2 36 _ F dr where F(r, y) = (x2 -...
Please answer all three, (:
Consider the spiral given parametrically by -0.3 sin (4t) = 6e -0.3t 6e Уб) cos (4) on the interval 0 s 1s 8 6 2 -2 -4 -6 4 5 -5 -4 -3 -2 -1 1 2 3 6 X 0 t 8 Fill in the expression which would complete the integral determining the arc length of this spiral C on dt sqrt(579.24 exp-0.3t)) Incorrect. Tries 5/8 Previous Tries Submit Answer Determine the arc length...
3. 8p] Show that the force field F(x,y, z) sin y, x cos y + cos z, -y sin z) is conservative and use this fact to evaluate the work done by F in moving a particle with unit mass along the curve C with parametrization r(t (sin t, t, 2t), 0 <t<T/2. 4. 8p] A thin wire has the shape of a helix x = sin t, 0 < t < 27r. If the t, y = cos t,...
Let F(x, y, z) = sin yi + (x cos y + cos z)j – ysin zk be a vector field in R3. (a) Verify that F is a conservative vector field. (b) Find a potential function f such that F = Vf. (C) Use the fundamental theorem of line integrals to evaluate ScF. dr along the curve C: r(t) = sin ti + tj + 2tk, 0 < t < A/2.