The intersection between the surface x + y + 2-2 and the circle x² + y2...
The intersection between the surface x +y +z = - 3 and the circle x2 + y2 = 9,2 =0 is Yanitiniz: O The point(0,0,0) O The point (-3,0,-3) o The point (-3,-3,0) O The point(0,0,-3) O The point(0, -3,0) The point (-3,0,0) o The points (0, -3,0) and (-3,0,0) O No intersection points
4. Let F(x, y, z)=(y,x,z2). Let S be the surface of the tetrahedron with the vertices (0,0,0), (2,0,0), (0,2,0), and (0,0,2). Use the divergence theorem to evaluate SS F.dS. (13 points)
co 5 points Determine the intersection point(s) between: (x + 2)+ (y – 1)2 = 1 and (y – 1)² = - (x + 1) State answer(s) as coordinate points, separated by commas as needed: type your answer....
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -2+1, y = 3 +t, z = 2t +21 and the surface z= x2 + y2 (b) At each point of intersection, find the cosine of the acute angle between the given line and the line normal to the surface. Enter your answers in order of ascending x-coordinate value. (a) (b) (x1,91,21) = (003 Edit cos 01 = ? Edit (x2, Y2, 22)...
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z − 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
Answer all 3 and I will positively rate your answer 1. F(x, y, z) = (x,y2, z3), S is a surface bounded by the cylinder x2 + y2 = 4,2 = 0 and z = 1. Evaluate the outward flux Sf. Nds using the Divergence Theorem. S 2. F(x, y, z) = (2x3, 2y3, 3z2), S is a surface bounded by the cylinder x2 + y2 = 4, z = 0 and z = 1. Evaluate the outward flux Sf....
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
Let z = x2 + y2 be the surface, and x = -1+t, y = 2+t, z = 2t + 7 be the line. Find the incorrect answer in the following Select one: The acute angle between tangent to the surface and the given line at the -1 4 point (0,3, 9) is į – cos V537 The normal to the surface at the point (0,3, 9) is 6 j - k. The line is normal to the surface. The...
Calculate the circulation of y F(x, y) = { x2+y2 » 22+y2 ) along a circle with radius 4 centered at the origin. Provide your answer below:
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...