5. Let C be the curve that is the intersection of the given surfaces. Find an equation of the cylinder perpendicular to the xy plane that contains the curve Identify the curve C'by name and d...
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?) is a given vector field. Find the circulation F dr
5. (a) [6] Let C be a simple closed curve given by the intersection between the cylinder 2y2 1 and the surface:-10 + 0.4xy, and F = 《2xz-2y, 2y2+ 2x, x2 + y2 + z?)...
Question 1. Let C be the intersection of the plane -2r +5y with the cylinder r2+y2= 1 Find a parameterization for the curve C, oriented so that C is traversed counterclockwise when viewed from the positive z-axis. Select bounds for the parameterization so the curve is traversed exactly once. Let F = (y,z,-a). Compute F ds. . C
Question 1. Let C be the intersection of the plane -2r +5y with the cylinder r2+y2= 1 Find a parameterization for the...
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane. (2) Determine the parametric equation of the tangent line to C at (1,1.0) (3) Find the plane that carries the tangent line found above and the vector (4) Set up but not solve, a formula that will determine the length of C for 1StS2
Let C be the parametric curve (1) Determine the point(s) of intersection of C with the xz plane....
1. Consider a curve C in the xy-plane given in polar form by r 2 = sin(2θ). (a) (3 points) Draw the graph of C. Particularly, be clear in showing the tangent lines to C at the pole. [Hint. The period is π.] (b) (2 points) Compute the area of the region inside C
1. (15 points) (a) (5 points) Find the equation of the plane a that contains points A(1,5,4) B(1,0, 1) and C(4, 0,5) (b) (5 points) Find the distance from the point D(2, 1,7) to this plane (c) (5 points) If plane 3 has equation y -3z+2x = 5, find a unit vector that is parallel to the intersection of a and B.
find the point of intersection of the line
1) Find the equation of the line passing through the points A(1,-5,-3)and B(2,-4,8) (3 marks) b) Find the equation of the plane perpendicular to the line in part (a) given that C(1,-9,6) is a point on the plane. (3 marks) c) Find the point of intersection of the line and the plane in parts (a) and (b) above respectively. (3 marks)
3. Find the points of intersection of the pairs of curves a. y = x² +3; y = 3x +1 b. 2x² +2 y2 = 5; xy = 1 4. Identify and sketch the curve represented by the given equation. x? - + y2 = 1 a. 4 (y+1) 4 b. (x - 1)? + 4 c. x² - y2 =-1
--> Econ Graph Review a) The equation of the line passing through the points (5, 1) and (8, 2) is ay = x + b. Find the values for constants a and b. Represent this function in a xy plane. b) Let L be the line passing through the point (4, 9) with slope 3/4. Represent this function using the y = mx + b formula. Find the y-intercept of L. c) Graph the following two equations on the same...
10. Stokes' Theorem and Surfac e Integrals of Vector Fields a. Stokes' Theorem: F-dr= b. Let S be th ky-plane. Draw a sketch of curve C in the xy-plane. et be the surface of the paraboloid z 4-x-y and Cis the trace of S in the c Let Fox.y.z) <2z, x, y>, Compute the curl (F) d. Find a parametrization of the surface S: G(u,v)- Compute N(u,v) F-dr Use Stokes' Theorem to compute , e.
10. Stokes' Theorem and Surfac...