On a plane flat surface with "up" given as +y and "right" given as +x, we...
On a plane flat surface with "up" given as +y and "right" given as +x, we add two vectors. One of them has components (2, 20) and the other is (-3,-21). What is the length of the resulting vector, and what direction is it pointing in?
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On a plane flat surface with "up" given as +y and "right" given
as +x, we...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g ...
Consider the surface given as a graph of the function g(x, y) = x∗y 2 ∗cos(y). The gradient of g represents the direction in which g increases the fastest. Notice that this is the direction in the xy plane corresponding to the steepest slope up the surface, with magnitude equal to the slope in that direction. 1. At the point (2, π), find the gradient, and explain what it means. 2. Use it to construct a vector in the tangent...
You are given two vectors, one pointing in the x direction and the other pointing in...
You are given two vectors, one pointing in the x direction and the other pointing in the y direction. Is it possible to find a third vector so that the sum of the three vectors is equal to zero? yes yes, but only because the vectors are perpendicular no only if the two vectors have the same magnitude A points in the-X direction with a magnitude of 12, what is the y component of A? Enter an exact number C...
Show work and please explain! 1. Vector addition and subtraction: We are given the magnitudes and...
Show work and please explain!
1. Vector addition and subtraction: We are given the magnitudes and directions of the vectors A and B as follows (a) Carefully sketch each vector individually, then sketch the sum C-A+B and sketch the difference D-A B. Try to make the lengths to scale and make the angles relatively accurate. (Use a protractor.) Use trigonometry to find the components of cach of the four vectors A, B, C, and D Use trigonometry to find the...
Activity 1-6: Addition and Subtraction of Vectors by Components If we add two vectors, we can...
Activity 1-6: Addition and Subtraction of Vectors by Components If we add two vectors, we can break up the addition by components. For example Since the x-components point in the same (or opposite direction), we can add the values of the components separately to get the overall vector component in that direction. Once we have the overall components, we can get the magnitude of the vector and its direction by using Pythagorean's theorem and trigonometry. In what follows, we will...
Please, include the explanations to your solution! Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the...
Please, include the explanations to your solution!
Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the planar surface in the xz-plane) (see figure). Let C be the semicircle and line segment that bound the cap of S in the plane z 64 with counterclockwise orientation. Let F (4z 3y,4x+3z,4y+3x. Complete parts (a) through (c) below 64...
A flat surface with area 0.14m^2 lies in the x-y plane, in a uniform electric field...
A flat surface with area 0.14m^2 lies in the x-y plane, in a uniform electric field given by E= 5.1i^+2.1j^+3.5k^ kN/C. find the flux through this surface
Find an equation of the plane tangent to the following surface at the given point. yz...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
2. A flat perfectly conducting surface in x-y plane is situated in a magnetic field H...
2. A flat perfectly conducting surface in x-y plane is situated in a magnetic field H = 3 cosx ax + z cosx ay A/m for z 20 and H = 0 for z > 0. Find the current density of the conducting surface.
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the r...
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
9. X-rays have intensity and direction that are given by a vector field F(x, y, z)...
9. X-rays have intensity and direction that are given by a vector field F(x, y, z) = (z?, sin(2) +y +278, z + cos(x) + sin(xy)). A tonsil (shown below) is given in spherical coordinates as p < 0. Find the flux of the X-ray field F through the surface p = 0 of the tonsil. The surface is oriented with outward pointing normal vectors.
You are given two vectors, one pointing in the x direction and the other pointing in the y direction. Is it possible to find a third vector so that the sum of the three vectors is equal to zero? yes yes, but only because the vectors are perpendicular no only if the two vectors have the same magnitude A points in the-X direction with a magnitude of 12, what is the y component of A? Enter an exact number C...
Show work and please explain!
1. Vector addition and subtraction: We are given the magnitudes and directions of the vectors A and B as follows (a) Carefully sketch each vector individually, then sketch the sum C-A+B and sketch the difference D-A B. Try to make the lengths to scale and make the angles relatively accurate. (Use a protractor.) Use trigonometry to find the components of cach of the four vectors A, B, C, and D Use trigonometry to find the...
Activity 1-6: Addition and Subtraction of Vectors by Components If we add two vectors, we can break up the addition by components. For example Since the x-components point in the same (or opposite direction), we can add the values of the components separately to get the overall vector component in that direction. Once we have the overall components, we can get the magnitude of the vector and its direction by using Pythagorean's theorem and trigonometry. In what follows, we will...
Please, include the explanations to your solution!
Begin with the paraboloid z #x2 + y2, for 0 s z s 64, and slice it with the plane y-0. Let S be the surface that remains for y 20 (including the planar surface in the xz-plane) (see figure). Let C be the semicircle and line segment that bound the cap of S in the plane z 64 with counterclockwise orientation. Let F (4z 3y,4x+3z,4y+3x. Complete parts (a) through (c) below 64...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
2. A flat perfectly conducting surface in x-y plane is situated in a magnetic field H = 3 cosx ax + z cosx ay A/m for z 20 and H = 0 for z > 0. Find the current density of the conducting surface.
21 Problem 20. Let S be the surface bounded by the graph of f(x,y)-2+y2 . the plane z 5; Os1; and .0sys1. In addition, let F be the vector field defined by F(x, y,z):i+ k. (1) By converting the resulting triple integral into cylindrical coordinates, find the exact value of the flux integral F.n do, assuming that S is oriented in the positive z-direction. (Recall that since the surface is oriented upwardly, you should use the vector -fx, -fy, 1)...
9. X-rays have intensity and direction that are given by a vector field F(x, y, z) = (z?, sin(2) +y +278, z + cos(x) + sin(xy)). A tonsil (shown below) is given in spherical coordinates as p < 0. Find the flux of the X-ray field F through the surface p = 0 of the tonsil. The surface is oriented with outward pointing normal vectors.
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