Problem 4: Vector Calculations Given the vectors: A=x2+y9 B=x4-y2+z3 C=x5+y+z2 Find the following: a) A•B b)...
Consider the given vector field. F(x, y, z) = (9 / sqrt(x2 + y2 + z2)) (x i + y j + z k) Find the curl of the vector field. Then find Divergence
Problem 4. Consider the field Z2[x]/(F), where $ = x5 + x2 + 1. In this field, we write abcde as a notation for ax4 + bx3 + cx2 + dx +e, where a, b, c, d, e are elements of Z2. For example, 11010 is a notation for the element 1x4 + 1x3 + 0x2 + 1x+0 = x4 + x3 + x. Compute the following. Make sure to write all of your answers either as polynomials of degree...
you are given two vectors: v=[x2 +y2+ z2, 2xyz, x+y+2z] u=[xy+z , xy2 z2 , x+3z] Calculate the following expressions: a) v+u b) v•u c) v x u d) div v
(a) Find and identify the traces of the quadric surface x2 + y2 ? z2 = 25 given the plane. x = k Find the trace. Identify the trace. y=k Find the trace. Identify the trace. z=k Find the trace Identify the trace. (b) If we change the equation in part (a) to x2 ? y2 + z2 = 25, how is the graph affected? (c) What if we change the equation in part (a) to x2 + y2 +...
You have been asked to find the points on the sphere x2 + y2 + z2 = 36 that are closest to and farthest from the point (1, 2, 2). Then which of the following is incorrect from the following: Select one: A. The point on the sphere farthest to the point (1,2,2) is (-2,-4,-4) B. The point on the sphere closest to the point (1,2,2) is (2, 4,4) C. The solutions to the question can be found by solving...
c. Now write the general solution in parametric form. x = X11 X2 X3 XA X5 = P + (vectors multiplied by free variables) (Fill in the particular vector p, then factor out any remaining free variables from your expression above.) (4 points) particular 1 X2 X3 II II X4 + X2 X5 + 0 0 LX6 0 X₂ X₂ X₃ X4 Xg X6 1 2 3 0 5 6 d. Write a vector equation equivalent to the reduced system:...
2: (a) Find all solutions (x, y) = Z2 to Pell's Equation x2 – 29 y2 = 1. (b) Find all solutions (x, y) € Z to the Pell-like equation x2 - 21 y2 = 4.
The magnetic field in a region of space is given by: Ba(x2+22)7+(y2+22)7+(x2+z2)k) where alpha is some constant, x, y, and z are the coordinates in space about the origin and i, j, and k are unit vectors pointing along the x, y, and z-axes Also in the region of space is a conducting square loop with side lengths of L which is placed parallel to the xy-plane, centered on the z-axis, and has a z-coordinate of z Find an expression...
Suppose you are given the following feature vectors: x1 = (1,0), x2 = (4,2), x3 = (0,-1), x4 = (-1,-1), x5 = (-2,1) Their corresponding labels are y1 = 1, y2 = 1, y3 = -1, y4 = -1, y5 = -1 Note: there is no bias term in this problem. Suppose we run perceptron on this dataset starting with w0 = (0,0). Write down the values of w1,w2,w3,w4 and w5 after each training instance, that is, wi is the...
Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2 + y2 +z" 1 and x2 + y2 + z2-4 given that the density at each point P(x, y, z) is inversely proportional to the distance from P to the origin and 8(o, 3,02 15 pts] (0, 1,0)-2/m3 from P to the origin and Use spherical coordinates to find the mass m of a solid Q that lies between the spheres x2...