4. Let ABCD be a rectangle with vertices A-(0,0), B 4,0) C(4,3), D (0,3) Suppose an...
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
(1 point) A uniform magnetic field B has constant strength b teslas in the 2-direction [ie., B = (0,0, b) ] (a) Verify that A Bx r is a vector potential for B, where r (x,y,0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. FIGURE 17 A= (4,0,4), С=(0,3,0), В= (4,3,0), D (0,0, 4), F (4,0, 0) Flux(B) (1 point) A uniform magnetic field B has constant strength b...
In the Kite ABCD with vertices A (-1, 4), B (1, 2), C (-1,0), and D (-5,2), the equal sides AD and DC are of length A 4 3 B 2. 1
DLM R A 2,3 -1,0 1,1 B -1,3 3,0 2,1 C 0,0 0,10 3,1 D 4,3 2,0 3,1 Part a: What are the pure strategies that are strictly dominated in the above game? Part 6: What are the rationalizable strategies for each player? What are all the rationalizable strategy profiles? Part c: Find all of the Nash equilibria of the game above.
In this problem, let li be the line that passes through the points A(1,2, 4) and B(-1,3,8), and let l2 be the line with symmetric equations x +1 = 2y = 32 — 3. Parts (e) and (f) relate to the vector field F = (xy, xz, yz). (a) Show that the lines li and l2 intersect. (b) Let P be the plane that contains both lines li and lz. Find an equation for P. (c) Show that the points...
1. Let u be a solution of the wave equation ue20. Let the points A. B, C. D be the vertices of the paralleogram formed by the two pairs of characteristic lines x-ct = cı, x-ct c2, x + ct = di, r + ct = d2. Show that u (A) + u (C) = u (B) + u (D). Use this to find u satisfying For which (r, t) can you determine u (x, t) uniquely this way? 1....
1. Let u be a solution of the wave equation u 0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines r-ctC1,x- ct-2,+ ct- di,r +ct- d2 Show that u (A)+u (C)-u (B) + u (D Use this to find u satisfying For which (x, t) can you determine u (x, t) uniquely this way? 2. Suppose u satisfies the wave equation utt -curr0 in the strip 0...
1. Let u be a solution of the wave equation u0. Let the points A, B, C, D be the vertices of the paralleogram formed by the two pairs of characteristic lines z--d-q,z-ct-c2, z + ct = di, z + ct d2. Show that u(A) u (C) u(B) +u(D) Use this to find u satisfying till- tLzz =0, u( s,s)-s, u(8,8)-82 for s > 0. For which (r, t) can you determine u (x, t) uniquely this way? 1. Let...
question 1 and 2 please, thank you. 1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
Let, R=(A,B,C,D,E,G) and let F be {A→BDG, BG→DE, B→D, D→A}. Argue that R is not in BCNF by finding one functional dependency in F that violates the definition of BCNF. Add one more non-trivial dependency to F so that R is in BCNF with respect to the new set of dependencies.