Given three 3D vertices A = (10, 0, 10), B = (10, 0, -5) and C = (10, 20, 0), for vertex D=(10, 15, 0), compute the three barycentric coordinates of D and explain whether or notD is a convex combination of A, B and C. If yes, what is the RGB color of D when giving the colors of A, B and C as (1, 0, 0) and (0, 1, 0) and (0, 0, 1), respectively?
B-1 Graph coloring Given an undirected graph G (V. E), a k-coloring of G is a function c : V → {0, 1, . . . ,k-1} such that c(u)≠c(v) for every edge (u, v) ∈ E. In other words, the numbers 0.1,... k-1 represent the k colors, and adjacent vertices different colors. must havec. Let d be the maximum degree of any vertex in a graph G. Prove that we can color G with d +1 colors.
7. (10 points) Consider the cube with the eight vertices (+1, +1, +1). Let A, B, and C be the midpoints of the three edges that join with the vertex (1,1,1). (a) What are the coordinates of A, B, and C? (b) What is the equation of the plane through A, B, and C? (c) What is the angle between the plane in (b) and the face x=1 of the cube?
please solve 3 and 4
TEN C hQuestione Each questio n s (A) (0) (C) and (D) out of whid ONLY ONE Lot L be the line belonging to the family of the straight lines ( 20% - a-b a be which farthest from the point (22) Area formed by the line L with coordinates A) 4/3 units (0) 92 units e) 49/8 sq unite (0) None of these A variable in Lis drawn through 10.) to meet the lines...
15. Three masses are placed in the vertices of a triangle with the following (x y) coordinates (all in meters): m:=1 kg at (0, 0); m2=2 kg at (9, 0); m3=3 kg at (0,8). Find the x-component of the center- of-mass position. A. 3 m B. 4 m C. 5 m D. 6 m E. 7 m
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...
Determine whether a figure with the given vertices is a parallelogram. Use the method indicated. A(4.5), B(-7, -10), C(-4,-9), D(7,6); Distance and Slope Formulas Yes: The opposite sides are congruent and have the same slope. No: The opposite sides have the same slope. No; The opposite sides are congruent and have the same slope. Yes, The opposite sides have the same slope.
Find, correct to the nearest degree, the three angles of the triangle with the given vertices. A(1, 0, -1), B(4, -4, 0), C(1, 2, 5) CAB = o LABC = o ZBCA = O
2. (5 Points) Given adjacency list representation of a digraph below with 10 vertices from 0 to 9, does it have a topological order? If so, provide one. Otherwise, explain why. 0: 4 2 1 3 1: 2 2: 3 3: 4: 2 5: 1 4 3 8 9 6: 3 2 1 9 7: 2 1 8: 2 1 4 6 9: 3 1 4
5 Three events all have coordinates y 0, but they have different x and t coordinates as given by the following table: Point 0 ns 10 ns 5 m 6 m 20 ns a. What is the proper distance or proper time separating A from B? one?), is one on the future light cone of the other, or are they Is one of these events in the absolute future of the other (which "elsewhere" from each other? b. Repeat, this...
There are three assets, A, B and C, where A is the market portfolio and C is the risk-free asset. The return on the market has a mean of 12% and a standard deviation of 20%. The risk-free asset yields a return of 4%. Asset B is a risky asset whose return has a standard deviation of 40% and a market beta of 1. Assume that the CAPM holds. Compute the expected return of asset B and its covariances with...