Question 1: (10 points) Determine whether the following Realation is an Equivalent Relation or not, and show the reason for your answer. If A={1,0} R= {(1,1), (0,0), (1,0), (0,1)}

whats this answer  Ginger records her grades for each assignment in science.

Solve the following initial value problem the initial conditions aw +3. = 12z+18 +9, Əz2 მი w(x, 0)=2x3+3x²+8x ду From (38) auction we obtain follow (x, 0) =i (6x²-6x+2).

Question 1 20 pts Test data on the bending strength of construction wood poles of various diameter are presented below assuming the same length. Kip- 1000 lbf. Using the following data with 2nd order Newton polynomial interpolation, we want to determine the strength of the material for x=4.9 in. Which data point will be used as x? After you found x0, enter the value of x-xo in the solution. Answer shall be in one decimal place. Distance (in) Strength (kips) 100 3.6 1.1 5.6 3.6 5.6 200 300 400 500

Test data on the bending strength of construction wood poles of various diameter are presented below assuming the same length. Kip- 1000 lbf. Using the following data with 2nd order Newton polynomial interpolation, we want to determine the strength of the material for x=4.3 in. Which data point will be used as x0? After you found x0, enter the value of x-xo in the solution. Answer shall be in one decimal place. Distance (in) Strength (kips) 100 2.7 1 6.8 0.6 5.7 200 300 400 500

2/2. prove that if G is Euler then so is L (G).

Q10. What are the chromatic numbers of the following two graphs? G H A. x(G) = 2 and x(H) = 2 B. x(G) = 2 and x(H) = 3 C. x(G) = 3 and x(H) = 2 D. X(G) = 3 and x(H) = 3 E. x(G) = 4 and x(H) = 3

a/Let G be agraph. Then X (6) > 3 if and only if G has an odd.

Q/Let G be agraph with n vertices,n2 = then G has at least two vertices which are not cut vertices.