Mathematics 2

Yanıt Açıklaması: This is a separable differential equation hence we may write This may be rewritten as if we say then the solution is The correct answer is A.

Yanıt Açıklaması: Since A is type of 2x3 and B is type of 3x1 then the matrix A . B must be type of 2x1. When we multiply these matrices we obtain

Yanıt Açıklaması: maximum {-1,0,-8}=0 and minimum {2,4,6,3}=2. Hence, 2+0=2. So the answer is D.

Yanıt Açıklaması: It is known that in a complete graph all of the vertices are adjacent to each other.

Yanıt Açıklaması: If the first player chooses 2nd row, the guaranteed value (income) for him is the minimal element of this row. minimum {1,3,4,2} = 1. Hence the answer is B.

Yanıt Açıklaması: The total revenue function may be found by integrating the marginal revenue, so that we have Now we need to calculate R(30) – R(20) . Hence the answer is D.

Yanıt Açıklaması: Since then is obtained.  Since is given, we  should have From this equation one has Then answer is

Yanıt Açıklaması: For each row write the lowest element to the right, and for each column write the greatest element below the matrix maximum {-3,-4,-1} = -1, minimum {2,-1,6,7} = -1. There exists an equilibrium pair (3rd row, 2nd column). The number -1, which lies in the intersection of 3rd row and 2nd column, is the lowest in the 3rd row, is the greatest in the 2nd column. Answer is D.

Yanıt Açıklaması: Since only b,c,d,e are adjacent to a, the answer is A.

Yanıt Açıklaması: We know by Euler’s theorem on planar graphs that the number of edges is equal to m = f + (n -2). Hence, the number of edges is 5+ (4 – 2) = 7. Answer is C.

Yanıt Açıklaması: We can directly calculate the integral The correct answer is E.

Yanıt Açıklaması: minimum {4,0,2,2,3}=0. The number 0 corresponds to the 2nd column. Hence the answer is B.

Yanıt Açıklaması: The lower value is the guaranteed result for Player I, the upper value is the guaranteed result for Player II. Player I, by choosing a row, maximizes the obtained element. Considering this, player needs to analyze each row to find the lower value on each row and then choosing the maximum among those numbers will give him the result. Each row has the lower value -6, -3 and -4 respectively. So max {-3, -4, -6} =-3 is obtained hence the correct answer is B.

Yanıt Açıklaması:

Yanıt Açıklaması: The constraint set has five corner points: The maximum value of the goal function at these points is attained at the point This value is 23. The correct answer is D.

Yanıt Açıklaması: If in the game matrix, there exists an element which is smallest in its row and greatest in its column then this row-column pair is an equilibrium pair. For each row write the lowest element to the right, and for each column write the greatest element below the matrix: Now, observe that max {-1, 0, 2} = 2 and min {2, 3, 4} = 2. Therefore, (2nd row, 3rd column) is an equilibrium pair. The correct answer is D.

Yanıt Açıklaması: is straight line with x-axis intercept (3,0), y-axis intercept (0,2). The point (0,0)  statisfies therefore  (0,0) belongs to the half plane Correct answer is B

Yanıt Açıklaması: Let us put and substitute it into the differential equation. Then the characteristic equation is We can write the solution like Using initial conditions we have Hence The correct answer is D.