Mathematics 2

Yanıt Açıklaması: When we calculate the image of (4,5) under given goal functions we have:

Yanıt Açıklaması: Consider the pair (7,3) The fist component 7 is the greatest among the first components in the  3 rd column . The second component is also the greats among the second components in the  2 nd row. Therefore the pair (7,3) . Correct answer is C

Yanıt Açıklaması: Consider the pair (3, 2). The first component 3 is the greatest among the first components in the 2nd column. The second component 2 is also the greatest among the second components in the 2nd row. Therefore, the corresponding pair, i.e. (2nd row, 2nd column) is an equilibrium pair. Answer is E.

Yanıt Açıklaması: The degree of a vertex in a graph is the number of edges incident with that vertex.The greatest degree in the given graph is 4.

Yanıt Açıklaması: Rewriting the differential equation in the standard form we have so To solve the equation we first compute the integrating factor On multiplying the equation by we obtain and therefore where c is an arbitrary constant. It follows that is the general solution of differential equation.

Yanıt Açıklaması: Hence the system of linear equations above can now be expressed as a single matrix equation that is

Yanıt Açıklaması: The number 0 corresponds to the 2 nd column. Correct answer is E.

Yanıt Açıklaması:

Yanıt Açıklaması: Correct answer is A.

Yanıt Açıklaması: If the first player chooses 2 nd row, the guaranteed value for him is the minimal element of this row. Minimum Correct answer is A.

Yanıt Açıklaması: Doğru cevap C’dir.

Yanıt Açıklaması: The number of edges in the complete graph K n is given by the formula So the number of edges in the complete graph K 7 is

Yanıt Açıklaması: We consider the subintervals and to evaluate . By definition we obtain Hence the right answer is E.

Yanıt Açıklaması: We will evaluate the intersection of the equations When we add them we get 3y=9 and y=3. For y=3 by the first equation we get x+6=4 that gives x=-2. Hence the corner point is (-2,3)

Yanıt Açıklaması: Intersection points of the line and coordinate axes are the pointsand coordinate axes are the points  (6,0) and (0,9). Since point (0,0) satisfy Hence, all points in the region which contains (0,0) are  the solution of the inequality. Thus, required region is

Yanıt Açıklaması: When we check each point: (it does not satisfy the second inequality) (it does not satisfy the second inequality) (it does not satisfy the second inequality) (it satisfies both of the inequalities) (it does not satisfy the first inequality)

Yanıt Açıklaması: An Eulerian walk is a walk that goes through every edge exactly once (the walk may or may not be closed). Since the walk e→d→c→a→d→b→c goes through every edge exactly once, it is an Eulerian walk. The correct answer is D.

Yanıt Açıklaması: Multiplying both sides of the first equation by -4 and adding to the second one we obtain Hence the solution is the point (-1,2)