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

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

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.

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.

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.

Hence the system of linear equations above can now be expressed as a single matrix equation

that is

The number 0 corresponds to the 2 nd column.

Correct answer is E.

Correct answer is A.

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.

Doğru cevap C’dir.

The number of edges in the complete graph K_n is given by the formula

So the number of edges in the complete graph K₇ is 

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. Correct answer is C.

We consider the subintervals

and

to evaluate

.

By definition we obtain

Hence the right answer is E.

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)

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

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)

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.

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)