Mathematics 2

Yanıt Açıklaması: Therefore the correct answer is the B option.

Yanıt Açıklaması: The number of labelled trees on 5 vertices is 5 5-2 =5 3 =125.

Yanıt Açıklaması: For the point (20, 5), F = 3x + 3y = 3.20 + 3.5 = 75

Yanıt Açıklaması: We must evaluate the values of the goal function at the corner points. Thus, the maximum of over the constraint set will occur at (10,20).

Yanıt Açıklaması: Correct answer is D.

Yanıt Açıklaması: the correct answer is B.

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

Yanıt Açıklaması: Let us determine the integral with Sarrus’ rule. For the determinant above we have If we solve this equation we get Therefore the correct answer is A.

Yanıt Açıklaması: The price may be found as Using the integral formula for the producer surplus, we obtain which is the required answer.

Yanıt Açıklaması: The coefficient matrix of the system of linear equations is The other matrices we use in the Cramer’s rule are The determinant of these matrices are Hence the solution of this system of linear equations is

Yanıt Açıklaması: The maximum value is 30. The correct answer is E.

Yanıt Açıklaması: Since a 31 =0 and b 31 =3 then it is clear that Furthermore, one can easily check that

Yanıt Açıklaması: When we consider the given matrix, we find maximum {-1,-2}=-1. So the answer is A.

Yanıt Açıklaması: minimum {5,5,3,6}=3.

Yanıt Açıklaması: From the system we have The corner points are: (0,0), (0,5), (2,5), (7,0). The maximum is attained at the point (2,5) and equals The correct answer is B.

Yanıt Açıklaması: We will use the Cramer’s rule. The system above can be written as for and The solution of this system of linear equations is where Now calculating determinants with the Sarrus’ rule we get Hence our solution becomes The correct answer is D.

Yanıt Açıklaması: We should find the corner points firstly. When we solve the equations we get a corner point (-3,1). In addition considering all constraints (especially x≤0, y≥0) we see that are other corner points of the constraint set. Secondly, we will find the values of these corner points under the goal function: The maximum value is 3/4.

Yanıt Açıklaması: olmak üzere sayısının şifrelenmişi olur. Doğru cevap E’dir.

Yanıt Açıklaması: The point (3,1) only.

Yanıt Açıklaması: Since a 2x3 matrix has 3 columns we can multiply it by a matrix which has 3 rows, so one example of this type of matrices is 3x4.