Mathematics 2

Yanıt Açıklaması: 1. 0 ≤ L(x) ≤ 1: because L(x) corresponds to a percentage 2. L(0) = 0: because no income is earned when no one is employed 3. L(1) = 1: because 100% of the income is earned by 100% of the people 4. L(x) ≤ x : because the lowest-paid 100x% of people cannot receive more than 100x% of total income

Yanıt Açıklaması: One can easily see that the solution of the system of equations is the point (4,3). Considering the other constraints we obtain that are other corner points. Thus, (0,4) is not a corner point of constraint set.

Yanıt Açıklaması: (1,1) , F = 1.1 – 2.1 = -1, (1,2) , F = 1.1 – 2.2 = -3, (2,4) , F = 1.2 – 2.4 = -6, (4,6) , F = 1.4 – 2.6 = -8,  max value = -1

Yanıt Açıklaması: the 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. Correct answer is A.

Yanıt Açıklaması: The coefficient matrix is Hence we have

Yanıt Açıklaması: The lowest element among the 2nd row elements {-4, -10, -7} is -10 and the lowest element among the 4th row elements {-2, 3, 0} is -2. Therefore the guaranteed values/wins for Player I is -10 and -2, summation of them is -12. The correct answer is E.

Yanıt Açıklaması: We need to check every point in the options if they satisfy the given inequality. Observe that for the point (4, 3) we have So the correct answer is D.

Yanıt Açıklaması: Over the interval [-1,1], Therefore,

Yanıt Açıklaması: The number 1 is the lowest in the 1st row, the greatest in the 3rd column. (1st row, 3rd column) is the equilibrium pair.

Yanıt Açıklaması: It’s obvious that (-2,3) satisfies each of the equations. Hence and Therefore, we have m-n=2-2=0

Yanıt Açıklaması: Since A and B are equal matrices then corresponding entries must be equal. This gives x+y=8 and x_y=4. When we solve this system of equations we get x=6 and y=2. Hence x . y=6 . 2=12

Yanıt Açıklaması: The number -1, which lies in the intersection of the 1st row and the 2nd column, is the lowest in the 1st row, is the greatest in the 2nd column. Therefore(1st row, 2nd column) is the equilibrium pair.

Yanıt Açıklaması: Integrating factor So the correct answer is C.

Yanıt Açıklaması: We should evaluate the definite integral to find the total profit over the period from 5 th to 10 th years: Hence, we find the total profit from 5 th to 10 th years as 875 million TL per year. The right answer is C.

Yanıt Açıklaması: Since a tree is a connected graph which contains no cycles.

Yanıt Açıklaması: m: row numbers n: column numbers m=3 and n=3 mxn=3x3

Yanıt Açıklaması: We know from handshaking lemma that in any graph the sum of all the degrees is an even number but, 2 + 2 + 3 + 1 +1 + 2 = 11 is not even. Hence answer is C.

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