Mathematics 2

Yanıt Açıklaması:

Yanıt Açıklaması: To answer this question we need to solve both equations simultaneously. So, multiply the first equation with -2 and add the two equations together: Now, substitute this value of x into any one of the equations to obtain the value y=-53/30. Hence the correct answer is B.

Yanıt Açıklaması: When we calculate the values we obtain: Thus, the maximum value is 82

Yanıt Açıklaması: We multiply first equation by 2 obtain the cofficient of the to have different signs. Hence the linear equations become Now we add the equations to eliminate the term then one has into the equation we obtain The solution is the ordered pair Correct answer is C.

Yanıt Açıklaması: As we can see below, the brown circles are the vertices that has degree three, which gives the answer as 4. The correct answer is E.

Yanıt Açıklaması: Consider the pair (4,6). The first component 4 is the greatest among the first components in the 2nd column. The second component 6 is also the greatest among the second components in the 3rd row. Therefore (3rd row, 2nd column)is an equilibrium pair.

Yanıt Açıklaması: When we evaluate the values of given corner points under the goal function f: Hence the minimum value of given constraint set is -15

Yanıt Açıklaması: The Gini index is calculated using the formula where L(x) is the Lorenz curve. Inserting L(x) given in the question we find; Therefore the correct answer is the C option.

Yanıt Açıklaması: The coefficient matrix of the given system of linear equations is We find the determinant of the coefficient matrix using Sarrus’ rule: and we find

Yanıt Açıklaması: Minimum Minimum Minimum Minimum The   maximum of the numbers -5,6,-1,1  is 6 .The corresponding row is the 2 nd row. Correct answer is D

Yanıt Açıklaması: Let G be a connected planar graph with n vertices and m edges, and let f be the number of regions in any plane diagram of G. Then f + n = m + 2 holds. This is called Euler’s theorem on planar graphs. Now for n=3 and m=6 we have f=6-3+2=5, which is the number of regions. Thus the correct answer is C.

Yanıt Açıklaması: The price may be found as S(10) = 2 + 2 = 4. Using the integral formula for the producer surplus, we obtain: which is the required answer. E is the correct answer.

Yanıt Açıklaması: From the linearity of the integral, we find Therefore the correct answer is the E option.

Yanıt Açıklaması: Since we obtain Hence

Yanıt Açıklaması: x - 2y = 8          -2x + 4y = -8 2x - 2y = 10       2x - 2y = 10 y = 1,   x – 2(1) =8,  x = 10,  (10, 8)

Yanıt Açıklaması: Since one has

Yanıt Açıklaması: 6=k.(-1)-1.8 k= -14

Yanıt Açıklaması: Since the curve intersects the required area  is evaluated with the definite integral and the limits of integration are changed from 0 to 4. Therefore, we have The right answer is E.

Yanıt Açıklaması: We need to solve the equations two at a time. Observe that For the point (0, 4) if we insert this point into first inequality we see that is not true. Also for the point (6, 0) if we insert this point into the third inequality we see that is not true. Therefore the points (0, 4) and (6, 0) do not belong the constraint set. The corner points for the constraint set are (0, 3), (-4, 0), (0, 0) and (-2/3, 10/3). Hence the correct answer is B.

Yanıt Açıklaması: Since there are 8 teams in this league, the corresponding graph must have 8 vertices.