Consider the following optimisation problem min f(x, y) = x + y – x² subject to x + y<1 x 2 0, y > 0. a) Find a critical point of the Lagrangian. b) Find a better solution to the problem above than the critical point of the Lagrangian calculated in a). c) What sufficient condition for the optimality of the Lagrangian solution is violated by the problem.

Q: 15 - How many significant figures are there in the number of 0.0308000?

A: The rule is: the zero before the non zero digit are considered as insignificant

Q: If n(A) = 2, n(B) = 5, and n(A ∪ B) = 7, find n(A ∩ B).

A:

Q: A = B = 2 (1) Find a matrix C which satisfies 3A + C = B. C = (2) Find a matrix D which satisfies A…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If n(A ∪ B) = 10, n(A) = 2 and n(B) = 12, then find n(A ∩ B).

A:

Q: 7) Prove by contradiction: For all prime numbers a, b, and c, a² + b² + c².

A: To prove for all prime numbers a, b, and c, a² + b² not equal to c^2.

Q: 1)   If A =         2  -1     and   B =         1          -2                           7   0…

A: We are given A=[2-17  0],  B=[1-23-3]

Q: If n(A) = 45, n(B) = 15, and n(A ∩ B) = 9, find n(A ∪ B).

A:

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A:

Q: If n(A ∪ B) = 97 and n(A) = n(B) = 66 find n(A ∩ B).

A: Given, n(A ∪ B) = 97 and n(A) = n(B) = 66

Q: Prove by induction that for sets A1, A2, . .,An, n A¡ i=1

A: For induction method we take a statement. We will show that the statement is true for n=1, n=2 then…

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A: Refer to the question. Use the venn diagram method to solve this problem.Now here n(A intersect B)…

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A:

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Q: If n(A) = 40, n(B) = 22, and n(A ∩ B) = 4, find n(A ∪ B).

A: topic - sets

Q: If n(A) = 41, n(B) = 15, and n(A ∩ B) = 2, find n(A ∪ B).

A: We will use the following n(A U B) = n(A) + n(B) - n(A ∩ B)

Q: If n(A) = 44, n(B) = 23, and n(A ∩ B) = 8, find n(A ∪ B).

A: Explanation of the solution is given below...

Q: If n(B) = 210, n(A ∩ B ∩ C) = 55, n(A ∩ B ∩ CC) = 20, and n(AC ∩ B ∩ C) = 65, what is n(AC ∩ B ∩…

A:

Q: then find, a) The first row of AB b) The third row of AB c) The second row of AB d) The first column…

A: I am attaching image so that you understand each and every step.

Q: 98! 1. Simplify. : 100! a) 100 x 99 x 98! b) 1 100 x 99 x 98 c) 100 × 99 d) 1 100 × 99

A:

Q: If n(A) = 46, n(B) = 19, and n(A ∩ B) = 5, find n(A ∪ B).

A: Using , n(A u B) = n(A) + n(B) - n(A intersection B),

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Q: 29. How many possible sets of four marbles are there?

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Q: If n(B) = 275, n(A ∩ B ∩ C) = 65, n(A ∩ B ∩ CC) = 50, and n(AC ∩ B ∩ C) = 145, what is n(AC ∩ B ∩…

A:

Q: If n(A) = 45, n(B) = 18, and n(A ∩ B) = 7, find n(A ∪ B).

A: Given that  n(A) = 45, n(B) = 18, and n(A ∩ B) = 7. We find n(A ∪ B).

Q: If A, B, and C are mutually independent, does A and (BNC) mutually independent?

A:

Q: (a) i3 (b) i4 (c) ¿5 %3D ||

A: Please refer the attached image for complete solution.

Q: If n(A) = 45, n(B) = 17, and n(A ∩ B) = 2, find n(A ∪ B)

A: Thanks for the question :)And your upvote will be really appreciable ;)

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Q: If n(A) = 47, n(B) = 19, and n(A ∩ B) = 4, find n(A ∪ B)

A:

Q: If n(A) = 46, n(B) = 21, and n(A ∩ B) = 6, find n(A ∪ B).

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 14x – 60x? – læ + 3)dx…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

Q: If n(A) = 40, n(B) = 24, and n(A ∩ B) = 1, find n(A ∪ B).

A: