Consider the following region R and the vector field F. a. Compute the two-dimensional divergence of the vector field. b. Evaluate both integrals in Green's Theorem and check for consistency. F = (-3y,6x); R is the triangle with vertices (0,0), (3,0), and (0,3).

Q: You roll twO six-sided fair dice. a. Let A be the event that the first die is odd and the second is…

A: Ans#  Given, roll two six sided fair dice                    Sample space (S) = {(1,1), (1,2),…

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A:

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A: Given: ∬Syze-y1+x2e2y+1dS            where Sis the surface z=xey, 0≤x≤2, 0≤y≤3.

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A: Solution

Q: 5. Determine whether the following series converge absolutely, converge con- ditionally, or diverge.…

A: According to the given information, it is required to test whether the series is convergent…

Q: (a) Solve the problem max x² + y² + z² subject to x² + y² + 4z² = 1 and x + 3y + 2z = 0 (b) Suppose…

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A: The test statistic for proportions difference, Z=p1-p2P^(1-P^)(1n1+1n2)where…

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A: Here, to find the set of points at which the function is continous.

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A:

Q: A=(x| x is a letter in the word mathematics}

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Q: Minimize : 4yi+2y2 +y3 yi +y2 +y3 2 4 Зу1 + у2 +3уз 2 6 yi +y2 +3y3 2 5

A: For convenience we take y_1=x_1, y_2=x_2 and y_3=x_3.

Q: 15n + 12n sin n? n² n-3 n=2 W?

A: Part (c) Given series is

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A: Dur to insufficient information of part (b) ,we will provide the solution only part(a) .

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A: (B) Obtain the proportion of her laps that are completed between 127 and 130 seconds. The proportion…

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A:

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A:

Q: Minimize : 20yı + 12y2 + 40y3 Yi +y2+5y3 2 20 2yı +y2 +y3 2 30 4.

A: The LPP is  MIN Z = 20y1 + 12y2 + 40y3subject toy1 + y2 + 45y3 &gt;= 202y1 + y2 + y3 &gt;= 30and…