Problem #5: Problem #5: Use the divergence theorem to find the outward flux F.nds of the vector field F = tan-¹ (5y + 2z)i + e²² + 4 cos xj + √√x² + y² + z² k, where S is the surface of the region bounded by the graphs of z = √√x² + y² and x² + y² +2² = 16. Enter your answer symbolically, as in these examples

Q: Σ 4" 3" -1

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Q: 1. Find the closest point from the origin to the surface ryz = 3.

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Q: V5 el 5 VI eg eg e3 e2 e 10 VA V2 es e5 V3 e6 eq V6

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Q: 16. Let us consider V = C² with the Euclidean inner product. Let us consider the linear T₁, T2, T3,…

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Q: solve the following equation In(t) = 3

A: The given equation is ln (t)=3

Q: Use the Laplace transform to solve 1 x = 4x + 1y y' = x(t) = y(t) = - 29x - 6y x(0) = 2, y(0) = - 12

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Q: If the half life of a radioactive substance is 14 days and there are 6.6 grams present initially,…

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Q: b) Solve the LP model using the Excel Solver and present your Answer and Sensitivity Reports as…

A: The LPP is  Maximize: 5300 x1+ 8000 x2 + 5500 x3 + 8200 x4Subject to:450 x1 + 470 x2 + 500 x3 + 550…

Q: One property of Laplace transforms can be expressed in terms of the inverse Laplace dF transform as…

A: Useful formula :

Q: 3. Discuss Q[√√2] and Q(√2).

A: Q[2] and Q(2) are both extensions of the rational numbers Q obtained by adjoining the square root of…

Q: (5) 3 IS IR²³ = Span { 1²₁, 0₂, 03 бран Е Is where &₁ = (1, 0, 1) ů √ 2 = (-1,1,2) √ ₁ = (0₂1,0) 3 ?

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Q: Amat 584 Give an om 3. 3. Give not in general position. 2 example of a set of the points in IR²

A: As per the question, we are tasked with finding an example of three points in ℝ² (the Euclidean…

Q: 7. Assume that Vi, i = 1,2 are vector spaces over F € {R, C} and (, );, i = 1, 2 is an inner product…

A: Let X is a vector space. A map V×V→F is said to be an inner product space if the following property…

Q: -ind three linearly independent solutions of the given third-order differential equation and vrite a…

A: Given a third order differential equation is z'''+4z''-16z'-64z=0   we need to find 3 linearly…

Q: The table below lists the height h (in cm), the age a (in years), the gender g (1="Male",…

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Q: (iv) (x+2y = 0 (ax+day=0 aER (Ab) = (1 2²10)₁₁ (63) If a to, then (A) = or(Alb) = 2 and there exists…

A: The given system is, x+2y=a,ax+2ay=0, where a∈ℝ To Explain: the conditions on a for which the system…

Q: Determine £¹{F}. F(s) = s²-14s+5 (s + 1)² (s +6)

A: Given that F(s)=s2-14s+5(s+1)2(s+6) We need to calculate the Laplace inverse of F(s).

Q: 24. Let A [A₁, A2, A3] be a (3 × 3) matrix and set = 2 a) Show that B - 3 1 00 -1 ] 3 4 AB = [2A₁ +…

A: Here, the given A=A1, A2, A3 be a 3×3 matrix and set  B=2003-10134.

Q: 3. Y at t = 2, Y¹ = y² + t² > Y(1) = 0, h = 0.1 and h = 0.05

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Q: . Determine the Laplace transforms of the following functions 1 and e4t COS (7) 3

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Q: Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (2,0,0) to…

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Q: s -2 19.5³ +85² + 7s

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Q: Which have a small standard deviation here ?

A: Standard deviation is the square root of variance of data

Q: 2. List all elements of A = M₂ (Z₂). Give the units in A, as well as the zero divisors in A.

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Q: a) Write the quadratic form 9r2+72+11x3-8x1x2+6x273 as XTAX, where X = and A is a symmetric matrix.…

A: (e) From the given Equation of conic:

Q: let (x,t) be a topological space prove that (x,t) is not connected if and only if there exist A,B…

A: Let (X,t)  be  not  connected.We  have  to  show  that  X=A∪B ,where  A and B are  elements  in t…

Q: y" = 2y^3 + 8y, where y = 2; y'= -8 when x = 4

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Q: Solve for Y(s), the Laplace transform of the solution y(t) to the initial value problem below. y'' -…

A: Given that y''-5y'+4y=6tet, with y(0)=5 and y'(0)=-2. We need to solve differential equation using…

Q: if 0 < x </ if / ≤ x ≤ 1. 0 fn(2)= x ln x (1 + x)² Determine whether fn(x) is Lebesgue integrable on…

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Q: Problem: You need to estimate the cost of materials required to completely renovate a 12 foot by 14…

A: We need to estimate the cost of materials required to completely renovate a 12 foot by 14 foot…

Q: Suppose you have a line with corresponding equation ax +by+c= 0; also suppose you have points (s, t)…

A: Line l: ax+by+c=0 The points (s,t) and (u,v) lie in opposite side of the line if as+bt+c and au+bv+c…

Q: Let a be a complex number with |a| < 1. Prove that 2 α 1 - āz =1_iff |z| = 1.

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Q: Compute the arc length of the figure. Hint: use the identity 1 + cos 0 = 2 cos² (2), and use the…

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Q: Find the line integral of F= (9x² - 6x) i+ 6z j+ k from (0,0,0) to (1,1,1) over each of the…

A: Given that F=9x2-6xi+6zj+k We need to find line integral from (0,0,0) to (1,1,1) over following…

Q: Two suppliers manufactured footballs, baseballs, and basketballs in the quantities and costs given…

A: Quantities…

Q: Find af ffy dv, IV, where E is the solid bounded by the parabolic cylinder z = x² and the planes y =…

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Q: Evaluate by the residue theorem: da fo z(z−oi), (a>0) [a]

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Q: 5.8 Calculate the volume of the region in 3 which is above the xy-plane, under the parabo- loid z =…

A: To Find: The volume of the region which is above the xy-plane, under the paraboloid z=x2+y2 and…

Q: Find the inverse laplace of: L-1{(s+2)/(s2+4s+20)}

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Q: can you find f(x) from the given graph

A: We have to find f(x) from the given graph

Q: Solve the initial value problem below. 2y (3) + 4y'' = 0, y(0) = -1, y'(0) = 0, y''(0) = 1 y(x) =

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Q: Solve using Runge Kutta method.  from t=0 to t=5 Step size = 0.5

A: To solve this third-order differential equation using the fourth-order Runge-Kutta method, we need…

Q: Evaluate by Residue Theorem 4 food, (a > 0)

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Q: 9-23 Four automobiles have entered Bubba’s Repair Shop for various types of work, ranging from a…

A: Job 1 Job 2 Job 3 Job 4 Billy 400 90 60 120 Taylor 650 120 90 180 Mark 480 120 80 180 John…

Q: 2. Construct a 2x2 matrix and obtain the Hill cipher for a message built using seven distinct…

A: To construct a 2 X 2 matrix for Hill Cipher, we need to choose four integers a, b, c, and d such…

Q: Solve the initial value problem below using the method of Laplace transforms w''+w=3t² +6, w(0) = 3,…

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Q: Let R be an integral domain. Show that every associate of a prime element in R is a prime element.…

A: We  have to show that every associate of a prime element in R is a prime element.  And every…

Q: Evaluate the line integral, where C is the given curve. xyz² ds, C is the line segment from (-3, 4,…

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Q: Let T be a linear transformation from R2 into R2 such that  T(1, 0) = (1, 1)  and  T(0, 1) = (−1,…

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Q: Pivot once as indicated in the given simplex tableau. Read the solution from the result. + Pivot…

A: The objective is to find the next simplex tableau and read the solution from it.