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Q: Let (x,d) be a metric space. Let {xn} be a sequence in x: When do you say (x,d) is compact? f)…

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Q: Find the surface area of the helicoid (spiral ramp) with vector equation F (u, v) = (u cos v, u sin…

A: Given, r¯(u,v) = ucosv,usinv,v, 0≤u≤30≤v≤3π   We have to find the surface area of the helicoid.

Q: +|m₁nEN ² mine 3. Let S = { (-1) ²² [ +1 +224131 Find all cluster points of S

A: S=-1m+n21m+2n+12n+3 m,n∈ℕ

Q: 5) Consider the following weighted graph: 11 6 H 5 6 A 10 E 9 14 8 3 16 4 B 3 12 C Use Kruskal's…

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Q: In the additive group of the integers modulo 12, the inverse of 5 is a) 4 b) 6 c) 5 d) 7 e) 10

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Q: Let G be a finite semigroup. Prove that there exists e∈ G such that e = e^2.

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Q: 2 RIEMANN SUMS Let f(x)=√x be a function on the interval [2,7], and let n = 10. Calculate the…

A: We can find Riemann sums .

Q: Compute the Laplace transform. Your answer should be a function of the variable s: s(πt)} = c{₁+ +…

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Q: 2. Draw the complete shear and bending moment diagrams. A -1 m- 800 N 1200 N·m -1 m. -1 m- 600 N -1…

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Q: Question 10. Find the Fourier cosine series forf (x) = x 72 if 0 ≤ x ≤ 1/1/0 if / ≤x≤L on 0 ≤ x ≤ L.

A: Given fx=L2        0≤x≤L2                                        0≤x≤Lx-L2    L2≤x≤LTo find:…

Q: Urgent need pls i will rate We have three vectors: X1 = [2, 5, 3, 0, 6] X2 = [1, 4, 2, 7, -2] X3 =…

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Q: 个 Find dw when r = 5 and s= -5 if w=(x+y+z)², x=r-s, y = cos (r+s), z = sin (r+s). aw ər r = 5₁ s=…

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Q: Exercise

A: We use properties of ring to prove our claim.

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: The given problem is to evaluate the given flux of  surface integral of vector field over the…

Q: Choose the equation that gives a parameterization for the surface graphed below. X 21 OF(u, v) OF(u,…

A: Given parametric surfaces are: r¯u,v=vcosu, vsinu, u+v2 r¯u,v=vcosu, vsinu, v2 r¯u,v=2+vcosu,…

Q: Determine the number of slack variables and name them. Then use the slack variables to convert each…

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Q: Suppose that E is the splitting field for some polynomial over GF(p).If Gal(E/GF(p)) = p6, how many…

A: Given: E is the splitting field for some polynomials over GF(p). And Gal(E/GF(p)) = p6. We have to…

Q: f(x, y) = ex (9x² - 9y²) Local maxima are Local minima are Saddle points are

A: Given, f(x,y) = e7x(9x2-9y2)   We have to find the local maximum, local minimum and saddle points.

Q: 8) Consider the following set of data: 13 7 19 4 46 25 45 14 b) Construct a Frequency Table. c)…

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Q: Use the vectorized Euler method with h=0.25 to find an approximation for the solution to the given…

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Q: Local linearization is used to justify L'Hopital's Rule when f and g are differentiable and…

A: Not only zero , when both f(a) and g(a) are infinite , in that case we can also use L'Hospital rule

Q: Find all limit cycles of system x₁ =−x₂ + x₁(1-x² - x²) (2 - x² - x²), x₂ = X₁ + X₂(1 − x² − x²)(2 −…

A: As per the system we are given a 2d nonlinear dynamic system and we have to find : The limit cycles…

Q: Let G be a group and let a be a fixed element of G. Show that H = {x E G |xa = ax} is a subgroup of…

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Q: Use the method of separation of variables to find the product solution of the PDES: (a) Ux = Uy (b)…

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Q: 1. Consider the conic C with equation: x² +2√3xy-y² = 2. Find the discriminant of C and hence state…

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Q: The total cost C(q) of producing a goods is given by: What is the fixed cost? fixed cost= dollars…

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Q: Problem: Using the language of differential forms, find the value of the integral of the vector…

A: Here, we need to find the integral of the vector field          A=2+z2∂x+y2∂y+2xz∂z along the curve…

Q: Prove that's is primep, then (a + b)P = (a + b)(mod p), Va; b EZ

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Q: - Let f(x, y) = x² + y²-4 and let C be the circle x² + y² = 9 traced once counterclockwise. Evaluate…

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Q: Use Gauss's law to find the charge contained in the solid hemisphere x² + y² + z²<a², z ≥ 0, if the…

A: Given Data: Let us consider the given data, The electric field  is E →=xi^+yj^+6zk^. Equation of the…

Q: PROBLEM 2: Solve for the optimal solution of the following OR Model: Minimize z = 80x + 60y…

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Q: -2 0-1 -6 -1 0

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Q: Let T : R³ → R³ by the linear transformation that projects u onto ʊ = (−1, 3, 1, 1, 2). (a) Find the…

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Q: 8. The polynomial x² a. Q and R e. C and z b. R

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Q: Consider the primal LP problem given below: The optimal tableau is given by: Basic Variables 1. 2 81…

A: In the given problem the optimal table of the linear programming problem is given.  If we solve by…

Q: Find the change of variable x = Py that transforms the quadratic form x¹ Ax into y¹ Dy as shown. -…

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Q: 9. Describe the surface x² + y² + 2² - 2x + 4y +1=0 with plain English.

A: The given problem is to describe the given surface x2+y2+z2-2x+4y+1=0.

Q: Which of the following is true regarding the function y = Arctan (ax+b)? O [none of the choices] The…

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Q: Let a be an element of a group G such that o(a) = r. Let m be a positive integer such that (m,r) =…

A: a∈GOa=rgcdm,r=1 We have to prove Oam=r

Q: 1. For the matrices A and B given: -3 5] 2 1 A = - 3 (a) Find the determinants of A and B

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Q: - (3) Prove that the sequence C(2n, k) = is increasing for k=0, 1, 2,..., n.

A: We know that C(2n,k) is maximum when k= n

Q: A group of students wish to charter a bus which holds at most 45 people to go to an educational…

A: As this question has multiple subparts, hence only first three parts will be solved. Let x≤40 people…

Q: Let a,b ∈ R such that ba=b and a is right quasi-regular. Show that b = 0

A: Given that a is right quasi-regular element in ring R. That means, a + x - a x = 0 has a solution x…

Q: Which of the following is true about the quadratic fit to the three points: (1,0), (3,2) and (5,3).…

A: There are given three points (1, 0), (3, 2), and (5, 3). our goal is to find the quadratic equation…

Q: The delta of an underlying asset (such as a stock) is 1.00 and therefore it can be used to hedge…

A: The given statement is  the delta of an underlying asset (such as a stock) is 1.00 and therefore it…

Q: Suppose: u(x, t) = x² + t², 0≤x≤ 1, 0st≤1, and consider Ax = 0.25, At = 0.5, then: Determine the…

A: Two dimensional functions are functions who has two inputs referred as two axes and output can be…

Q: Prove that fo f = Idom f iff f-¹ is a function from ran f to dom f.

A: Prove That : f-1of=Idom iff f-1is a function from ran f to dom f.

Q: Approximate the area under the curve f(x) = 3²-1 on [2, 4] using midpoints and 4 rectangles (round…

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Q: Suppose y Σan" on an open interval I that contains the origin. Express the following as a n=0…

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Q: If one of the vertices of the square circumscribing the circle |z1|= √2 is 2 + √3i, find the other…

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