What is the coefficient of xy³ when (2y-x)° is expanded by the binomial theorem?

Q: Calculate the line integral [F•dr, where F = 3x°yi + x'j in two cases for C1 and C2. These two…

A: The given vector is F=3x2yi+x3j Here we use Green's theorem. So the Green's theorem is…

Q: =At iteration i=3, b .2 f (x) = x³ – x – 2

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Q: ミ xy

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Q: Determine the set which is equal to this infinite union: 4 1 7 n n=1 Justify your solution.

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Q: Using the theorem on determinants, show that 1 a a2 A = 1 b b2 = (b – a)(c – a)(c - b) 11 - с с2

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Q: Problem 5. Find all primes p such that 1+p: 2P is a perfect square.

A: We have to find all prime p such that 1 + p×2p is a perfect square.

Q: Use Gauss-Jacobi Method to solve for the System of Linear Algebraic Equations. Use at least 4…

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Q: (iii) 1 + 1 33 + ... 22 + 22 33+

A: given series test for comparison tests - apply this comparison test to a given series the auxiliary…

Q: Problem 3: Given the nth-term formula below, compute the first five terms of the sequence: an n=…

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Q: For problems 1-2, find a general solution to the system x' = Ax where [6 1. A =

A: According to Bartleby guidelines, I am solving only the first question.Please resubmit the question…

Q: for your public transportation system. The community cannot spend more than $100, 000 for the…

A: Lets,   the numbers of small van= V         the numbers of small van= B Therefore,  the constraints…

Q: f(x)=x3-7x²+8x-3 iF Xo =5

A: Using Newton-Raphson Method we determine the approximation to the solution, where  f(x)=…

Q: Definition of Laplace Transformation. Definition Let f(t) be a function on [0, x). The Laplace…

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Q: 2 = 1+ 2i 2- i and w = what is z + 3w ? a. 7+i C. 5+ i b. 7-i d. 5-i

A: Solution

Q: Use Green's theorem to find the area integral if V(x.y) = (x²+y®)į+ (x²=y®\j¸ where C is a solid…

A: The given vector is Vx,y=x2+y2i+x2-y2 j and  The given parabola is y=2-x2. We know the Green's…

Q: 1.) An open box is to be made with a volume of 36,000 cm3. Find the least material or surface area…

A: Given : Volume=36,000 cubic centimeter. length=2×width Let, Length=l Width=w height=h Volume=l×w×h

Q: Let m, n ɛ Z+ such that gcd(m, n) = 1. Suppose there are M and N abelian groups, up to isomorphism,…

A: Given that m,n∈ℤ+ such that gcdm,n=1. Suppose that there are M and N abelian groups, up to…

Q: . Use Taylor's neries, to prove that ein z tan (x+ h)3tan" % + (h sin z). sin 3z sin 2z + (h sin zj…

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Q: 6- If a,b,c,d>0, use the properties of logarithms to simplify and then Tnd the exact numerical value…

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Q: Define analytically the periodic functions shown. 1 f(x) 2 2 4 6 8 -1

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Q: ERROR CORRECTION TEST ITEM: DIRECTIONS: The entire test has been answered for you. Your job is to…

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Q: 12. The graph of f is shown below on the xy-plane. Explain why y = 0.8(x – 1) + 0.4(x – 1)² + 0.1(x…

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Q: Find the centroid of the solid of revolution obtained by rotating the region bounded by y=x^3, y=8,…

A: We have to find the centroid of solid.

Q: f(t) = sin* 3t

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Q: Q3) By using Graphical Method. Find the optimum solution of X1 and X2 that the maximize Z=X1 + X2…

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Q: 6x-7 4. S 를 In(4x2 + 1)-2 n(2x + 1)-승Tan-1(2x)| + C (2x+1)(4x2+1)

A: 4 Given integral is ∫6x−72x+14x2+1dx. First of all we will take a partial fraction of 6x−72x+14x2+1,…

Q: f(t) = t cos 4t 8s 8s А. (s² –16)? С. (s2+16)2 s2+16 В. (s2 –16)2 s2-16 D. (s²+16)²

A: To find the Laplace transformation.

Q: A set S of vertices is an independent set if there are no edges between any two vertices in S (e.g.,…

A: The statement is not true.

Q: ) (4,0) ) (이14) ) (4,시) S. x* dy - 2y dx whare L is 2° J. circle arc x+y% =1, x >O X 70

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Q: Exercise 4 Let X andY be a normed vector spaces and let T: X → Y be a linear operator. Define ||2||a…

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Q: A graph has a. Vertices O b. edges O c. A function that tells which two vertices are connected by a…

A: Note: We will answer the first question only as the exact one is not specified. Please resubmit the…

Q: Find the coefficient of sin nx in the Fourier series expansion of f (x) = x² (0 <x < 2n)

A: We find the coefficient of sin(nx) in the Fourier series expansion of f(x)=x2(0&lt;x&lt;2π).

Q: Let X = {1, 2, 3, 4, 5} and Y = {3, 4}. We define the relation R on the set P (X) by the formula (A…

A: Here, I have shown that the given relation is an equivalence relation and found out the equivalence…

Q: fj+1 - fj-1 2Ax Assuming a uniform grid spacing of Ax, derive a finite difference approximation to…

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Q: 3. Your class adviser announces that everyone should buy a permutation lock for their lockers. Ramon…

A: Both permutation and combination are arrangement but in permutation order matters and in combination…

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

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Q: Tank # 1 initially holds 50 gals of brine with a concentration of 1 lb/gal, while Tank # 2 initially…

A: Given: Tank1: The volume of tank 1=50 gals x1(t)= amount of salt at time tx1(0)=50 gals× 1…

Q: w the depth first traversal of the following graph. Start at vertex 1. Ties are resolved in…

A: Here I run a python script and see the result.

Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

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Q: Let I = {(a, 0) | a e Z}. Show that I is a prime ideal, but not a maximal ideal of the ring Z×Z.

A: Ideal of a ring

Q: Find a power series representation for the function H(x) = S" arctan(z²) dz. And Find the 7th degree…

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Q: f(t) = e4t cos 3t 3 s-4 A. s2-8s+25 С. s2-8s+25 3 s-4 В. s2-8s-7 D. s2-8s-7

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Q: The equations of three lines are given below. Line 1: 3y=-4x+5 Line 2: 6x-8y=8 4. Line 3: y= For…

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Q: Example 1.4.1 As an easy exercise, check that you believe that lim [0, 1- 1/n] = [0, 1) n-00 lim [0,…

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Q: Express the griven below in rectangulat form Co (cos le0° + i sin 180°) a. le + oI b.-et Di -1 + oi

A: Solution

Q: find the coordinates of the centroid of the plane area bounded by the parabola y=4-x^2 and the…

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Q: TABLE 18.1 Data to be fit with spline functions. i X; fi 1 3.0 2.5 4.5 1.0 3 7.0 2.5 9.0 0.5

A: Assuming first two points (3.0,2.5) and (4.5,1.0) has been joined by a straight line.

Q: By using method of undetermined coefficient solve (D² – 3D + 2)y = ex + e2x ;D = 4 ? dx

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Q: Solve the following initial value problem using Laplace transformation 2- 2y = 4x? with y(0) =…

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Q: Exercises 6.1 In Exercises 1-8, show that the given set of functions is orthogonal with respect to…

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