1 Find the eigenvalues and eigenbases of the matrix A = 0 0 -21 0 0 0 4

Q: Use Green's Theorem to evaluate: C F . dr = where F = (√x + 4y, 3x + 4y) and C is the boundary of…

A: Solution :-

Q: y = A sin sin 5x + Bcos 5x; + + 25y = 0

A: Since all are different so as per our guideline, we are supposed to solve only first question.…

Q: 4. Find MacLaurin's series (i) using the known function series (see slide 30 from the Lecture Notes…

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Q: Let C(n) be the constant term in the expansion of (x + 6). Prove by induction that C(n) = 6 for all…

A: We have used Mathematical Induction to prove the statement (Can be found in next step);

Q: O Compute the Transitive Closure of the following relations on the set A={1,2,3,4}. (i) R₁ = {(1,2),…

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

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Q: - Evaluate the limit lim and justify your answer. S ng"-3 sin - dr 1 + xn n

A: As per the question we are given an improper Integral whose integrand is a functional sequence. And…

Q: Suppose the vector field v(x, y, z) = (2x − 1) i + (−x − 3) j + (2z − 1) k represents the velocity…

A: We will use stokes theorem  f a simple, closed, smooth boundary curve C  with positive orientation…

Q: Question 12 A company selling widgets has found that the number of items sold a depends upon the…

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Q: nholme's theorem: for any prime p > 5, we have (p - 1)! Q:=Σ · = 0 (p?).

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Q: Prove that f: R→ R is continuous. 2. Suppose that the function f: [0, 1] → R is continuous and that…

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Q: 나이 4y = S =

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Q: dt -We can get the roots m² +Gm +8 -0 corresponcting by using it's ^ auxiliary equation

A: Here we find characteristics roots. Complementary Solution  Particular solution.

Q: fy y³dx - x³dy, where C is the boundary of the region between the circles x² + y² = C Evaluate 2 and…

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Q: Justify: Q by indicating the rules of inference applied on the following steps together with the…

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Q: Let Note: M = Find formulas for the entries of M", where n is a positive integer. (Your formulas…

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Q: We have 50 points (small dots), what would the minimum area required be if every point has to be 300…

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Q: c. A chemist conducted an experiment on compounds. He mixed 20% of 9.47 grams of one compound with…

A: According to the guidelines, one question can be answered. Please repost other question separately.…

Q: 7) y = 1 2 sin (20 + 150) - 1 60 120° 180° 240° 300° 360 8) y = 4sin 4sin (+45)+1 A 180° 360° 540°…

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Q: 1. Ytt = 4yxx, 0 0; y(0,1)= y(л,t) = 0, y(x,0) = sin 2x, yt (x, 0) = 0 10

A: Since there are two questions, therefore find the solution of the first question.

Q: A sequence of numbers A,,, n = 1, 2, 3, ... is defined as follows: 2n 3 = 44 = 2/1/2 and for each n…

A: The given problem is to prove the given summation is less than 1 when A1=1/2 and…

Q: Find the area of region enclosed by x = t - t³, y = t − t², 0 ≤ t ≤ 1 using Green's Theorem.

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Q: 5. In the following exercises, identify the single rigid motion that is involved, and then locate…

A: Given a few diagrams, to determine which transformation is used to form the image from the original…

Q: A population of ants is growing at a rate of 46% per year, they start with 245 ants in their colony.…

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Q: Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the…

A: The given function fx=1+cosx2, -π≤x≤π. We have to find the upper Riemann sum and lower Riemann sum…

Q: Find a potential function f for the field F=e4y+52 (3 i+ 12xj+ 15x k). A potential function is…

A: Since both questions are different. So as per our guideline, we are supposed to solve only one…

Q: nd x-1 2 - у-г 3 x-2 3 2-3 ។ y-g I also obtain the equation of the lime e shortest distance, of

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Q: Suppose the class equation of a group G is |G| = 1 + 4 + 5 + 5 + 5. Show that G has an element of…

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Q: Over the time interval 1 ≤ t ≤ 6, a particle moves along a straight line with a velocity of v(t) = 8…

A: Given:The particle moves along a straight line with velocity: vt=8t-4  m/s; 1≤t≤6.The positive value…

Q: Mdzy d+² = Му-кан Determine the position. y of the object at time + if Y it is dropped from a…

A: Md2ydx2=Mg-kdydty0=y0

Q: .2п 0 cos² t 2 COS 13 + 12 cost dt

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Q: Questions: 1. Let A = {1,2,3,4,5). Let F be the set of all functions from A to A. Let R be the…

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

Q: Consider the power series (-1)^x^ n=1 9m (n²+4) M8 interval of convergence gues From x = to x =…

A: Ratio test -: If a series ∑n=1∞anxn is given and  limn→∞an+1an=L if L<1,then series converges…

Q: Use the Gram-Schmidt process to produce an orthogonal basis for the column space of matrix A. An…

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Q: 1. DETAILS Consider the given function and the given interval. f(x) = 2.r (1+x2)2 [0, 2] (a) Find…

A: The given function is f(x)=2x1+x22, and the interval is 0,2. (a) To Find: Average value of the…

Q: + 2850-361 4 a) Figure 4 shows a graph of the form y=Acos (be+p) ii) b iii) p 4 2 O -2 Determine the…

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Q: Evaluate the following summations. 2 (©) Σ=_3 k3. (d) 3 Σ=o 3*

A: We have to evaluate the following summations. (c)  ∑k=-32  k3(d) ∑k=03  3k   Here, let assume k ∈ Z.

Q: Find Singular Value Decomposition of A = 322 2 3

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Q: 3) d²x cl+²2 Now + 8clx dt (D² + 80 +25)X = 10 ult) u(t)=0 when, + 20 2 (0² + 80 +25) x = 0…

A: For first part, We know that series of (1+x)-1 = 1 + x + x2 + ... Using this we expand where x =…

Q: Find the divergence of the vector field ♬ = F div F =

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Q: Give a specific reason why the following set R does not define an equivalence relation on the set…

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Q: Does the function 5 3-x f(x)= have a vertical asymptote at x = 3? Why or why not? (Completing a…

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Q: 4. Derive the following formula: ° cos(ar) = cos(br) dx = (b − a) (a≥0, b≥0). - COS x²

A: Use Integration by parts to solve.

Q: ||projn (x) || = x. n |n||2 || n x. n |n||²

A: Given:  projnx=x·nn2n=x·nn2n. To do: We have to explain how the expression factored out.

Q: Prove each of the following statements using mathematical induction. (d) Prove that for any positive…

A: We have to prove ∑j=1n1jj+1=1-1n+1

Q: Prove each of the following statements using mathematical induction. (b) For any n ≥ 1, the…

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Q: According to the graph, define the input, including units.(b)  According to the graph, define the…

A: A graph of the regression equation is given, we have to find the input and output variables and…

Q: 6. The velocity of a fluid for (x, y, z) is given by v = (ax +by, cx + dy,0) a. Find the conditions…

A: Incompressible vector field: divergence of vector equal to 0 Irrotational vector field: curl of…

Q: Sketch the solid whose volume is given by the iterated integral and rewrite the integral using the…

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Q: all appl Evaluate the upper and lower sums for angles are assumed to have the same width. f(x) = 1 +…

A: We can solve this by using Riemann sum. As given information we are just solving for n = 6