1. d²y(t) dt² + 8 dy(t) dt + 25y(t) = 10u(t)

Q: Let f be a positive, continuous, and decreasing function for x ≥ 1, such that a = f(n). If the…

A: Given Data: Let us consider the given data, ∑n=1∞1n2+1, twelve terms.

Q: Shapley value of each senior = (31 + 3(1/2 + 1/2 + 1))/5040 = 37/840 Shapley value of each junior =…

A: Sure, I can explain where the numbers 31 and 30 come from in the calculation of the Shapley values

Q: Consider the series. 00 Σxin n n = 2 (a) Determine the convergence or divergence of the series for x…

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Q: A fluid has density 600 kg/m³ and flows with velocity xi+yj + zk, where x, y, and z are measured in…

A: From the given information we get:

Q: 1. COMPUTE USING FLOATING POINT MATH поїхаж Х 23 AND 1.1x23 - liolxay www

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Q: Use the Laplace transform to solve the given system of differential equations. dx dt dy dt x(0) = 0,…

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

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Q: (2) Let R = Z[√5] and R* = R−0. Consider the nomm map N : R* → Z*. If a, b = Z, we set N(a+b√-5) =…

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Q: A colony of bacteria is increasing at the rate of 15% each hour. There are 2,500 bacteria in the…

A: Given that, the initial amount of bacteria in the colony = 2500 rate of growth = 15% per hour We…

Q: Diagonalize the following matrix. One eigenvalue is λ = 5 and one eigenvector is (-2,1,3). -1-12 6 3…

A: Given that, diagonalize the following matrix.

Q: 3.8 Prove the following [see Exercise 7.5]: (a) lim[√n² +1 − n] = 0 (c) lim[√4n² + n − 2n] = 1/ (b)…

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Q: A cable television company has 8500 subscribers in a suburban community. The company offers two…

A: Given, A cable company has 8500 subscribers n(A) = 2350 n(B) = 1980 5220 : do not recieve any…

Q: 6.2.1.b Find the cluster points of (see _picture). For each cluster point, find a subsequence…

A: Given the sequence :  {sin(n+1/n)π/2} We have to find all the cluster points of this sequence. Also…

Q: dx Use residues to derive the integration of ²1 0

A: 1. Residue at a pole z=a of order 1:limz→a(z-a)f(z)2.Residue Theorem: ∫cf(z)dz=2πi[Sum of Residues…

Q: Determine which graph applies to the function f(t) = e-fu(t − 1) — u(t − 2)} a. f(t) 0 1 f(t) 0 b.…

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Q: Consider the function ƒ : R → R defined by 2x + 5, ax² + x, Show that there is a value of a for…

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Q: Calculate the following intergal (cos(x) (√(1-x²)))"¹ 2 11+ sin(2x√(1-x²)) π log dx

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Q: (4x² - y²) dx = xydy

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Q: 4. Two surfaces: 4x² + y² = 4 and z = √3x intersect over a curve. Find the length of this curve (you…

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Q: Wie the ouatratic formula to sol -2y=3y^(2)-1

A: Given, Quadratic equation is  -2y = 3y2 - 1

Q: Solve the differential equation below using series methods. y"+5xy-3y = 0, y(0) = 2, y'(0) = 4 The…

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Q: We defined: = f(x) dx = x (x) dx + f(x) dx How can I show by example that the above is not: lim,…

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Q: Evaluate. Round your answer to the nearest thousandth. log_(4)41

A: Given that the logarithm log441

Q: Next ques Solve the equation log_(5)(x+3)+log_(5)(x-1)=1

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Q: Let f be in R[a, b]. Prove that -f is in R[a, b] and -f(x -f(x) dx f(x) dx -

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Q: The tangent plane at a point Po (f(uo.Vo) 9 (uo.vo),h(uo.vo)) on a parametrized surface r(u,v) =…

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Q: A student is taking an exam consisting of essay questions and short-answer questions. Let x be the…

A: Consider the objective function 20x+6y. Using the given feasible region to maximize the objective…

Q: 38. T is the reflection through the yz-coordinate plane: T(x, y, z)=(x, y, z)

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Q: Find a geometric power series for the function, centered at 0, by the following methods. 1 f(x) = 7…

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Q: Let's now consider W, the subspace of R5 having basis 14 V1 = 1 -6 8 2 Evaluate (Sage) " V2 = 10 -3…

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Q: Find the equation in standard form of the parabola with focus (2, -3) and directrix x = 5.

A: The parabola with focus 2, -3 and directrix x=5. To find the equation of the parabola.

Q: A population of beetles with four age groups is described by the matrix 4 3 27 0 0 0 0.4 0 0 0 0.1 0…

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Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

A: (.)  Given system is ,                 x' =  13-428-10x and   x1=4e6t7e6t  ,   x2=e-3t4e-3t The…

Q: 9.39. Let K/F be a Galois extension of fields. For subgroups H₁, H₂ C G(K/F), we define H₁ H₂ H =…

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Q: Q2) Solve the following PDE using the Laplace transformation: ди ди + 0, x>0, t> 0, and u(x,0) = 0,…

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Q: Determine {f}, where the periodic function is described by its graphs. Half-rectified sine wave…

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Q: Rewrite the expression as a sum or difference of multiples of logarithms. log_(7)(19w)

A: Given that, rewrite the given expression as a sum or difference of multipls of logarithms.

Q: y' - 2 y/(x + 1) = (x + 1)³, y(0)=1/2

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Q: (a) (i) (ii) Find the value of the function: f(x, y, z)= ysin(xz) + exp(xyz) at the point (1, 1, 0).…

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Q: 8.7 Show the following sequences do not converge. (a) cos(T) 3 (c) sin() (b) Sn = (-1)" n -

A: A series is said to be convergent if it exist at limit infinity.

Q: An ornithologist is studying a population of female starlings as it changes each year. They are…

A: Leslie matrix is a square matrix referred as a population projection matrix. This is of the form…

Q: Set Problem is in NP.

A: (a).According to the question,  To prove that the Exactly Half Independent Set Problem is in NP, we…

Q: V3 V2 XK V11 V10 05 Figure 1: Graph G. V12 1. (a) Give a vertex cover of size 5 in the graph G in…

A: Vertex cover: In graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices…

Q: Prove that each component of X is open. 14. Let X be the set of reals with the usual topology, and…

A: First, let's identify the components of S.

Q: Let R be acommutative ring and A be a nonempty set in R. Consider the annihiltor of A, which is…

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Q: Use Euler's method with step size 0.25 to compute the approximate y-values y1, Y2, y3, and y4 of the…

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Q: 4. T(V₁, V2, V3) = (v₂ − V₁, V₁ + V₂, 2v₁), v = (2, 3, 0), w = (-11, -1, 10)

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Q: I. Find dy/dx. II. Find the points on the curve where the tangent is horizontal. III. Find the…

A: x=t3-3ty=t3-3t2

Q: Determine whether the series is convergent or divergent. n=1 10-42-2 (-4)3n+1 The series ?…

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Q: *2.2.18 Find the present value at time 0 of an n-year continuous annuity based on force of interest…

A: We have find the present value at time 0 and n year continuosly