(1 Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by the quations For this system, the smaller eigenvalue is dx dt dy dt = 0.8x + 2y, = 3x + 2.22044604925031e - 16y. and the larger eigenvalue is

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A: Let the function f(x) be defined in [−π , π] then the Fourier series of f(x) is of the…

Q: Show that the roots of the following polynomials are ill conditioned. (a) x³ − 3x² + 3x – 1 (b) (x −…

A: Given:The polynomials are:(i) (ii) (iii) Aim:To show that the polynomial is ill-conditioned.Concept…

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Q: Let A = {x N: 4 < x≤ 11} and B = {x € N : x is even} a. Find An B. b. Find A \ B.

A: The given sets  and .The aim is to find the sets  and .

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Q: Find E₁ = Consider the following Gauss-Jordan reduction: 1 0 0 0 3 0 1 18 -9 0 1 0 0 1 0 1/ 2/ E₂ =…

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Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

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Q: Compute the curl of each of the following vectors: V = (yz, xz, xy) F = (x, y, z) 5-(2²+²+2 = Note:…

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Q: Problem Consider the vector a shown below and the two reference frames A = = {A, â1, â2, â3} and B…

A: Given:The vector  is shown and two references frames  and . and are two positive numbers.To Find:(a)…

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Q: Find side b of the oblique triangle given that B = 11 and side a = 312 and side c = 251. Round your…

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Q: Question 2 (a) Given matrix A: (i) (ii) (iii) ГО A = 1 0 -37 1 1 L2 0 5 Show with working that the…

A: Our objective is given below:

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A: We have to find the domain and range of the graph.In pair of (x,y) x is domain and y is range.

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Q: Question 1. A group G is called divisible if it satisfies the following two properties: (1) G is an…

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Q: Question 7. Let g(X) = X¹ + X³ + X² + 1 € F₂[X]. We consider a [7, 3]- cyclic code C of generator…

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Q: Section 1.3 Classification of Differential Equations: Problem 5 Which of the following functions are…

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Q: suppose you have $100,000 to invest in stocks. if you invest $1000 in any particular stock your…

A: Let X be a $1000 investment. Then the expected profit of X isE(X) = 200(0.25) + 100(0.25) + 0(0.25)…

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Q: (a) Estimate the values of f(-15, 30) and f(-15, 30). (Round your answers to two decimal place f-15,…

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Q: Review the table with fees for Bank A and Federal Credit Union (FCU) B. Monthly Fee Minimum Balance…

A: A.   False    B. True   C.False D.TRUE

Q: Find the following cardinalities: a. A = {5, 10, 15, ..., 75} |A| = b. A = {x € Z: - 100 ≤ x ≤ - 17}…

A: We have to find the cardinality of the following setsWe know thatThe cardinality of the set is the…

Q: 2. Find the slope of the tangent line to the parametric curve x=4/t, y = 2t³ - t +1 at t=2

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Q: Q1: Check whether (K,*) forms a group, where "*" refers to the matrix multiplication and K = {h₁,…

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Q: Rewrite the integral: (x-3y)dA where R is the triangular region with vertices (0,0), (2, 1), (1, 2)…

A: Equation of the side S1: y=12xEquation of the side S2: y=2xEquation of the side S3: y=3−xFrom the…

Q: (The function f(x) is shown in blue, and g(x) in black; click on the graph to get a larger version.

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Q: In each of the following, sketch a single spinner with the following characteristics: The outcomes…

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Q: 7 a = 2 b= 2.6 2 XC= 3.4 3.2 3 28 For the above plot of the positive z half of a hyperboloid of two…

A: Given:A plot is given for the positive  half of a hyperboloid of two sheets .To Find:The parameters…

Q: y = x-9 +10 3(x-9) determine instantaneous rate of at x = A choose an A value in the domain change

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Q: 4. Let A be an n x n matrix. Run Picard iterations for the problem Jx' = Ax x(0) = U xER" and…

A: Let   be an   matrix.Consider  the system  : ,Assume  that Moreover,Thus,   satisfies  the given…

Q: B: Solve the following equation by Finite Differences Method, choose h = 0.25 d²y dx² - y=x+y y(0) =…

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Q: 1. Calculate the solution of the differential equation y²dy − x²(1 + y³) = 0, dx satisfying the…

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Q: Compute the determinant of matrix H and discuss the implication for model rationality:

A: Given:The matrix is .To Find:The determinant of the matrix.Concept Used:The determinant of the…

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A: Given that S is the portion of the  plane that lies inside the box defined by the .

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A: Given information:Water runs into vase of height 35 centimetres at a constant rate.The vase is full…

Q: 4. Consider the sequence of functions {x(t)}% defined by xo(t) 2k+1(t) = 2 = ot So cos²(7)xk(t)dt, k…

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Q: 2.52. Let G be a group and Z the center of G. If T is any auto- morphism of G, prove that T(Z) CZ.

A: Group: A group is a set G together with a binary operation (often denoted by multiplication or…

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A: We have to prove that 5 root 6 is not rational.That is we have to prove that  is irrational.We know…

Q: All vectors and subspaces are in R". Check the true statements below: A. If W is a subspace of R"…

A: Some statements are given.Check whether it is True or False.