Topology Proof: Please write out nicely Consider the number line R with the topology τ = {∅, R,(−∞, a); a ∈ R}. Is the set A = (−3, 0] compact? Prove your answer!

Q: Using the big M method to find the maximum value. Maximize P=8x₁ +5x₂+6×3 subject to 2x₁ + x2 + 2x3…

A: Introducing slack variable S and artificial variable A  . Maximize P=8x1+5x2+6x3 +0S-MA Sub. To…

Q: 1. Suppose that An is an eigenvalue with eigenfunction yn of y"+y=0, 0<x<L, y(0) = 0, y(L) = 0.…

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Q: Show that {1, cos(kx) | k ¤ N} is an orthogonal family on [0, π] with inner product (f,g) = f* f(x)…

A: Since first and second subparts are not interlinked so as per our guideline, we are supposed to…

Q: - State the coordinates of the 3 elbow points of ƒ (x) = bª . State the equation of the asymptote…

A: If the value of the independent variable gets closer to infinity or the opposite of infinity, a…

Q: Evaluate the surface integral. x²yz ds, S is the part of the plane z = 1+ 2x + 3y that lies above…

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Q: Consider the following curve. x = sin(6t), y = -cos(6t), z = 24t Using the given parametric…

A: Consider the following curve. x=sin(6t), y=-cos(6t), z=24t We have to find r'(t) and Ir'(t)|. We…

Q: Let A be a 3 x 3 diagonalizable matrix whose eigenvalues are X₁ = 3, A₂ = −2, and A3 = -1 with…

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Q: 1. y" + 5y' +6y= 2e-t, y(0) = -1, y'(0) = 1

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: solve the following DE X^4 y' + 66x^3 y = x ^-2 cosx

A: The given differential equation is  x4y'+66x3y=x-2cosx.   The by parts formula of integration is…

Q: b) 3. In Exercises a and b, find an LU-decomposition of the coefficient matrix, and then use the…

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Q: An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 9% and the mutual fund…

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Q: A group of investors decide to invest $500,000 in the stocks of three companies. Company D sells for…

A: Given x represent company D shares, y represent company E shares and z represent company F shares.…

Q: (a) Let λ be an eigenvalue of A. Explain why a set of basic X-eigenvectors is linearly independent.…

A: (a) Recall that a set of vectors {v1, v2, ..., vk} is linearly independent if the only solution to…

Q: Do the following integrals. You can (but don't have to) look up integrals online (e.g. on the…

A: a)∫0xax-b3dx b) ∫titftt2+adt c) ∫1πlny2+ady To Find: Integal value using the online calculator and…

Q: Verify the maximum principle and the mean-value property by analyzing the solution.

A: To solve the Laplace equation in the disk of radius a, we assume that the solution can be written in…

Q: 2. For each of the following questions, justify your answer using complementary slack- ness and if…

A: If x* and y* be feasible solution to the primal and the dual LPP respectively then a necessary and…

Q: Use a left sum and a right sum with rectangles of equal width for the given value of n to…

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Q: 143. Find a quadratic polynomial f(1) = 5, ƒ' (1) = 3 and ƒ˜(1) = −6. such that

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: 4 $ 9.5 9 8.5 8 7.5 7 6.5 Find the surface area of the portion of the semi cone z = √² + y² that…

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Q: Now you'll evaluate the integral In this integral, f(x,y) = Setting up the double integral over the…

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Q: Given: (x is number of items) Demand function: d(x) = 864.9 -0.6x² Supply function: s(x) = 0.3x²…

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Q: 2. The graph represents the reciprocal function of fix). What is the equation of fix)? b. f(x)=2x²-1…

A: This graph represents the reciprocal function of f(x) =  -2x2 + 1. Therefore the equation of f(x) =…

Q: 3. Find the Taylor polynomials p3 and p4 centered at x = 0. 4. Use p4(x) to approximate to 3 decimal…

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Q: Find the area of the half ellipse x² 4 and the y-coordinate of its center Use x = E = {(x, y) | y =…

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Q: The value of fæe da where b = 5.6, by using the two-point Gauss quadrature method of integration is

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Q: Find an LU factorization of the matrix A (with L unit lower triangular). A = 4 -8 6 - 16 12 -4 2 1-2…

A: Introduction: For any matrix its LU decomposition is contained the lower triangular matrix L and the…

Q: 60 cm in diameter and 5 cm deep, find the focus

A: diameter of parabolic reflector = 60cm &amp; 5 cm

Q: (d) Plot the aggregated annual series and produce a boxplot that summarises the observed values for…

A: We are to consider the time series data mdeaths available in R. (d) Plot the aggregated annual…

Q: 3 (4)

A: We have to calculate 1131211-1=?   Matrix multiplication defined as:…

Q: 10. (a) Find the Fourier Series S(x) of f(x) = cos(x/2), -<x<T. (b) Graph S(r) for −3″ < x < 3. Does…

A: Given function is not defined at x=π and x=-π.  We can it extended to define a value at those…

Q: y" + 4y' + 5y = e-t (cost + 3 sin t), y(0) = 0, y' (0) = 4

A: The given problem is to find the solution for the given initial value problem with given initial…

Q: Problem 8. For f and g as in the previous two with the respect to the standard ba g as a matrix

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Q: Solve the given differential equation by separation of variables. dp dt P-p²

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Q: The population of a country was 5.372 million in 1990. The approximate growth rate of the country's…

A: Here, ft=0.09486952e0.01766t and F0=5.372 million. To Find: (a) Function of Ft. (b) To estimate the…

Q: The objective function for the following minimization problem is P = Y + 2X. (0,9) Cost -Y +2X X =…

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Q: Question 9 The solution of the following recurrence relation with the given initial condition is: a…

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Q: CODE NOT WOKRING !can you insert equations and number and variables in the code so i can insert my…

A: As per the question we have to create a genetic algorithm code in MATLAB that maximizes 4 different…

Q: An object is dropped straight down from a helicopter. The object falls faster and faster out its…

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Q: For the Beverton-Holt model given by the DDS P If P₁ = 1200, find P₁, P₂, and P3. Round your answers…

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Q: Given: (x is number of items) Demand function: d(x) = 548.8 -0.3x² Supply function: s(x) = 0.4x²…

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Q: 2. (a) (b) (c) For the DE (x-4) y² +3(x-2)y'+ 5y = 0 Find all singular points. Show your work! Find…

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Q: Exercise (4) ² = 1: Show that the cycloid C defined via C(x, y) = -2r-y y [x(0)=r(0-sin(0))] v(0) =…

A: The cycloid is defined via C(x,y)=x(θ)=r(θ-sinθ)y(θ)=r(1-cosθ),  where  θ  is a parameter. Now we…

Q: Write a derivative formula for the function. f'(x) = f(x) = 7(6x) VX

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Q: If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus

A: We have to find the focus of the given parabola.

Q: Write the system of equations as an augmented matrix. 5r+ 3c = -1 4c = 6 -2y y -7y +4r +3c 14

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Q: Let A = 1 -2 -1 -5 -2 5 -2 -2 2 a) Is matrix A diagonalizable? P b) If A is diagonalizable, find an…

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Q: Give an exact expression for y as a function of z, angle B and angle Cif A = 45° and D = 60°.…

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Q: (8x) 1. Expand the following expression: z = ln 2. Expand the following expression: z = In(e-5y²) 3.…

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Q: Find the surface area of the portion of the bowl z=8-2²-² that lies above the plane z = 4. When…

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Q: (d) Now invent another vector field F and repeat steps (a) and (b). (a) W/L

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