Theorem: If r is a real number and r^2 = 3 then r is irrational number.   Use the theorem that if 3|a^2 then 3|a to write a well constructed proof by mimicking the proof that the sqrt(2) is irrational.

Q: Question 6. Prove by using elementary argument that any polynomial with real coefficients of degree…

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Q: Brad decides to purchase a $325,000 house. He wants to finance the entire balance. He has received…

A: Given thatBrad decides to purchase a $325,000 house. He wants to finance the entire balance. He has…

Q: (a) Prove that m³ + 2n² = 36 has no solution in positive integers. (b) Prove that for every n € Z,…

A: Since  and  are positive integers, . Case 1:     Since , it has no solution when Case 2:       is an…

Q: If f(1) = -5.4, f'(x) is continuous, and f'(x)dx = 20, what is the value of f(4)?

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Q: 20. The lim √x² −4= X→-2+ a) √8 b) -4 c) 0 d) does not exist

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A: Given that a sheet of cardboard 14 in. by 9 in. by cutting congruent squares from the corners and…

Q: What is the size of the resulting product matrix AB if A € M9x5 and B € M5x14 ? AB has rows and…

A: We have to find the size of the matrix AB where size of A and B is given.

Q: A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero…

A: Let x be the ounces of fruit and y be the ounces of nuts. objective function:Min. Subject to the…

Q: 3. Let T: R² R² be the linear transformation which first reflects points through the line X₁ = X₂…

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Q: The following problem refers to the stock table for ABC Inc. (a tire company) given below. Use the…

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Q: The website for the nonprofit organization Charity: Water¹ discusses the need for clean water around…

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Q: Consider the initial value problem a. Form the complementary solution to the homogeneous equation.…

A: (.)  Given,     (.) Complementary solution of the system  where  is a  matrix is given by,…

Q: Find the following for a $200,000 fixed-rate mortgage and the given informati a) Monthly mortgage…

A: Given that, the fixed rate mortgage cost is .From the given information, it is observed that ,  and…

Q: Question 1 An object is pulled along the ground by exerting a force of 25 pounds a rope that makes a…

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Q: make a regression analysis about any healthcare issue

A: Let's perform a simple regression analysis on a healthcare issue. We'll analyze the relationship…

Q: Consider the differential equation y' = 1 – y.

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Q: 2. The function f is twice differentiable for x > 0 with f(1) = 16 and f"(1) = 24. Values of f', the…

A: The given data is

Q: I must get from A to B across a rectangular manmade pond. The pond is 4 km in width, and 12 km long.…

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Q: Find all the cosets of the subgroup in Z18

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Q: A singular value decomposition -0.5 0.5 A=UEVT 0.5 0.5 0.5 0 5 0.5 0.5 -0.5 0 0 -0.5 0.5 0.5 0.5 0…

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Q: LO 5 Analyze the graph below. Which of the following is/are true? -10 as x→ 3, f (x) →→∞ as x→ 3¹, f…

A: By using given graph we check which of the following given limits are true.

Q: Without actually solving the given differential equation, find the minimum radius of convergence R…

A: The differential equation isThe singular points arethe minimum radius of convergence for…

Q: Give a counterexample to each of the following claims. Describe in a sentence or two why your…

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

Q: Hello there! Can you help me solve a problem? Th

A: Given matrix is,

Q: Q10): Let A 14 A 1 5 0 03 3 (a) Is 2 in the span of the columns of A? What about 2? -1 1₁ 3

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Q: Use Cramer's rule to compute the solution of the system. 5x₁ + 2x₂ = 19 4x₁ + 6x₂ = 24 What is the…

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Q: Consider the Initial Value Problem: x₁ = x2 X₁ = v1 = x2 = 2x1 + 2x2 - 4x1 - 2x₂¹ (a) Find the…

A: (a)

Q: B5. If f(x, y) = xy² + x³y and y² = x³ + y³, find expressions for the partial derivatives af df df…

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Q: Solve the system dx dt x(0) = = -22 18 with the initial value 1 x(t) = -27 23 2 8

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Q: Is T ={∅, X, {1, a}, {1, b}, {2, c}, {1, a, b}, {1}} a topology on X = {1, 2, a, b, c}? Why?

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Q: Using Newtons method, find the root of the function in the interval correct within 4 decimal places.…

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Q: 5. Find the adjoint of the matrix 2 A-(-¹13) = using the Euclidean dot product on R2 for the inner…

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Q: Use Laplace transforms to solve the following initial value problem. x'' + 4x' + 13x = te¯¹; x(0) =…

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Q: nd the least square regression line for set of points {(1,3), (2,4), (3,4), (4,6)}

A: The given set of points .The aim is to find the equation of the regression line for this data.

Q: Explain the difference between a periodic function and a sinusoidal function. Include an image or…

A: The difference between a periodic and sinusoidal function is shown below in tabular form:

Q: 8. xy" - xy + y = 0 y₁(x) = x

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Q: For each of the following functions determine whether it is convex, concave, quasiconvex, or…

A: Q(d) asked and answered.

Q: Use interval notation to report domain, range, increasing, decreasing, constant. x=5 I F (1,3) (1,0)…

A: The graph of the functions are given.The aim is to find the domain, range, increasing, decreasing,…

Q: For the input/output table, give a Boolean expression that is a sum of minterms and is equivalent to…

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Q: An obligation can be settled by making a payment of $12,000 now and a final payment of $32,000 in 4…

A: Advance maths

Q: [12 Let M Find formulas for the entries of M", where n is a positive integer. 88 MT

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Q: Using the limit definition of derivitive, find the derivitive of the following: a) f(x)=2 b)…

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Q: Find the vector equation that represents the curve of intersection of the cylinder x² + y² = 9 and…

A: Given:Cylinder: Surface: We have to find the vector equation that represents the curve of…

Q: Question 9. Expand each of the following functions in a Taylor series about the indicated point and…

A: Let us find the Taylor series expansion and the radius of convergence of the series expansions.

Q: Note that: arctan (1) = π/4. 1. Find and plot all the roots in the complex plane of -1-j

A: De-Moiverse theorem(cos⁡(x)+isin⁡(x))n=(cos⁡(nx)+isin⁡(nx)).the polar form :…

Q: 4. Find upper and lower bounds for the sequence 3n+7 n n=1

A: To find the upper and lower bounds for the sequence .Concepts used:Let  be a sequence. Then a number…

Q: PROBLEMS: Section 3.3 For Problems 1-10, a differential equation and one solution are given. Use…

A: We solve the given differential equation by method of reduction of order.

Q: Let A and B be A = 0 2-3 -13-468 0 2 B = E = || 0-2 0 -2 -1 Find an elementary matrix E such that EA…

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Q: rivative of a Quadratic Function g(x)=-2x² +5x-1 g'(x)=-4x+5 h(x)=1.5x? _7 h'(x)=3x j'(x)=-10x+2.5…

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Q: Prove that the sum of two rational numbers is rational

A: A rational number is a type of real number that can be expressed as the quotient or fraction of two…