1. Suppose that r ER and x > 0. Show that if for every & ER with e > 0 we have = 0. xe, then x =

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Q: Using partial fractions where required determine x(t) for the following Laplace functions. s(s+1)…

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Q: 1. Two matrix vectors a and b are given as a = -0--0 and b Find (alb).

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Q: Evaluate the integral .2п 6²³ 0 I = cos(20) 5+4cos(0) - dᎾ

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Q: T([²₂]). T: R² R³ by T = -X1 2x1 + x₂ 3x12x2. e can write T() = A where A =

A: Matrix of the linear map

Q: 3. Draw the Venn Diagrams for each of these combinations of sets A, B and C. a) An B nc b) An (B-C)

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Q: The tota number of hours, measured in units of 100 hours, that a family runs a vacuum cleaner over a…

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Q: Recall the function introduced in class: Use induction to prove that for all positive integers n,…

A: We use a famous result from number theory known as Bertrands postulate

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Q: You decide to begin selling ice cream cones at the local park. Your cost for each ice cream cone is…

A: Given, you decide to begin selling ice cream cones at the local park. Your cost for eachice cream…

Q: The Hilbert matrix Hn is the n X n matrix [hij], where hij = 1/(i + j — 1). Prove that the matrix H,…

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Q: The Maclaurin series expansion for sin x is: sin x = x - x³ x5 x7 x⁹ + 5! 7! 9! 3! Use this…

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Q: The graph below shows the lines determined by the two equations in our system: -10 10 2,0 -10 B 18…

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Q: 4. Let an be recursively defined by ao = 3, an+1 = a - = 3, an+1 = a - an for n ≥ 0. Find lim an.…

A: Let  be recursively defined by ,  for .Find .

Q: Here are the data for the past 21 months for actual sales of a particular product:   LAST YEAR THIS…

A: LAST YEARTHIS…

Q: List five vectors in Span (V₁, V2). Do not make a sketch. 11 9 -5 V₂ 11 -7 3

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Q: Evaluate cosh(1+j)

A: We have to evaluatecosh(1+j)We know that

Q: 2. The graph of y = f(x) - g(x) is shown. Determine the approximate solution to the inequalityf(x) <…

A: The graph of  is shown. Determine the approximate solution to the inequality .

Q: Solve the matrix equation Ax = b, where The solution is: x1 = X2 = 2 A = - [ ²8 22] = [21] and b=…

A: To solve given system of equation, first we form an augmented matrix. Then we apply row operations…

Q: Let T be a one-to-one linear transformation from R" to Rs. ⠀ 1. What can one say about the…

A: Given that  be a one-to-one linear transformation.The objective is to find the relationship between…

Q: f(x) = x² - 4x-15 X₁ = 0 X₁ = 8 TL = 0.01

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Q: Find the velocity (t) and the speed (t) of a particle with position defined for all real numbers t.…

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Q: 2. Consider the Newton polynomial Pn(x) = ao+a1(xr-xo) + a₂(x-xo)(x − x₁) +... +an(x-xo)(x -…

A: Given that   that interpolate then we have Now  ,       putting

Q: It is known that vectors p = (1 2 3), q = (-4 -4 -6), the basis frame is formed by three orthogonal…

A: Given that, Now, find the inner product, cross product and angle between

Q: B C B H A Which of the following subgraphs S, T, U and V are vertex-induced subgraphs of R? Graph R…

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Q: 1 and 2 questions

A: The objective of the question is to determine the stability of the equilibrium points of two given…

Q: Use the revenue function above to answer this question. Find the average rate of change in revenue…

A: The objective of this question is to find the average rate of change in revenue when the production…

Q: Draw the graph represented by the cross- product A x B if A = {x€ Z| x? =x} B = { x€ R] − 2 < x < 3}

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Q: Solve using excel Shelby Shelving is a small company that manufactures two types of shelves for…

A: Profit per ton-Model S-Materail price    =175Stamping         =24(.3*80)Forming…

Q: Find the Laplace transform F(s) = L[f(t)] for each of the following functions. For full credit, show…

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Q: Theorem 12.8 Let A be an n × n matrix. The following statements are equivalent. 1. The columns of…

A: Theorem 12.8 provides a set of equivalent statements about a square matrix A of order n×n. Here are…

Q: Solve the initial value problem y' + 6xy = 0, y(π) = 5

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Q: Let P(x, y) be an abstract predicate. Which of the propositions below are equivalent to the…

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Q: Find the value of the Wronskian to nearest integer when a = 1 for the following basis. {eªx, e-1.5″}

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Q: Let u= -87 --- 201 46 W= -27 For what value of h is w in the plane spanned by u and v

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Q: Question 2. Provide an e-8 proof of the following statement. 1 If f is a function continuous at x…

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Q: The start-up procedure for a batch reactor includes a heating step where the reactor temperature is…

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Q: 5. Find U₁₁ A; and ₁ A; if for every positive integer i, a) A¡ = {i, i + 1, i + 2, . . .}. b) A =…

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Q: Solve and choose the graph that represents the solution. x²y" + xy +9y = 0, y(1) = 1, y' (1) = 2.5

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Q: Without using a calculator, show that 2023 (1+i√3)2 = 2º (1+qi√3). where p and q are integers to be…

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Q: It is known that Prove the following statement Fact. max(f, g) = f+g-|f-gl 2 If f and g are…

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Q: Describe set of points that satisfy inequalities A. X2+Y2+Z2 less than or equal to 1 B. X2+Y2+Z2…

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Q: Challenge 1: Show that the sum of any two consecutive whole numbers is an odd number. Challenge 2:…

A: Definition: Consecutive whole numbers are numbers that follow each other in order without any gaps.…

Q: s) Show that the following initial value problem has a unique solution, y' = ycos (t), 0 ≤t≤ 1, y…

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Q: Problem 6 Using the relationship between Euler and polar notations, find expressions for cos 30 and…

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Q: Initial value problems always begin at zero. True False

A: Definition:  An Ordinary Differential Equation (ODE) is an equation that involves derivatives of one…

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A: Given Diophantine problem is  and Let ,  be the particular solution of above equation .then so we…

Q: Jeff Heun, president of Sheridan Always, agrees to construct a concrete cart path at Dakota Golf…

A: Actual contract amount : $183000Completion on time amount :$38,800every week late the performance…

Q: {(8): a, b, c € Z} and for all such A E L let f, g, h : L→ Z be given by f(A) = a, g(A) = tr(A),…

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Q: Give a direct E-d proof that lim x-2 √x - √√2 x-2 = 1 2√2

A: Answer :