How many positive integers less than or equal to 1,500 are multiples of either 3 or 5? Do not answer this question by listing out all the possibilities. Instead, think carefully and use the principle of inclusion-exclusion. Hint: think about multiples of 15...

Q: Compute the work done by the vector field F(x, y, z) = (1+²) moving a particle: 1+2, 2², 2yz) when…

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Q: Obtain a formula for the polynomial p(x₁) = yi p of least degree that takes these values: p'(x₁) = 0…

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Q: Tove that S L { cosh at} = 35 ₁² s>lal > 5-a² 2

A: In this question, we will find the Laplace transformation.

Q: 3. Use the definition of a convex set to show that if S₁ and S₂ are convex sets in R+", then so is…

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Q: Please write 2(b) again

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Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: The derivative of the function f is defined by f'(x) = x³ +3 cos (x² + 5). Find the x values in the…

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Q: Find Q for the QR factorization of A Q = Ex: 1.23 V1 = J]-[ 1 0 -3 0 2 -30 0 -10 3 -30, V3 = -2]…

A: Given  and the orthogonal vectors are                 ,     ,            Now normalized the above…

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Q: Establish (1 + √2)^²) Convergence and find the limits of:

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Q: The supply and demand equations of two interdependent commodities are Qs, = 4(P₁-1)-5. Qs₂ = P₁ -3.…

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Q: Consider the matrix A given below. . . A = Determine if x = 0 -1 0 1 0 6 2 3 5 10 -10 - -6 is an…

A: Consider the matrix A given below.A = [[0, - 1, 0], [- 6, 1, 0], [6, 2, 3]]Determine if x = [[5],…

Q: Evaluate each of the following contour integrals: (1) fc sin z 22+77² dz; |z - 2i = 2

A: where Note: According to the guidelines we are allowed to solve one question at a time. Please post…

Q: = 1. Compute the normal curvature and the geodesic curvature of the circle a(t) = (cost, sint, 1) on…

A: We have to compute the normal curvature and the geodesic curvature of the circle a(t) = (cost, sint,…

Q: 1. Prove the following polynomial is e(n). Use algebraic manipulations. P(n) = 5n+20 n³ - 10 n² + 10

A: To show that: P(n)=O(n4)We will use the definition of big oh notation to show this, we will find a…

Q: Find a formula for the nth partial sum of the telescoping series below and use it to determine if…

A: We find Nth partial sum of this series

Q: Assuming all members are eligible, but no one can hold more than one office, list and count the…

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Q: 5: Find the Laplace transform of 3 + t5 + sin(πt).

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Q: Let R be a ring and M a module over R. Let S be a non- empty set and let {x; : i E S} be a basis of…

A: Given that R be a ring and M a module over R. Let S be a non-empty set and let {xi : i∈ S } be a…

Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

A: A continuously differentiable function has a derivative at every point, and that derivative is…

Q: Jaylen and Zan are married, filing jointly. Their total adjusted gross income was $87,000 and they…

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Q: Suppose that a fourth order differential equation has a solution y = -8e4x cos(x). (a) Find such a…

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Q: Let the function x(1) be given by the conditions x (0) = 1 and x (1) = 1x(1) + 2[x(1)]² Determine…

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Q: Use  DeMoivre’s theorem  ( Cos(x) + jSin(x))n = Cos(nx) + jSin(nx) to show that Sin3θ=3sinθ- 4…

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Q: Find II IX, and y for the lamina bounded by the graphs of the equations. y = √√x, y=0, x=2, p = kxy…

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Q: Consider the graph below. What is the betweenness centrality of the vertex B? Give your answer…

A: Given Information:A graph is given.To find:The betweenness centrality of the vertex .Concept…

Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: Question 2. Find the limit lim (x,y) (0,0) 2¹+ y² + ys

A: Q2: we have to find out  if exists.we claim that Now using A.MG.M  , so we get  ,but So we get Now…

Q: a. Find f'(-2) and f"(-2) b. At which value(s) of x does f(x) have a relative extremum on [2,6]?…

A: f' (-2) = 1f'' (-2) = -(1/2)

Q: Which of the following would form an equivalent relation? Given the set of people in the world, we…

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 4 - 4…

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Q: A regional municipality is studying a water supply plan for its tri-city and surrounding area to the…

A: Present worth at year 2030Hence, present worth at year 2030 will be $158.147096 million

Q: Mark all true statements (there might be more than one statement that is true). 0 Suppose that f and…

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Q: Determine whether there exists an invertible matrix A if A² = AB + 2A, where B is the following…

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Q: Which of the following is the fully factored form of x3 + 3x² - x - 3? O a) (x+3)(x² - 1) b) x²(x +…

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Q: 1. Write down the geodesic equations in the Schwarzschild geometry in Schwarzschild co- ordinates…

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Q: Determine the value of the parameter t for which the following system has a unique solution and…

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Q: Can a topology on an infinite set not be discrete and indiscrete in which every subset is clopen?

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Q: You wrote that a sequence is contractive if: |Xn+2 - Xn| <= |Xn - Xn-1|........ But I thought it…

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Q: 2. Solve for m, 2 2m² = 3 - 5m

A: (.) Given,

Q: 6. Let f: Q R be defined by f(x) Show that f is continuous. 0, :{ 1, = if x € (-∞, √2) nQ if x €…

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Q: We learned how the diagonal on the unit square lead Pythagoras to discover not all magnitudes are…

A: We first draw the diagram using ruler and label the figure.

Q: Show that if (XN) is bounded sequences, theN (XN) Converges if and only if lim sup (X₁) = lim iNf…

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Q: Which set of values for x should be tested to determine the possible zeros of 2x³ - 3x² + 3x - 10? O…

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Q: dy y(cos 2t)ety — 2(sin2t)ety + 2t + (t(cos2t)ety – 3)- dt = = 0, y(0) = 0

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Q: Prove that (p^(p^q))^(pvq) is equivalent to (p^q) using logical equivalences. You must clearly label…

A: We have to prove  is equivalent to Note: According to the guidelines we are allowed to solve one…

Q: ove the following corollary of the projection theorem: Given a linear variety VC R* associated with…

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Q: Click and drag the given steps to their corresponding step number to prove (A-C) n (C-B) = 0. Step 1…

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Q: 1. Due to the quarantine, the demand for Nine Tendo On/Off console suddenly peaked and is expected…

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Q: The data in the table below, also shown in the figure, is taken from the CDC growth tables for…

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