prove, for all integers x, if x mod 3 does not equal 0, then 3 | (x2 +2)

Q: Find the binomial expansion of (1 - x)-¹ up to and including the term in x².

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Q: A formula of order 4 for approximating the first derivative of a function f gives: f(0) 1.0982 for h…

A: Solution:- option (2) is correct

Q: 10. The graph of a function is given below. Determine the intervals on which the function is concave…

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Q: How to find the cofactor of a 4x3 matrix?

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Q: 3. Use Method of Variation of Parameters: [D² - 8D + 16]y = exsec²x

A: First we will find the complementary function of a given differential equation the we will use…

Q: III. In the figure below, locate where dacoboa (P) is. Your illustration should contain the line…

A: From the given data, Assuming the illustration in a 2D space. Let P=α,β Then, O be the origin.

Q: Problem Solve the following PDE problem using Laplace transforms 8²u a²u c² + sin(x) at² əx² where…

A: Taking the Laplace transform and applying the initial condition we obtain…

Q: Q3) Prove or disprove 1. If (G, *) is an abelian group, then the map : G→ G defined by p(x): is a…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: SturmLiouville 10 Consider the differential equation (4x² − 1) y" + 4xy' + λ y = 0 - (a) For what…

A: Kindly note that this is a multiple-question post having two or more unrelated questions. So, as per…

Q: Suppose you place a $35 bet on a horse with a 2:7 odds against winnning. Determine the winning…

A: Solution :-

Q: Q3. (a) Find the binomial expansion of (1-x)-1 up to and including the term in x².

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Q: PROBLEM S Prove that in any bi-right quadrilateral CABDC, LC> ZD if and only if BD > AC. (Assume ZA…

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Q: C find the first order partial derivative of f(x, y, z) = e-32 C²³²² + x³y² 2²³ 3.4.5

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The following data gives an approximation to the integral M= f(x) dx N₁(h) = 1.2341, N₁ ( = 1.0282.…

A: Solution :-

Q: The approximation of I cos (x²+5) dx using simple Simpson's rule is:

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Q: Question 1 Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9) (b) (d) (c)…

A: Inverse Laplace transform: It is the inverse operation of the Laplace transform and it is denoted by…

Q: 10. The graph of a function is given below. Determine the intervals on which the function is concave…

A: Given: A graph of a function, To determine: The intervals in which the function is concave up and…

Q: In a geometrical progression first term and common ratio are both (√3+ i). 1 Then Then the absolute…

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Q: 3. Consider the vector field F(x, y) = (2xy, x² - sin y). Evaluate F.ds π where is the curve c(t) =…

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Q: A jet engine (derived from Moore-Greitzer) can be modelled as the following ODE: (1,0)) (-1,0) -…

A: Solution : The values provided in the question are as follows: Let IVP :    x1(0)x2(0) = 62-1 We…

Q: The degree of precision of a quadrature formula whose error term is 2² f() is: 3 5 2 O This option…

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Q: n [0, 1] Find the area and perimeter of the region bounded by y = sin x and y = cos(x) on

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Q: 7. Determine which of the following functions are differentiable at all the z-plane or some region…

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Q: 3) Evaluate the iterated integral by converting the to polar coordinates -√₂x-x² a) √²ty² dydx…

A: Given that, The integrated integral: (a) ∫02∫02x-x2x2+y2dydx,  such that , the region is…

Q: Let B be the sphere x² + y² + z² = 1. The volume of the portion of B contained in the first octant…

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Q: Simplify A-1 1 (adj A) T JAI 12 + 10j j - 3j-5 2 2j 4j+2 4 -s-j 10-2j

A: Solution

Q: (ii) Consider the following reduced row-echelon form matrix: 1 2 0 4 0 5 001206 00001 7, Assuming…

A: Solution

Q: Show that if v is a harmonic conjugate for u, then -u is a harmonic conjugate for v.

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Q: PROBLEM S Prove that in any bi-right quadrilateral CABDC, ZC> ZD if and only if BD >AC. (Assume ZA…

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Q: 3. y = (1 + tan² (12))'

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Q: Consider the following system, y" = f(x), y(0) + y (0) = 0; y(1) = 0, and a. Find it's Green's…

A: Given :y'' = f(x),y(0)+y'(0) =0,y(1) =0.First we will solve y'' = 0.y(x) = Ax+By(1) = 0 ⇒ A+B = 0…

Q: Define a relation on N by (a,b) ER if and only if E N. Which of the following properties does b…

A: Given, A relation R on N by a,b∈R if and only if ab∈N.

Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: A triangular region is defined by the following system of linear inequalities: y≤ 2x + 5 ys-2x+9 y≥…

A: In this question, the concept of Inequality is applied. Inequality Equations in mathematics aren't…

Q: Use a triple integral to determine the volume V of the region below z = 6 - x, above z = -2√√x² + y²…

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Q: The following data gives an approximation to the integral M= f(x) dx N₁(h) = 2.2341, N₁ = 2.0282.…

A: Solution :-

Q: Question 1 Determine the inverse Laplace transforms of: 2s²-5s-1 (a) (s+3)(s²+9)

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Q: and te are fundamental solutions of the fol- Problem 1. We know that e lowing equation: d²y dy (1)…

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Q: Find the number(s) b such that the average value of f(x) = 6x² on the interval [0, b] is equal to…

A: Given :

Q: 19. f(1) = 2¹ 21. f(t)=4-10 23. f(t)=12+61-3 25. f(t)= (t + 1)³ 27. f(1) = 1 + e 29. f(1) = (1 + ²)2…

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Q: e) Express 120° and -1° in radian.

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Q: A girl is flying a kite on a string. The kite is 120 ft. above the ground and the wind is blowing…

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: 5. f(x) = 1 1- x² 2 7. f(x) = () = 3 ² x x² 2 9. f(x) = x4 + 16

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Q: Let B be the sphere x² + y² + z² = 1. The volume of the portion of B contained in the first octant…

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Q: 31. f(t) = 4²-5 sin 3r

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Q: 3. Find the Taylor series of f(x) at the given value.. X £.(x)... b. f(x) = cox az ..A=... a. C. X…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

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Q: 3. Use Method of Variation of Parameters: [D² - 8D + 16]y = e4x sec²x

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Q: The condition that the roots of the equation x³ - px² +qx-r=0 may be in arithmetical progression is…

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Q: (a) Find the binomial expansion of (1-x)-1 up to and including the term in x².

A: Solution