Prove: Let p be a prime number and m EN such that m

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Q: S dx 2 x² + 10x +30

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Q: Consider the following set in a divisibility problem. 1. A {3, 4, 12, 24, 48, 72} a) R = {(a, b) | a…

A: According to our guidelines , we can answer only three subparts and rest can be reposted. I solve…

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Q: 8. Express the given function using unit step functions and compute its Laplace transform y=sint A 1…

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Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim [₁ sin nx dx = 0. n-∞ JA

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Q: Construct the Lagrange interpolating polynomial for the following data set 0.1 0 0.2 0.4 X f(x) 0.74…

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Q: Let A € M₂, (C). Then, for a E o(A), GEO.MUL(A) ≤ ALG.MUL₁(A).

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Q: a. w = √√x² + y² + z² xy b. w = x+y+z c. w = In√√x² + y² + z² 1

A: Use the procedure of partial derivatives to find with respect to x y and z as in next step.

Q: Prove that if v>-1/2 H₂ {xv-1 e-ax; p} = L{xº J₁ (px); a} = 2Upr (v + 1/2) √√ (a² + p²)+1/2

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Q: 2. Let the production function be as follow: q(L,K) = 10.7 K0.3 Also assume w=2 and r=4 a. Find out…

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Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: 03, 2020,

A: a. A sample will be the subset of population and population i the entire set under study.

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A: Introduction: The products of the segments of two chords intersecting inside a circle are equal.…

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A: To check: whether the given function f(t)=0.027t2+0.216t+53.296 represents a good model for the data…

Q: S Given that cos bt}(s) = s²+b²¹ Click here to view the table of properties of Laplace transforms.…

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Q: A tank contains 1, 500 L of water and 20 kg of dissolved salt. Fresh water is entering the tank at…

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Q: 22. Find expressions for f(g(x)) and g(f(x)), and state their domains a) f(x)=√√√x;g(x)=x²-4 f(g(x))…

A: Solution :- The domain of a function is the set of input or argument values for which the function…

Q: the number of combinations of 10 distinct objects taken six at a time = the number of combinations…

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Q: Given dy_y-x, with y = 1 for x = 0; dx y + x VO GRA mately for x = 0.1 by Euler's method (Five…

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Q: Find the explicit solution of the initial value problem, x+y = x² ln(x) y² where y(1) = 2 and x > 0.…

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Q: Find the LU factorization of the following matrices without pivoting 1 2 3 a) A=2 5 4 354 1 -1 1 -1…

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Q: OL XL 2, 4 Utt = Uxx u (o₁ t) = u(2₁ t) = 0 u(x₁0) = I sIMITX COSTTX ut (x,0) = 0 Solve the heat…

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Q: The figure below shows the graph of a quadratic function, f(x), whose limit at an unspecified…

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Q: For the function below, how many regions are at least needed to facilitate the tracing of the curve?…

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Q: Assume that is a continuous real function on (a, b) such that √(x + 1) = 1 / 0 (0) + = 10 (19) Q(x)…

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Q: m=120 income = 2* →> x₁ good I \p₁₂ = 3€ →→x₂ good 2 3/5 U (X₁, X₂) = x, 2/5x₂3 Price P au Sollution…

A: For this we already have equation as : 3p1x1=2p2x2  -----(1)and p1x1+p2x2=m------(2)

Q: Define the linear transformation T: R → RM by T(v) = Av. Find the dimensions of R and Rm. -1 -1 A =…

A: The linear transformation is a map that relates two vector spaces. Every linear transformation has…

Q: L-1 = 10s² (s + 7)

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Q: Question 8 Given f (x, y, z) = zey - x sin-¹(3), what is fzz |ƒ(0,2,1)? 2e² 1 1 √√3 1 √3 none of the…

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Q: Find the total a.f(x, y) = ex² + y²₁ derivative of the function: b. z = x siny - y sinx,

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Q: et F be the collection of

A: To define, T(G)=∫G(z-y)dG(y),G∈F

Q: If A = [0, 2π] and A is measurable, prove that lim cos nx dx = lim sin nx dx = 0. n∞ JA

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Q: Find the equation of the tangent plane to the graph of exy² + zy¹ = 61+1 at the point (0, -2,6).…

A: The gradient of a surface includes the partial derivatives of the function. It is always directed in…

Q: Q1. (a) Is there a real solution to the equation x7-5x¹-8x + 11 = 0 between x = 0 and x=1? Prove…

A: (a) To examine: whether a real solution to the equation x7-5x4-8x+11=0 exist or not. (b) To find:…

Q: To identify the most efficient model for a windmill, Gandalf Engineering Company designs the…

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Q: 29. The parabolic reflector of an automobile headlight is 12 cm. in diameter and 4 cm. in depth.…

A: Given information Diameter =  12 cm depth = 4 cm

Q: Solve the following integral step by step senx -dx ex

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Q: Let X be a Banach space and T = B(X) an operator with ||T|| € (T). Show that || id +T|| = = 1 +…

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Q: show that the function 3x²y-y³ ty is he harmonic and then find it's Harmonic conjugate v (x, y)

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Q: 2 21 Compute the adjoint matrix and inverse matrix of the following matrix: -1 1 2 1 1 If the…

A: Explanation of the answer is as follows

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Q: 8. Express the given function using unit step functions and compute its Laplace transform y=sint A 1…

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Q: Evaluate 1 cos²x 1 cot x -)dx sin x

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