For any collection C of subsets of a set X there exists a smallest algebra S of sets which contains C (i.e. there exists an algebra $ containing C which is such that if F is any algebra containing C, then F contains $.

Q: H.W: Estimate the root of the equation for the following equation using Secant Method: 1. x3 – 5x =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4. If fige Lim. 1/2 show that fy & LUTY.

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Q: Determine the values of a, if any, for which all solutions of the differential equation y" − (2a −…

A: This is second order differential equation, it has two linearly independent solutions, if both are…

Q: 2. Determine the positive real root of In(x²) = 0.7 (a) graphically, (b) using three iterations of…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: By using fixed point approach solve the Value of A = √² + √2 + √2 === Solve the equation 5x-4 cosx =…

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Q: How do you calculate the volume of a sphere if you know the radius? I need to make accurate to 2…

A: V=(4/3)pi5832 V=4pi1944 V=pi7776 now put pi=22/7 not 3.14 directly othwrise it will create error

Q: = Compute the area of the region bounded by y hyperbolic or inverse hyperbolic functions. 1 √x²+16…

A: We compute the area of the region bounded by y=1/√(x2+16) over the interval [ 0,3 ] hyperbolic or…

Q: If the Neumann problem for a bounded region has a solution, then it is either unique or it differs…

A: see my solution

Q: Hello can you please make me two equations of two lines that can not determine a plane and explain…

A: Explanation of the answer is as follows

Q: 1) (x + ye²) dx - xex dy = 0

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Q: What interest rate was applied if a loan of ₱65,468 will amount to ₱125,000 borrowed for 2.5 years…

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Q: (b) (-a)b = −(ab) = a(−b) for all a,b € R.

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Q: Given the scalar functionf (x, y) = 2xy, calculate the line integral along the ellipse curve ²² +²²=…

A: We have to find the line integral along the given curve.

Q: Using the Euclidian algorithm find the inverse of the following 1) 57 modulo 113 2)13 modulo 20…

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Q: Given the following initial value problem. dy/dt- yt 1.1y where y(0) = 1 The solution at t 0.75; Le…

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Q: Solve the following initial value problem using Laplace transform method: y' +6y=e4t; y (0) = 2.

A: We solve by using Laplace Transform.

Q: 5. Solve the equation y-y'y"=1, given that y=√2 and y'- and y'= when r=0.

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Q: Given the data x₁ i Y₁ 0 0 1 0.5 a. Construct the least squares polynomial of degree 1, and compute…

A: Given the data   xi 0 1 2 3 4 yi 0 0.5 0.4 1 2

Q: a.V odv

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Q: L. Find the coordinates of point P with respect to the coordinate system S, where S = {0, (1/√√2,…

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Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

A: We know that the volume of the solid generated by revolving the region between a curve y=f(x) and a…

Q: 2 y = 0.38 sin x-.49x²

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Q: b) Evaluate the contour integral i ΙΣ where C {z : |z - i| = 3} and oriented counter clock-wise.

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Q: let 2^k+1 be a prime number. prove that then k=0 or k=2^n for some n =0

A: We have given that , 2k+1  be a prime number . We need to prove that , k = 0  or  k = 2n When k = 0…

Q: If ~1,..., η € C, with n > 2, use induction to prove that TU Σ j=1 = n Σ j=1

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Q: 3 16 If 7 is an 7(2)= [ Rational irrational About Then entir what 1

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Q: Let f: R" x R → R define as follows f(x,y) = a, then f is

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Q: For n > 1 we have Σμ(α) d|n = [1] = Τ if n = 1 if n > 1.

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Q: 1. a- Find a result by using variable separation for ý=secy h- xy = x + y

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Q: develop a curriculum for a university for accreditation as an ICT coordinator to offer mathematics.…

A: Need and Significance of the study:- The scenario of the classroom is changing. There is a…

Q: 6) The starting salary for a delivery driver is $35,000 per year with a yearly increase of 3%. Which…

A: Follow the steps/

Q: Determine whether the transformation (a) is one-to-one. T (1)-1 = 1+2 3+2x4+4x5 -2x1 - x₂ + 2x3 -…

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Q: Prove that at a party where there are at least two people, there are two people w know the same…

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Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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Q: (b) Obtain 3 non zero terms of the Maclaurins series for sin²x. Hence, evaluate sin² x 0.5 1.0.5 5…

A: The given problem is to evaluate the given definite integral using Maclaurin series of sin2x upto 3…

Q: A map f:x-y is said to be an open map if for every open set U of X, the set f(u) is open in Y. Show…

A: Given, a map f: X→Y is said to be an open map if for every open set U of X, the set f(U) is open in…

Q: f is represented by the matrix: A = (0 2) (7 8) Show that f is invertible and find the…

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Q: 4. If tige Lim. 1/2 show that fy & L'UM.

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Q: IfS is a semiring, then the following statements hold: 8 () For every (4) of pairwise disjoint…

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Q: Question Graph the following function: Provide your answer below: Drag the movable black point to…

A: To Sketch: The Graph of y=4cotx+π6-3 with explanation.

Q: Determine the convergence of the following sequences. {sech n} a.

A: We have to solve given Questions.

Q: Calculate Find the arc length of r(t) = (t³ + 2,4t³ + 6), 0≤ t ≤1

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Q: 1. 3y(x²-1)dx + (x³ +8y-3x)dy = 0

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Q: define A(x) by A(x) = Σ a(n), n≤x a: Let a(n) be an arithmetical function. We y<n<x where A(x) = 0…

A: As per the question we have to prove the given Abel's Summation Theorem, which is an applied form of…

Q: SHOW that the continuous image Path - connected space is path Connected.

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Q: It is given that 2+i is one of the eigenvalues of the coefficient matrix of the following system of…

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Q: Sketch the graph of the function. (3x + 3, X ≤ -1 k(x) = 3x²-2, -1 1 y

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Q: A 25-year mortgage on a house requires payments of $915.60 at the end of each month. If the interest…

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Q: (3-1/2+1) ⁹

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