Find the center and radius of the sphere: 3x² + 3y² + 3z² -6x - 12y + 18z + 150 O Center (1, 2, -3); Radius = 3 Center (1, 2, -3); Radius = 1 Center (-1, -2, 3); Radius = 1 O Center (-1, -2, 3); Radius = √3 O none of these

Q: Problem 8 5 Let A= 2 Calculate the eigenvalues A₁ and A₂ of A, and the corresponding eigenvectors ₁…

A: Introduction: In linear algebra, eigenvalues are related to eigenvectors. In the analysis of linear…

Q: Characterize the following function in terms of notation. (a) f(n) = (n² + 2)(10n³ +5n-6)n¹, n ≥ 0.…

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Q: oblem 5. Let P, be the vector space of all polynomials of degree 2 or less, and let H be the…

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Q: 3x + 2y = 4 2x − y =-9 x + 3y = 13

A: We have: 3x+2y=42x-y=-9x+3y=13 This can be written as: 322-113xy=4-913 The augmented matrix is…

Q: Q3/Solve the non-homogenous equation a³y Əx³ +1= cos(2x - 1)

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Q: Q3) Consider the initial-value problem dx=y-x,y(0) = 0.5 Use Euler's method with h= 0.1 to obtain an…

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Q: Let T : R² → R² be the linear transformation that first rotates points clockwise through 60° (π/3…

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Q: L-1 { s-1 (s² +9) Find laplace inverse.

A: To Find: Laplace Inverse i.e., ℒ-1s-1s2+9

Q: 6. Given the function ƒ (x) = x² + x − 3, find f (x + 1). 7. h(x) = 2x+ 1, find h(3) 1 8. Given f…

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Q: Prove that for the general equation of degree 2 Ax² + Bxy + Cy² + Dx + Ey+F = 0 that the angle of…

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Q: A = 20 02 0-1 0 -1 2

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Q: 9. Find the numerical Integration of ſo cos(x) + sin (x) where n = 4 using trapezoidal rule.

A: Trapezoidal rule: ∫abydx=h2(y0+2(y1+y2+y3+...+yn-1)+yn) Here, h=b-aN and N is the number of…

Q: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

A: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

Q: At Fanshawe, students spend an average of 12.47 minutes per class texting. Suppose the minutes spent…

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Q: Partial Derivative: Determine all the partial derivatives of the following unless otherwise…

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Q: The average number of classic comic books sold per week at your store is 28. What is the probability…

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Q: solve 2 (pedoe tydy +2d₂) ² 2 = {(2²-x²=y²2) (seds tydy + z dz/d2} z

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Q: Prove that A(n) log(p), if n = pk, where p is a prime, and k ≥ 1; = otherwise. 1(n) = Σμ(n/d)log(d)…

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Q: 5. Solve the system of linear equation: * x1 + x₂ x2 = 2 x1 - x2 = 2i

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Q: Let f be a mapping from [1,+∞[ to [1,+∞[, defined by f(x)=x+1/x. Then f is continuous but it is not…

A: A function is homeomorphic when it follows the bijection. The bijective property is one of the…

Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

A: Introduction: In mathematics, differentiation is the process of determining the derivative, or rate…

Q: 3 co ós co -6 -3 144 -4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4…

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Q: 6. Evaluate the inverse z-transform of x(z)= 2z-1 (1-2z-1)2

A: Given: xz=2z-11-2z-12 To find: Inverse z-transform of given function.

Q: taxi has 2 passengers when it starts at A. It must drop off one person at B and the third at C. The…

A: GIVEN THAT A taxi has 2 passengers when it starts at A. It must drop off one person at B and the…

Q: For which real r> 0 does the series n=1 converge, and for which real r> 0 does the series diverge?…

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Q: 3. Show that if n = 3 mod 4, then n cannot be the sum of squares of two integers.(i.e there are no…

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Q: Determine the following estimate without using a calculator. Then use a calculator to perform the…

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Q: 2.3: Determine the spectra of the signals: (a) x(n) = cos/₂ (b) x(n) = Cos kn/3 (C) x(n) has period…

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Q: Q1: Determine whether f(x)= [0,1]. √xsin().if x=0 0.if x=0 is of bounded variation on

A: Given :   f(x) = xsin1x,if x≠00if x=0 To find : Whether f(x) is of bounded variation on [0, 1].

Q: 3 Do not use a calculator in this question. The polynomial p(x) is ax³-4x²+bx+18. It is given that…

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Q: Timothy wants to estimate the percentage of homeowners that own at least one dog. He surveys 100…

A: To find out which of the given is a parameter :- A parameter is a numerical value that states…

Q: 4. Find the derivative of f(x) - 7. A. 7 B. 0 5. What is the derivative of In(x)? A. xln(x) B. 1/x…

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Q: Using 2014 as the base period, compute a simple price index for each of the following commodities.…

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Q: Q₁: Which of the following are always true, and which one are not (for five only)? Give reason(s)…

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Q: 29. 29. Find inverse Laplace transform of 1 (a) g2 — 38 + 2 )b( - 1 s3(s+1)

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Q: A waiting-line system that meets the assumptions of M/M/1 has A-1,-4. For this system, what is the…

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Q: 1 (i) Show that 2x-1 is a factor of 2x³-5x2 + 10x -4.

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Q: /Solve the non-homogenous equation+1 = cos(2x - 1)

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Q: 03 // A)) Find the volume of solid below? =Y+X x² + 3² AC D4

A: Given solid is

Q: -1 3 -6 -4 -3 4 Let y = V1 = | 5 -1 Compute the distance d from y to the subspace of R4 spanned by…

A: We have v1=-1-44-1   , v2=0220 Now,  v1· v2=-1-44-1·0220=-1×0+-42+42-10=0 So, we see that v1· v2=0…

Q: Write the equation of the trigonometric graph.

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Q: the following quation sutisfied Cauchy - Rieman. equation es 4 * = Z² سلام

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Q: Sketch and shade the region bounded by the curves y=√x and y=x³,then determine the volume of the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 2. Using the Fundamental Theorem of Arithmetic, prove that for all a, b, c E Z, if alc, blc and (a,…

A: Every integer can be factored uniquely into primes upto order of arrangement. (a,b)=1. Then there…

Q: Q/ if f contineous map Prove that f(B) ≤ f(B), VBsy

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Q: Suppose Jane borrows $2000 at an interest rate of 16% compounded each year. Assume that no payments…

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Q: 2(b) Th picopert matrix not to Prove matria does r

A: A matrix is defined as a rectangular array of numbers or objects. The arrangement takes place into a…

Q: USINg Laplace's transform, solve: +∞ Cos (7x) dx X²+25

A: Laplace transformation has wide range of application sin different fields of mathematics. In…

Q: Suppose T : Rn → Rn is a linear transformation. Prove that T is an isometry if and only if T(v) ·…

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Q: 1(x) = 1 (x)= 0, −1 < x < 0 -1 1, 0<x<3 0, 0,5 < x < 0 x, 0<x<0,5

A: The given function functions are        (i) fx=0,   -1&lt;x&lt;01,       0&lt;x&lt;3 and      (ii)…