Which of the following third degree interpolation polynomials can be developed from the given data set below. X 0 2 4 6 y 2 4 40 14

Q: 33. Find the sum of the following arithmetic series. Σ(8i +3) i=1 A. 726 B. 4,587 C. 561 D. 2,538

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Q: II. Find the inverse of each matrix. -9 6 2. 4 -8

A: Let us consider a 2x2 matrix A=abcd The inverse of the matrix exists if the determinant of the…

Q: sin(2x³) x² 11. Approximate justify your result. within 0.0001 if x = 1/3 using its Mac expansion…

A: Solution: Given function is, f(x)=sin2x3x2 sin(x)=∑n=0∞-1nx2n+12n+1! f(x)=∑n=0∞-1n2x32n+12n+1! x2…

Q: Verify that y = ODE y" + 3y' + 2y = 4x². -4e-x-2e-2x + 2x² - 6x +7 is a solution of the SHOW ALL…

A: We have to verify that y=-4e-x-2e-2x+2x2-6x+7 is a solution of the ordinary differential equation…

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A: Given that an altitude is drawn from the vertex of an isosceles triangle, forming a right angle and…

Q: Find the inverse of the congruence 6x = 1 (mod 29) using Euclidean algorithm. (Show your work)

A: The given problem is to solve the given modular equation by find the inverse of congruence using the…

Q: Use a linear approximation to estimate the following quantity. Choose a value of a to produce a…

A: We need to find ln0.93 Now, the formula for linear approximation is: Lx=fa+f'ax-a Let us assume that…

Q: 1. Let V be the set of all 2 x 2 matrices 4-[*]s a. Is V close under addition? Show your proof. b.…

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Q: Let us solve the following equation via separation of variables 8²u(x, t) Ət² 8²u(x, t) dx² a) After…

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Q: Q1:- (A) Discuss the convergence of the given sequence : a(n) = cosh ln(n) (B) Evaluate: f dxdy…

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Q: We will define a checkerboard matrix to be a square matrix A = (aij), where 1 if i + j is even = Aij…

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Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2) s²-4 2

A: L{cosat}=s/(s^2+a^2) L{coshat}=s/(s^2-a^2)

Q: 12. Z z²+1

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Q: Determine whether W = {(a,2,b)la, b ER} is a subspace of R³.

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Q: 9.4 Find a matrix P and a diagonal matrix D such that P-¹AP = D. 9.5 Find A23. (You may write 223,…

A: This is a problem of Vector Space.

Q: Find a differential equation that corresponds to the given direction field. Consider differential…

A: To find the differential equation that correspond to the given direction field :-

Q: Exercise 25.7.1. Give the Taylor series of the function 1 f(x):= 3x² around the point c = 1 and give…

A: Taylor Series :- Let f(x) be a real function then Taylor Series about a function x = a is fx ≈ f'(a)…

Q: Janie's generous Grandma Mae put $400 in a college fund for her 1st birthday, $500 for her 2nd…

A: Introduction: A function is an expression, rule, or law in mathematics that defines a relationship…

Q: Find the area of the region that lies inside r = 2 + cos 2θ but outside the curve r = 2 + sin θ

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Q: Solve for the missing lengths and angles.

A: Introduction: If two triangle sides are congruent, the angles opposite these sides are also…

Q: The function f(t) = 1500 represents the rate of flow of money in dollars per year. Assume a 15-year…

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Q: 1. Consider the ordinary differential equation = (1-x-¹)y, with the initial values x = 1, y = 1.…

A: The fourth order Runge-Kutta method uses the following formulas to approximate the values of y at…

Q: 24. Given the linear congruence (16x is congruent to 72 mod 24.) How many possible incongruent…

A: 24. To find the number of incongruent solutions of16x≡72mod 24

Q: (c) Give an example of a linear combination that resulted in the zero vector that did NOT have O's…

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Q: Use the chain rule to find where First the pieces: End result (in terms of just t): = 历 内 z = x²y +…

A: Here given that                       z=x2y+xy2,  x=3-t3,  y=3-t6 We have to find dzdt by using…

Q: Obtain the general solution to the equation. dx + 6x = 9y8 dy The general solution is x(y) = y-…

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Q: I. Solve the following Linear Systems of Equations by Gaussian Elimination: 2.) 3x + 3z = 0 2x +2y =…

A: We have: 3x+3z=02x+2y=23y+3z=3 Writing this in matrix form: 303220033xyz=023 The augmented matrix…

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: Given :Ambient temperature = 85° FRate constant = 0.04 min-1

Q: Solve the given differential equation. All solutions should be found. dy 3x = e³x + 7y dx NOTE: Use…

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Q: QUESTION 10 Let f(x) = sina and g(x) = cos x, and W = span{f,g}. 10.1 Use the Wronskian to show that…

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Q: Let A ST and assume that det(A)- 2. Find det(-2A), det(A-1), det((2A)), det(3(AT)-¹), and a det e C…

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Q: 02 2 1 0 -1 23 -2 1 3 -3 1 2 is row equivalent to the matrix D = 1 0 -1 -3 01 1 2 00 1 00 The matrix…

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Q: Exercise 25.7.1. Give the Taylor series of the function 1 f(x):= 3x² around the point c = 1 and give…

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Q: First the pieces: 8 End result (in terms of just t):

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Q: 2. Find the basis for the nullspace of A, and the nullity and rank of A

A: This is a problem of linear transformation.

Q: Use the above to solve the following system of differential equations: 31= x1+2x2 3/2 = 2x1 + x2

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Q: 1. Let V be the set of all 2 x 2 matrices 4- such that the product abcd =0 with standard operations…

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Q: Use separation of variables to find a product solution to the following: ди ди x=y Ox ду u=c --( *…

A: This is a problem of the partial differential equations.

Q: 11. Minor and Cofactor 1. Find the cofactor of 6 in matrix D 9 8 4 2 7 -9 3 4 D = 6 -3 2 3 9 3 2 8 ㅋ

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Q: 2. Determine one real root of 2xcos2x — (x − 2)² = 0 on the (2, 3) using the Regula-Falsi interval…

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Q: Evaluate each determinant. -3 2 4 -5 -3 -5 1 5 دل در 3

A: We have to calculate the determinant of  -34-52-3-5135 to find determinant  expand the matrix along…

Q: 7. Study the Venn diagram below and then answer the following questions: 15 B A 9 4 8 300 7 5 2 1 10…

A: Only D and E asked and answered.

Q: 20) See the diagram' to the right. Find the missing side. а. 553 в. лот с. 355 d.8 ? W aft 6

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Q: If V is the space of all vectors in R*that are orthogonal to W = Span{(1,0,2,1),(0,0,1,5)}, then…

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Q: Find the volume of the colid obtained by rotating about th bounded by y=2x² axu the region and yo

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Q: Let f be the linear transformation represented by the matrix 4 A = 32) -2-4 Find the factor by which…

A: The absolute value of the determinant of a matrix of order 2 is the factor by which f scales areas.…

Q: A function f(x) is given as ex (x2+5x+2) + 1 = 0. Between 0 and -1,find the root between a and b…

A: option(c) is correct

Q: The statement form (ac) ⇒ (bc) is equivalent to O [(~avc) ^ (av~c)] ^ [(~b v c) ^ (b v~c)] ~[(~a v…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: In Let x, y ER" be given. (a) If ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: Solve the DE using laplace transformation: x'''(t)-3x''(t)-4x'(t)+12x(t)=12e^(-t); x(0)=4, x'(0)=2,…

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