Use Lagrange interpolating polynomial of third order to find the general polynomial equation and evaluate the unused motor oil at T (25 °C) and T (57 °C) based on the following data; T 0 20 40 60 80 f(x) 3.85 0.8 0.212 0.1 0

Q: Example 7.33. Find the cubic spline interpolation for the data : x: 1 2 3 4 5 f(x): 1 0 1 0 1

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Q: divided in 4 categories: newborn, young, mature, and old. The following is the Leslie matrix hat…

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Q: 3. Solve the linear system below a + 2b − c +4d = 6 -a-4b +2c + 2d = 4 2a + 2b − c + 2d = 4 a + 2b +…

A: (a). Cramer's Rule

Q: 2TT Ex. 5/14.2 sindy dx 0

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Q: How many iterations is done in order to find the root of the following using bisection method? f(x)…

A: We have given function f(x)=x4-2x3+x2-3x+3 for[0,5]. We need to find number of iteration is done in…

Q: Solve the and many differential equation d/an (D²+1) {D-5)³y=0;

A: Given differential equation:D2+1D-53y=0To find: General solution of the differential equation.

Q: y = y= 1 sinx-cost It Sinh tesy 1 sinxtrost 1+ sinx-cOS X Xi-2-5 Newton method of optimization

A: We can solve this using formula of baton rajaon method

Q: Let I = [0, 1] be the unit interval. Construct a sequence of closed sets A₁ A₂ A3... in the…

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Q: An estimate value of f(x) dx is 10 using trapezoidal 2 - interval rule. W is an estimate value of…

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Q: 5. (a) Evaluate the polynomial y = x³ - 8x² + 12x −0.45 at a = 2.378. Use 4-digit arithmetic with…

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Q: 1 1 −1 2 1 2 1 Let A = and T the corresponding linear trans- 1 0 2 1 1 −1 2 3 formation of R4, find…

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Q: By the Fundamental Theorem of Calculus 2+x² Newton-Leibnitz, Theorem) evaluate √x dx

A: We have to evaluate  the given integral  ∫142+x2xdx  by using fundamental theorem of calculus.

Q: Find the variance stabilizing transformation g(y) for a response variable y, E(y) = µ and V(y) = √ī.

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Q: 4. A wooden rectangular box is to be made of lumber that is 2/3 in. thick. The inside length is to…

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Q: Let X be a normed space, Xn, Yn EX such that Xnx, Yny, then 1-Xn + Yn → 4- ||xn-ynll→→llx - yll.…

A: Given that X is a normed space, xn, yn ∈X such that xn→x, yn→y. To find: 1. xn+ yn→x+y…

Q: Consider the matrix 0 1 0 1 2001 A = 0 1 1 0 0 1 0 1, (a) By hand, compute the determinant of A. (b)…

A: The given matrix is                   A=0101200101100101 To find : (a) det A              (b)…

Q: Write [0, 5, 1, -7, 0] as a linear combination of [0, 1, 2, 0, 0]; [0, 1, 0, 0, 0]; [0, 1, 0, 0, 1];…

A: We want to write [0, 5, 1, -7, 0] as a linear combination of given vectors.

Q: Using two intervals of Simpson's 1/3 rule, an estimate value of f(x) dx is 11.51. The estimate of…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A: We need to find the equation of the surface. Please find step by step solution below:

Q: A contractor builds storage sheds in two high end models, the Chelan and the Orondo. Each Chelan…

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Q: 2. Given the matrix A below, 1 0 00 11 0 2 1 1 A = 2 1 0 1 2 0 1 4 solve for det inv A. The several…

A: Given the matrix A=1001021121012014. We have to find the det(A-1).   Definition (Inverse of a…

Q: Using Gaussian integration, (a) 2 ¹₁ f(2x + 3) dx (c) 3 ¹₁ f(3x + 2) dx the integral ff(x) dx is…

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Q: 2. Using the fact that D₁ ((2 − x)−¹) = (2 − x)-², find the Maclaurin series for 4x³ f(x) = (2 -…

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Q: For the following linear system, find the inverse of the coefficient matrix using Gaussian…

A: The given system is: 6x+3y+2z=66x+4y+3z=020x+15y+12z=0 To find: Inverse using Gaussian-elimination…

Q: For the following linear system, find the inverse of the coefficient matrix using Gaussian…

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Q: (1-9²) dx + (1+x¹) dy = 0 2x² dy dx csc (X) ý xe VX-2 =

A: The given differential equations are solved as shown below.

Q: Determine the value of z in the below equation, giving the answer in the form x + yi. z-8=i (7-2z)

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Q: TE 4 To approximate cos(x) dx would Simpson's Rule, Midpoint Rule, or Trapezoidal Rule give a better…

A: We know ∫0π2cos(x)dx = 1

Q: The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x = 3…

A: We want to find required polynomial.

Q: A bag of candy contains 84 pieces of 5 different types. The Pigeonhole Principle guarantees there…

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Q: Consider the following matrix: 3 4 0 8 0 7 0 4 A=0 2 0 3 0201 3 4 0 10 0 70 6, (a) Find a basis for…

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Q: Consider the given graph below: A PA B с 31/4 E E LL F G 0 1/4 11/2 5/4 31/2 717/4 D Let y = a…

A: Note: y= a sin[k(x-b)] + c  2a is the amplitude of oscillation, c is the vertical shift and 2π/k is…

Q: Example 7.30. Using Hermita's intropolation, find the value of f(- 0.5) from the following data: : 1…

A: Given data is x -1 0 1 f(x) 1 1 3 f'(x) -5 1 7 Using Hermite's interpolation, the value of…

Q: 1 A spring is such that a 4-lb weight stretches it 6 in. An impressed force; -cos8t is acting on the…

A: We have to determine the position of the weight as a function of time x(t).

Q: A car dealership has 6 red, 10 silver, and 5 black cars on the lot. Ten cars are randomly chosen to…

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Q: Exatuate the integral pvz O√3 √4-X² √EX 9 (√x ² + y² dy dx

A: Evaluation of double integral by conversion to polar coordinates.

Q: H-w.4 Find the volumes for the following solids whose Weights are defined by Z(x,y) and bases are…

A: Volume bounded by xy-plane plane.

Q: whose Find the volumes for the following solids heights are defined by E(x,y) and bases are the…

A: Volume bounded by xy-plane

Q: 5. Solve the following quadratic congruence using the "completing the square" method: 9x² +66x +49 =…

A: 5. Given equation is 9x2+66x+49≡0(mod 79)   To Solve: Above quadratic congruence using the…

Q: 9. Using integration by parts, Then k is? (a) - 1.5136 [*²x³ cos(x²) dx = k − [*³x sin(x²) dx -…

A: Given integral is ∫02x3cosx2dx

Q: Test the convergence of the power series below: 00 (-2)" 3η – 2 (3x – 5)" ΣΩ n=1

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Q: Q2: 1. Solve the following equation exactly ý + 2xy = x and y(0) = 1.5, h = 0.1 2. Use the Euler…

A: Given y'+2xy=x, y0=1.5, h=0.1

Q: determine the Laplace transform of the 21. given function using Table attached

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Q: Use Newton's method to approximate all the intersection points of the following pair of curves. Some…

A: we have y = 36x and y = x2+4 36x = x2+4 x2+4-36x = 0 f(x) = x2+4-36x f'(x) = 2x-18x-12 = 2x-18x

Q: 1. Let 7 = {1,2). a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) = 0}. b. Draw the the…

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Q: Find the value of k so that the given differential equation is exact. (³+kxy-2x) dx + (3xy² +…

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Q: Question 9 Calculate the indefinite integral below, with the method of u-substitution. In x [112 dx…

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Q: y = √√²+csc²(πx) 2 COS os(3 cos-¹(x)) - a X

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Q: Calculate the Radius of Convergence

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Q: 6. If a series Eu, converges to the sum u then so does any series obtained from Eu, by rouping the…

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