From the following table, estimate the number of students who ob- tained marks between 40 and 45: Marks: 30-40 40-50 50-60 60-70 70-80 No. of students: 31 42 51 35 31

Q: Q 1. (a). Apply Newton's Forward interpolation formula and find y(25) fromthe given data. X 2 6. 10…

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Q: Determine one real root of 2xcos2x – (x – 2) = 0 cn the interval (2, 3)using the Regula-Falsi…

A: Given 2x(cos(2x)) - (x-2)2 = 0  Let f(x)=-(x-2)2 + 2x(cos(2x)

Q: B. Find a root of the function f(x) = x² + e* by using Newton-Raphsson.

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Q: 69. Let f(x) = sin e. a. Find a Trapezoid Rule approximation to sin e dx using n = 40 subintervals.…

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Q: Solve the following ODE using variation of parameters i) y(3) + 4y" + 5y' + 2y = ex

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Q: Question is attached: solve for z

A: Quadratic formula:

Q: Solve the following equation using Gauss Seidel method. Show the first two iterations in detail. x-…

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Q: s there a formula to calculate:  If A and B are dependent and P (A/B) = 0.35 then  P(B/A) = P (A…

A: A and B are dependent P(A/B)=0.35   we know that, P(A/B)=P(A and B)/ P(B) P(B/A)=P(A and B)/P(A)

Q: a²u, a?u at2 0 =

A: Here, we can solve by multiple methods. We have the following differential equation.…

Q: By using formulation in Newton Method, show that the solution of the secant method p can be…

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Q: 2. Perform just two iterations to solve the following set of non-linear equations using Newton…

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

A: Here -(x-2)2 + 2x(cos(2x)) = 0Let  f(x) = -(x-2)2 + 2x(cos(2x))

Q: 2 Vi – 1 - ) dt

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Q: a. Use the Bi-section method, to approximate v2 in three steps in the interval (1,2| (use 3 digits…

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Q: Given P(D/M)=(P(M/D)P(D))/(PM), Solve the following 1. Discuss the True negative from the main…

A: Given: True negative from the main reverse tree

Q: If the Equation Hx = c is inconsistent for some c in Rn, what can you say about the equation Hx = 0?…

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Q: Could you derive the equation from this for βi that is used by the Newton algorithm

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Q: solve the following non-linear equation with  Regula falsi method xex - cosx = 0

A: Given equation is, xex-cosx=0 Let, fx=xex-cosx Here at x=0,  fx=0e0-cos0=-1 and at x=1,…

Q: Solve for the following using propagations of error: C=A/B *hint: use the quotient rule

A: Let ∆A, ∆B be absolute errors in the measurement of A and B. And let ∆C be the corresponding…

Q: Calculate the resultant (i) V₁ - V₂ - V3 and (ii) V₂ + V₁ − V3 when V₁ = 80 N at 55° V₂ = 90 N at…

A: Given details: v1 = 80 N at 55ov2 = 90 N at 120ov3 = 110 N at 110o (i) v1 - v2 - v3 = 80 sin (55) i^…

Q: (a) Evaluate I = SoSi L' dxdydz. (b) In how many possible orders can you calculate I? Do all give…

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Q: Solve the following system of equations using Cramer’s rule [5] { −3? + 2? − 6? = 6 5? + 7? − 5? = 6…

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Q: dr a) de rcose + rsene subject to r(0) = 1 (solve by separation of variables)

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Q: use Rung-kutta method to so lve

A: It is given that y'=y with the initial condition y0=1. Comparing with the initial value problem…

Q: Find the root of x3−2x +14=0, correct to 3 decimal places using the Newton-Raphson method.

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Q: Perform just two iterations to solve the following set of non-linear equations using Newton Raphson…

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Q: Starting with x0 - 1.5, yo 1.2, the values x3 and y3 obtained using the pair formulae /+-y.. Y... -x…

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Q: Solve the following equation using the Galerkin's method (at lease 2 parameter solution). Please…

A: Given that,

Q: Q 1. (a). Apply Newton's Forward interpolation formula and find y(25) from the given data. X : 6. 10…

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Q: Suppose three similar geometric figures are constructed off the three sides of a right triangle in…

A: Consider a right triangle with the length of the altitude a, the length of the base b and the length…

Q: to estimate what the demand for electricity was at the time. a) Construct a backward difference…

A: The function value at a point can be interpolated using newton's backward difference interpolation…