20 Using Simpson's 1/3 Rule, approximate the 0 places. Express final answer to 4 decimal places. 200z 5+Z 15 dz Use n=20. Calculate up to 4 decimal

Q: Q4: Solve the following problems using dual simplex method. 3x2 > 15. = 5x₁ + 8x₂ 5x2 >-60 2x₁ + 3x₂…

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Q: Find the Laplace transform of the function f(t). f(t) = sin 3t if 0≤t 4T

A: By the definition of Laplace Transform:L[f(t)]=∫0∞f(t)e-stdt           =∫04π(sin…

Q: Prove that (a ↔ a ^ b) ^ (b ↔ ¬a) = (a b) by using logical equivalences.

A: Logical equivalence is a relationship between two statements or propositions where they have the…

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Q: the surface area E = 9(x1 4₁2)

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Q: √6V 18-√10-√x x =? = 36

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Q: (d) For which e E {0, 1, ..., 9), is 12e128 divisible by 8? Find all such e. 1

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Q: Solve the given initial-value problem. X(t) = X' = 1 1 1 -6 2-3 X, X(0) 1 -2 2 -3

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Q: 3. Consider the function f(x, y) = −4+ 6x² + 3y² and point P(-1,-2). On the grid, label P and graph…

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Q: Which Riemann sum represents the illustration shown? 3 L 2 1 2 4 6 4 O 8 10 √xi. Axi √æi. Axi xi.…

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Q: (3) Solve the following terminal value problem: The following answers are proposed. (a) 142³(-) (b)…

A: It is given that Ft+3xFx+x22Fxx-3F=0,            FT,x=x2

Q: n² (a) Show for all x E R, the sum E-1 COS converges uniformly. (b) Show for all x E R, the sum Ex=1…

A: Convergence of the series

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Q: Recall that if S = {v₁, v2, ..., Vn} is a set of vectors in Rm, then the subspace W spanned by S is…

A: As per the question, we are given a subspace W in ℝ4 spanned by a set of vectors S. Our objective is…

Q: Solve the differential equation using Laplace transforms. The solution is y(t) and y(t) = = y" - y2y…

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Q: The point (0, 5, 20) is a critical point of the function f(x, y). The 2nd partials matrix at the…

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Q: In a game of craps, you roll two fair dice. Whether you win or lose depends on the sum of the…

A: a) We have to find values that X can takeb)We have to find probability distribution of X

Q: Show that at least ten of any 64 days chosen must fall on the same day of the week. We prove this…

A: Step - 1 Step - 2

Q: 2 3 For A = 0 -1 0 orthogonal matrix Q. V₁ = Ex: 5 1 -2, find the orthogonal vectors V₁, V2 and V3…

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Q: (12) Let dS₁ = 0.1S₂dt +0.2S₁dW₁ and dS₂ = 0.15Sądt +0.3S₂dW₂, where W₁, W₂ are dependent Wiener…

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Q: Let ƒ(x) be a polynomial of degree n > 0 in a polynomial ring K [x] over a field K. Prove that any…

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Q: In this problem we will show that the volume of a right cone of radius r and height h is given by rh…

A: (a) To Write: Integral as function of two variables for the volume of the cone. (b) To Evaluate: The…

Q: 1 For what value of x does the function f(x) = 3x³ — 4x attain the absolute maximum in the interval…

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Q: M = Find the matrix M of the linear transformation T: R³ → R² given by T 21 X2 X3 = 4x1 + x₂ + 2x3…

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Q: An oceanographer measured the length, in meters, of a deepwater wave and its speed, in meters per…

A: To find Linear Regression line Equation, Here Least Squares Method is used. Wavelength  X (m)…

Q: For what values of b does the following set of vectors form a basis? 3 3 {··A) 4 12 5 15

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Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. 8-{8}-(-6) B…

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Q: Solve the initial value problem y"'-3y"+4y'-2y=0 y(0)=1, y'(0)=y"(0)=0

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Q: A delivery truck must deliver packages to 6 different store locations (A, B, C, D, E, and F). The…

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Q: Let Tri³ ³(R) denote the vector space of all upper triangular real (33)-matrices. Find a basis and…

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Q: The following table shows the length, in centimeters, of the humerus and the total wingspan, in…

A: The given data, Humerus, x Wingspan, y 24 32 22 17 13 4.4 3.2 1.5 20 27 15 15 9 4.4 2.9 610…

Q: [(78)4:S (+9172 11/11

A: note : As per the instruction we will only solve the question number (4)   As per the question we…

Q: Find the rule for the geometric sequence given below. 3an - 1 and ao an = 5.

A: The given sequence rule an=3an-1 and a0=5. We have to find the general formula for the sequence.

Q: amourd of Money year ? at the end of each .. If additional (2000) was rd at The 3 borrowed find…

A: If P be the principal amount, R be the rate of interest and T be the time period then SI = PRT/100

Q: Find the general solution y"+2y'+y=e^(-x)(ln(x))

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Q: 1. Find homogenous solution of the following S.L.D.E using Cramer's rule.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: 7. k=1 8. Σιγκ

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Q: 1. Consider the plane in R³ that goes through the point (2,1,3) and is perpendicular to the vector…

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Q: Qs) By using 4th order Runge-kutta method, solve the following differential equations: (ii) y' = 3x…

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Q: Write an equivalent statement that does not use the if ... then connective. Use the fact that p→q is…

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Q: Find the inverse Laplace transform of -8s F(s) = e s² - 18 - 12 f(t) = =. (Use step(t-c) for uc(t).)

A: The given problem is to find the Inverse Laplace transform of the given function F(S) to find the…

Q: Distance is measured in megaparsecs (1 Mpc is approximately 3,260 light-years), and velocity is…

A: Distance (Mpc) Velocity (km/s) 51.8 4,575 12.2 1,234 271 17,685 46.2 3,842 58.2 5,108…

Q: 1+3+5++ (2n + 1) = (n + 1)².

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Q: Use technology to perform the following steps for the sequence given. a. Calculate and then plot the…

A: We have, an=nsin1n. To Do: We have to calculate the first 25 terms of the sequence and check whether…

Q: 1. Prove that if S is a subring of a ring R then the following are true: (a) Os = OR (b) if 1R € S,…

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Q: is P= of A Please write down B-matrix of where B is the set

A: In C = P D P-1 the columns of C are actually the eigenvectors of the matrix C.  Ck = (P D P-1)k = (P…

Q: Use the method of Laplace transform to solve the initia. value problem: y" - y - 12y = et, y(0) = 2,…

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Q: Find the area under one arch of the trochoid x = = 80 — 5 sin(0), y = 8 -5 cos(0). Area =

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Q: 13. (V 2) Let V = P3 and H be the set of polynomials such that P(1) = 0. Is H a subspace of V?…

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Q: 5. Show that in any row of mn + 1 distinct real numbers there is either an increasing subsequence of…

A: A classic result known as the Erdos–Szekeres theorem or the Dilworth's theorem.