Q7. Find the Laplace transform of the periodic function f(t)= sin at for 0

Q: minimize subject to (xyz)-¹ x + 2y + 2z ≤ 72 x, y, z 20

A: Since you have posted multiple questions, we will solve only the first question for you.

Q: Apply the technique of linear algebra to find the argumented matrix in linear system of following…

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Q: the number of days the Company should operate each refinery operate in order to meet the terms of…

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Q: Consider the matrix mapping A:Rº→R³ where 1 0 4 0 0 2 1 3 1 2 4 0 0 A = 200 2 0 Sub-Task (1). Find a…

A: Given : A=210400022131000240 To Find :(1) basis, dimension of kerA               :(2) basis…

Q: Evaluate П+24 dx

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Q: 7. Find: y = In √6x-5 Lex (x+1)³.

A: Sol:- ddxln6x+5exx+13Apply the chain ruledfudx=dfdu·dudxf=lnu,…

Q: 3. The graph below represents f(x). a) State the number of stationary points and label them…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 3. Let R be a ring and b E R be a fixed element. Let and prove that T is a subring of R T = {rb | r…

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Q: Find the flux of F across S, [/F. F. N ds where N is the upward unit normal vector to S. F(x, y, z)…

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Q: erential equation of a physical system satisfies the followin dP a =ag - bP dt

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Q: Q4. (a) For the following Nonhomogeneous Linear System of DE, what are the eigen values,…

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Q: In In = (a) Prove the reduction formulae 1 -- sinn-1 x cos x + n (HINT: Use integration by parts…

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Q: Exercise 1.14. Show that the series ∞ Σ n=1 converges absolutely for |z| < 1. 12+ 2z10n 272 5zn² −…

A: Given: The series is ∑n=1∞zn212+2z10n-5zn2-3z3+2z10n2 . To prove: The given series converges…

Q: ind the Laplace transform of the periodic function f(t) = 50=[²₁ 1 for 0<t<2 for 2<t<4

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Q: Assume that P and Q are two positive distinct real roots of the quadratic equation (²₂. - -…

A: given quadratic equation t2-P+Qt+PQ=0 here assume that P and Q are two positive distinct roots of…

Q: Suppose that the acceleration vector is a(t) = (e²t + 2t, e²t – 3,0) and also that the velocity…

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Q: = 0 4. Solve by hand the problem ut = Uxx in the interval [0, 1] with ux at both ends. Use the…

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Q: Given a function f(t) = (¹-43² +18+360, which of the following functions g(t) satisfies the property…

A: Formula ℒδ(t-a)f(t)=f(a)e-as We have ℒδ(t-a)f(t)=ℒδ(t-6)t4-43t2+18t+360

Q: anthe problem I+y: Itt y' year=e. and approximate y and 1 2 h = 0.2, 0.1

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Q: Apply Optimal Runge-Kutta methed and y for the 3 obtain y, 1₂ and y² = t + 2y year=1 for the problem…

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Q: Find the approximate root of function f (x) = 0.48x³ - 2.7x - 5.36 by using the newton raphson…

A: Given function fx=0.48x3-2.7x-5.36             ……………………1 Initial guess x0=3.5

Q: Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R² → R²:…

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Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

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Q: For any collection a of subsets of X, there i ntaining a.

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Q: Let X={x=(x1, x2, X3, X4) : Xi E {1,2,3,4,5,6,7,8,9,10,11,12} for i=1,2,3,4 such that x1 < x2 < X3 <…

A: Given: X=x=x1, x2, x3, x4 :xi∈1,2,3,4,5,6,7,8,9,10,11,12for i=1,2,3,4 such that x1&lt;x2&lt;x3&lt;x4…

Q: (a) For each of the following functions decide whether it is one-to-one and whether it is onto. Give…

A: (a) It is given that fx=2x. So, fx1=2x1 and fx2=2x2. Let fx1=fx2. Simplify the equation fx1=fx2.…

Q: given in polar coordinates. (i) Create a table r(0) 0 r(0) r(0) -5m/12 76 r = 5 cos² (0/2), (-= < 0…

A: Given a function is polar coordinates rθ=5cos2θ2 where -π≤θ≤π To create a table for different values…

Q: Show that v = A = (7) -29 35 eigenvalue. 35850). " -20 26 is an eigenvector of the matrix and find…

A: To Show: v=74 is an eigenvector of the matrix A=-2935-2026, and find the corresponding eigenvalue.

Q: 1. The von Bertalanffy equation is defined by the Ordinary Differential Equations as follows: W' (t)…

A: Given: The differential equation is W't=αWtλ−βWt. The given initial condition is W=100 at t=0. To…

Q: Apply Euler method and Richardson extrapolation for h = 0.2, 0.1 the problem: and abtain g y' = ty…

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Q: a) Examine if the following limit exists, If the limit exist, specify the value of the limit value.…

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Q: 8x + 11 = 2(4x-7)+25

A: Given equation 8x+11= 2(4x-7)+25 We need to calculate the value of x 8x+11= 8x-14+25 8x+11=8x+11…

Q: Let (an) be a sequence in which every term is from some given finite set R. Prove that (an) has a…

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Q: 2. Let f(x,y) = + (y + 2)² + 2 a) Sketch the level curve for f(x,y) = 6. (Ch. 10.5, 12.1) b) Find…

A: Given function is fx,y=x24+(y+2)2+2 Solution a) Level curve for fx,y=6 is an ellipse x242+y+224=1

Q: a). We can use the equation of a curve in polar coordinates to compute some areas bounded by such…

A: (a) Given that the equation of a curve in polar coordinates to compute some areas bounded by…

Q: 4. Use residue theory to calculate the following integrals: 3x Loo (2²+49) (4² - 2x + 5) (a) P.V.…

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Q: for the graph determine between the vertices and the excentricity 40

A: To determine the distance between two vertices and define the eccentricity of the graph.

Q: d (n, m): = 0 si n = m si n‡m 5-c(n-m)

A: Question seems wrong

Q: 4. (a) Calculate the chromatic number of a graph whose chromatic polynomial is t(t-1)(t - 2)².

A: A naive way to find the chromatic number of a graph from its chromatic polynomial P(n) is        –…

Q: find the approximate root of function f(x) = 3.43x³ -6.4cos(x) - 9.61 by using the Newton raphson…

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Q: x² 3x2 1. 1x² <3(x+5) 4 (x+4)(x-3) 28 5.5(x + 4) + 2(x - 3) ≤ 0

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Q: Draw cobweb diagram for the recurrence relations. Xn 1.5xn-1-2

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Q: Use a comparsion test to determine whether the following series converges or 2" sin²(5n) 4" + cos² n…

A: Given series is ∑n=1∞2nsin25n4n + cos2n

Q: Apply Optimal Runge-Kutta methed and obtain y₁, 1₂ and y² = + + 2y y(a)=1 3 for the problem , h =…

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Q: Find the values of the circular directions for all sides of the polygon in the first question if you…

A: Given: A polygon ABCDEF. The circular direction of the side AB is 306°30'. The internal angles of…

Q: A system is represented by the transfer function Y(s) 10.4 s² + 47s + 160 = R(s) s³ + 14s² + 56s +…

A: We need to determine the state variable representation of the transfer function:…

Q: Q7. Using Simpson's Rule evaluate the integral (√x+1) dx using 8 subintervals.

A: In this question,  we have to evaluate the integral ∫08x+1dx using 8 subintervals by Simpson's Rule.

Q: 24U₂ Use linearization (either with the Jacobian matrix or a change of variables defined by a…

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Q: Q5. Using forward, backward and central difference formula, determine the first order derivative at…

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Q: In the local boating pond there are 10 plain woode boats, each with a different number. The owner de…

A: There are 10 boats. Out of which 4 are painted and rest are unpainted. So out of 10 we need to…