Consider the following nonhomogeneous heat boundary-value problem (BVP): u, (x,t) u (x,t) + cos x, 00 u(0,1)=0, t>0 t>0 = 0, 4x u(x,0)= +cos x + 1, #+2 Determine u(x,t) by applying the substitution u(x,t)=v(x,t)+w(x).

Q: prove that u=y3-3x²y is a harmonic function determine its harmonic conjugate and find the…

A: consider u(x,y)=y3-3x2y

Q: need 14 and 16 solved ↓ In Problems 9-26, find a particular solution to the differential equation.…

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Q: Solve the system by graphing. 5x-2y = 20 10x - 4y = -40 Use the graphing tool to graph the system.…

A: The given system of equation is as follows 5x-2y=2010x-4y=-40 Plot the first equation on graph  Make…

Q: Find the solution of the differential equation dy dx + x³y = 2x³ (x > 0) with the initial condition…

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Q: Solution by Diagonalization: In Problem below, find the general solution of the given system. X'

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Q: • Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: -Find the intercepts, the symmetry for the polar equation r = cos20 anc draw it.

A: A polar coordinate is represented as r, θ, where the length such that r=x2+y2 and θ is the angle…

Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of : 2 (1) lim,-ol; (2) lim 0 x ³ (tan-¹x-x)…

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Q: o find the smallest positive root of tan x-x=0 which of the following re-arrangemen propriate? e the…

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Q: 4. Let V = R(2) [2] with the inner product of Example (5.3). Find a basis for the orthogonal…

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Q: Let y = n=0 y' - 7y +11 x³ = 0, y(1)=4. Find 03. a3 03 = a3 None 269 3 268 3 271 3 a (x-1)" be the…

A: We have given a differential equation ,  y' - 7y + 11x3 = 0   with  y1 = 4 Let y = ∑n=0∞ anx-1n  be…

Q: 1. Figure out the Z transform F(z) of the unit ramp function f(t). f(t) = { t20 t<0

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Q: Example 2 Let A [a], B [bi] be two nxn matrices in Mnxn with inner product (A, B) tr (ATB) a₁1b11 +…

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Q: Exercise 1. Find minimum of the function F(x) with constrains x e D,, i.e. solve the problem: F(x) =…

A: Disclaimer: “Since you have asked multiple questions we will solve the first question for you. If…

Q: Calculate FdV where F =2i+2z j+yk and V is a space bounded by z=0, z = 4 and x² + y² = 9. X 4 Z ФС 3…

A: Here we can use spherical coordinate but we use peoperty of triple and double integration that it…

Q: Volume of the function g(x, y)=√√64-x² - y² over the semicircle bounded by x² + y² ≤ 64, x ≥ 0.

A: here we can use polar coordinate by this integration will be very easy.

Q: 2 NFAS Consider the following NFA N: a 3 a 3 a,b a) What is the 5-tuple which represents this NFA? 2…

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Q: Ay Define f by f(x,y)=√ h(t) dt, where h is some continuous function of one variable such that h(0)…

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Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

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Q: Given 3 y₁ = x²³₁ (0,00) is soln to x²y²-6y=0 find y₂ and show linea independence.

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Q: using Newton's approach combined with Forner method find an approximation for groot of equation X²+…

A: Given polynomial is p(x)=x3+x2+2x-1       (1) By Horner method…

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: 3. the answer is False (or) Td because, the sun is a planet is true  but 3 is not an even number  so…

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: 7. False  Because Modus tolens is a law of inference.

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Q: end of its life. Operating anc the city's MARR is 7% per ye

A: Given: Life of sewage system is 40 years. Interest rate is 0.8

Q: b) Hence or otherwise prove that there do not exist three consecutive integer values of n for which…

A: First let us assume that 29n+5 is a perfect square for some consecutive integers n and n+1. Then…

Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: Introduction: Whether a set is finite or infinite is determined based upon its cardinality. When the…

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Q: The speed of sound in air changes with the temperature. When the temperature T is 32 degrees…

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Q: Consider the following. B = {(0, -1, -2), (4, 1, 2), (12, 3, 7)}, B' = {(-3, -2, -6), (2, 1, 3), (2,…

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Q: I. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: Part (3) We have the statement "If the sun is a planet then 3 is even" Let p=sun is a planet Let q=3…

Q: 1. Modified TRUE or FALSE. Write Tolits if statement is true and Tol if statement is false. For…

A: 7. False  Since Modus tolens is a low of inference.

Q: consider the ff. function: f(x, y) = cot" "^ (1+x) - 2x + ³y 3y 2e

A: Given the function             f(x, y)=cot-1(1+x)-2ex+3y Where              x=s2+t2,  and…

Q: Find the Taylor or McLaurin series for the following functions f(x) = xe-*, a=0

A: Here f(x)=xe-x,a=0. We find the Maclaurin series of f(x).

Q: (ve-2x + y²) dx - e-2x dy = 0 6. (ye

A: We need to identify the given first order differential equation as homogeneous, Bernoulli, linear…

Q: Consider the diffusion equation: Ut(x, t)=kUxx(x, t), U(x,0) = f(x), U (0,t) = U(l, t) = 0, 0≤x≤l,…

A: Crank and Nicolson (1947) proposed and used a method that reduces the total volume of calculation…

Q: Let E₁ 8 E₂ be subsets of a normed space X and E₁ + E₂ = Gu+y:xε E₁ g y ε E ₂ } . Then prove that if…

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Q: Solve the linear system corresponding to the following augmented matrix: 3 6 24 [294] 2 3 11 O A.…

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Q: Year 1 3 5 7 10 Population 16,763 17,007 17,226 17,418 17,639 Determine a model for the given data…

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Q: Solve the following initial value problems by Laplace transform technique

A: We have given a differential equation ,  y'' + 2y' + 5y = 50t - 100   ,  y2 = -4  , y'2 = 14 This is…

Q: The equation u = 2uxx is

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Q: ..Σn n=1 n²e-n³ determine if each of the following series is convergent or divergent: 2. ∞ n=1 n+ 1…

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Q: Complete the following steps for the given function, interval, and value of n. a. Sketch the graph…

A: Mid point Riemann sum formula  ∫abf(x)dx≈Δxfxo+x12+fx1+x22+fx2+x32+fx3+x42+......+fxn-1+xn2where…

Q: 5. Write two propositions p and q in the form of complete sentences. Then formulate the compound…

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Q: The ideal gas law crates that the preccure [p], temperature [T], & volume [v] of a confined gas are…

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Q: Find Taylor Series for F(x)=X/(1+X²) at (x=1),

A: Sol:- Taylor series of function fx at 'a' is defined as:  fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+……

Q: Verify that there is no magic square of order 2.

A: We will verify that there is no magic square of order 2 using the proof by contradiction.

Q: It is given that a+B+y=3₁ a² +² + y² = 5₁ a² + B² + y² = 6. has roots a, B. y. The cubic equation x³…

A: Given that the cubic equation x3+b x2+c x+d=0 has roots α, β, γ   Also, given α+β+γ=3,   α2+β2+γ2=5,…

Q: I was given a point, for example, (1,2,3), and was asked to find the exact speed but I was not given…

A: If given position vector of a moving particle at time t is a function of time then we have to put…