Solve the following ordinary differential equations: 4x dx dt d²x dt² dx dt - 3=0

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A: To Show- Show that for any odd prime p, the Gauss, Gp, can be rewritten as Gp = ∑x=0p-1ζpx2.

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Q: lim n→∞ n² n² 9n² +10n +3 = 9.

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Q: State the order of the given ordinary differential equation. 2y 0²y = √ ₁ + (2x) ° 1 dx² Determine…

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Q: 2. Suppose that a firm's production function is y = a ln x₁ + b ln x₂ + (1 - a - b) ln x3 where a…

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Q: 4) Consider the following system X₁=X₂-\ X₂=X₁²-x₁ - x₂ +1 Find the equlbrium. Plot Phas Portrail of…

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Q: a. If AER dxd satisfies A¡¡>0 for i=1,...,d, then A is invertible. dxd b. When A,BER are both…

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Q: Prove that the original sequence sn converges.

A: Hint: A sequence is convergent if and only if every sub sequence of the sequence is convergent.

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Q: (a) Let V = C² be the vector space over C and let a = {u₁ = (i, 1), u₂ = (1,0)} be vectors in V.…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Example 2: If 2x+3 is a factor of f(x) = 6x³ +5x²-16x-15, determine the other factors and sketch a…

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Q: sx 14-X Find the Fourier transform of function f(x) = , 0<x< 14 14 < X <16

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A: As per the given data lets draw a free body diagram

Q: 1. The following formula relates the volume (V) and surface area (S) of a sphere. V(S) = (4m) + x 3…

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Q: Graph of the function f(x) = x3  is translated horizontally to create g(x) . If the point (4,8) is…

A: Graph of the function f(x) = x3  is translated horizontally to create g(x) if the point (4,8) is on…

Q: Find the Fourier Transform of Hence Prove that f(x): cos(sx) + Ssin(sx) 1+s² -ds = x 0 OEIN 0 2 Tex…

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Q: 2.3 Consider the nonlinear system =y+x(x² + y2-1) sin. y=-x + y (x² + y2 - 1) sin 1 ² + y² - 1 1…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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Q: 10:37 01 -1 02-2 R3 → R3 -2R₂ 1 0 -2 0 1 -1 00 V₁ X2 YO x3 thus, we get x1 - 2x3 = 0 - x₂x3 = 0 let…

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Q: Bionomial Theorem  Find the 5th term in the expansion of (1-2x)10

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Q: 7. Consider the bisection method starting with the interval [1.0, 2.5]. Find the width of the…

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Q: Prove that (z - x)(z - y) = (y - x)?. a:= is not a rational number. Hint: Express (x - x) and (z -…

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Q: Find did You -The Sum use (3/5) ? to find the sum. 2 + nti nzo what Theorems

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A: 1) Given p(x)=x³-5x²-x-10 Put x=2. Then P(2)=2³-5*2²-2-10 =8-5*4-12 =-24

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Q: • Consider the following system. X = 9-1 133₂ = 34²-34-35+1 al find the equilibrium points of the…

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Q: Prove the following equality using combinatorial proof. (No not a combinatorial proof.) (↓) = n-1 Σ…

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Q: Solve the ff. ordinary differential equation dy dx sin (x + y)

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Q: PROBLEM 2 Find the root of the following equation using Newton-Raphson Method and compare the result…

A: Given problem is fx = e-0.5x 4-x -2 Initial guess x0=2 First derivative of function:- f'x =-0.5…