Consider the system below * + dž³ + kx = o Show that V(x) =(kx² + x³) is a Lyapunov function. Is the system Lyapunov stable, asymptotically stable?

Q: Cite 1 example of real-life application of midline theorem.

A: Midline theorem:  In the triangle, the line segment that joins the midpoints of two sides of a trian...

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A: There is no such introduction for the solution.I have explained it within the solution.Please go thr...

Q: (xy² – x – y² + 1)dx = (xy + x – y– 1)dy %3D

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Q: Answer number 14 only

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Q: 3. Apply Euler-Maruyama method as one step to solve the SDE dy =at 3 y dt+ dB 5 t y(1) = 2

A: Given dy=3-y5-tdt+dBty1=2

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Q: Given the differential equation y ′′ + 2y ′ = x with the boundary values y (3.5) = 2 and y (4.5) = 8...

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Q: Consider the matrix A a) Decompose the matrix A decompose matrix A by using LU factorization proce...

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Q: Consider a poputation Piti satistying the extinction expiosion equation-ap - bP. where B= aPis the s...

A: Given- Consider a population Pt satisfyinf the extinction explosion equation dPdt = aP2 - bP, where ...

Q: Find U35

A: We have to find the elements of the group U35. We know that U35 is a group with respect to the opera...

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Q: ls yogurt at three locations. Location I sells 58 gal of nonfat, 50 gal of regular, and 26 gal of cr...

A: Introduction: A matrix is a set of numbers that are arranged in a fixed number of rows and columns. ...

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = A x + x+ x²+ x3 + ... -) +В х x²+ x³ + + x+ an...

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Q: What is the differential equation of the family of straight lines whose slope and x - intercept are ...

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Q: Find a particular solution yp of the given equation. Primes denote derivatives with respect ס 2y" + ...

A: The given differential is non homogeneous differential equation with constant coefficient.  

Q: f(x+h)-f(x) Find the difference quotient where h 0, for the function below. h f(x) =-5x+1 Simplify y...

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Q: Let F be a nonempty family of transitive relations. Prove that intersection F is a transitive relati...

A: Given F be a nonempty family of transitive relations. We have to prove that the intersection F is a ...

Q: Given the differential equation y′ (t) + y (t) = t with the starting condition y (3.0) = 1.0. Using ...

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Q: Albert's graduation picnic will cost $9 if it has 3 attendees. At most how many attendees can there ...

A: Given that  Cost of a Alberts graduation picnic if it has 3 attendees=$9 Albert budget=$15 To find N...

Q: Use zero- through third-order Taylor series expansions to predict f(3) for f (x) = 25x – 6x² + 7x – ...

A: To find the n-th order Taylor series of a function f(x) at the point x=c and the percent relative er...

Q: Use the decimal grid to write the pe 0.53

A: Here it's given 0.53

Q: Show that in S7, the equation a2

A: Given n be an even positive integer.    To prove that An has an element of order greater than n if a...

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Q: 3) Given the function f (x) = x – Cos x Using the bisection method in the interval (0, "), find the ...

A: Given function is fx=x-cosx initial guess:- x0=0,   x1=π2 True value xr = 0.7391 (by graphically)

Q: 1. Find all units in Z[V-3]. Justify your answer. 2. Prove that 2 is an irreducible element in Z[V-3...

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Q: HOMOGENEOUS EQUATIONS Find the general solution of the following differential equations 1) y' - ay =...

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other quest...

Q: Find the standard equation of the sphere that has (2,0,-4) and (4,8,-3) as endpo

A: Introduction: The distance formula between two points (a,b,c) and (x,y,z) is given by, d=(x-a)2+(y-b...

Q: Use linear approximation, i.e. the tangent line, to approximate V125.1 as follows. Let f(x) = Vã and...

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Q: Problem 7.3.4. Show that (n)=1 diverges to infinity.

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Q: A particular solution of the DE y" + y = tan (t) can be found by the method of undetermined coeffici...

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Q: Find the inverse, if it exists, for the given matrix. 1 -1 3 1 3 2 -3 2 Select the correct choice be...

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Q: plot the point given in polar coordination (3,-3π/4). find three aditional polar representation of t...

A: This is a problem of polar to cartesian conversion and the idea of parametrization.

Q: dr r2 ;r(1) = 2 dø

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Q: 2. Identify the elementary propositions that formed the following compound prepositions. Represent t...

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Q: 7xy" – y + 10y = 0. (1) Since P(x) = or Q(x) = are not analytic at x = 0, x = is a singular point of...

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Q: Obtain the Maclaurin series expansion (up to 6 terms) and compact form of the function: f(x) = 2sinh...

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Q: Determine whether the statement below is true or false. Justify the answer. The solution set of a li...

A: To find- Determine whether the statement below is true or false. Justify the answer. The solution se...

Q: F- 03. Evaluate the following integrat ja-* (1 – x – 4x³ + 2x)dx (a) analytically; (b) single applic...

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Q: 3. Show that d is a direction of unboundedness for the following set of constraints. - r2 + 3 = 4 + ...

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Q: Write an expression for w in terms of x. Simplify your answer.

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Q: 0.08 m3 = kg %3D

A: We know that  1m3 = 1000kg  

Q: Determine whether the following statements are true or false. Explain why or why not. 1. The curvatu...

A: determine whether the following statements are true or false. explain why or why not . 1) the curvat...

Q: Can someone please help me with my problem in Differential Equations. Please write the complete solu...

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