(8) The equation my" +cy' + ky = F describes the motion of a mass m attached to a spring with spring constant k with frication propor- tional to the velocity and external force F acting on the mass. Let A and are real numbers and let m, k > 0, c≥ 0 be so that 4km - c² > 0. Prove that y = Ae2mt sin (√ k c2 t+o m 4m² satisfies my" +cy' + ky = 0.

Q: Apply the Bubble Sort algorithm. def BubbleSort(a): n = len(a) for i in range(0, n): for i in…

A: Value of a = [a0, a1, a2, a3, a4] after the 2nd pass ( after i = 1 and before i = 2) when input is a…

Q: can you please not use radians?

A: (1) (2) If a regular polygon has n sides, its every edge forms equal angle at the center and that…

Q: For the list [44, 18, 74, 61, 42, 31], how will the array elements look like after second pass…

A: After the second pass of Insertion Sort, the array will be: [18, 44, 74, 61, 42, 31]The first two…

Q: Problem 15. 1. Find (FG) (1). 2. Find (FG) (6). 3. Find (Go F) (1). 4. Find (GF) (6). Define F: R→ R…

A:

Q: ∞ k=1 Does the series to show all your work justifying your answer. (−1)k+1 1 converge absolutely,…

A:

Q: A north-south highway intersects an east-west highway at point P. A vehicle crosses P at 1:00 p.m.,…

A: A north-south highway intersects an east-west highway at point . A vehicle crosses  at  travelling…

Q: Both part (a.) and (b.) please.

A: Refer the below solution for given question, if any doubt please comment Explanation:Solution…

Q: Consider the piecewise function f(x) = { x, −2 0.

A: Given function is the following : Here is periodic function with period and continuous on .Noted…

Q: Let φ : G → H be an onto homomorphism.(a) Assume that G is abelian. Does this imply that H is…

A: Let's analyze each part of the question: (a)  Assume φ: G → H is an onto homomorphism and G is…

Q: Complex Analysis: Find the principal value of f(z) = z^z and then find the real and imaginary parts…

A: Ans: The real part of f(z) is, rzcos(zθ) and the imaginary part of f(z) is rzsin(zθ).…

Q: Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it…

A: Answer:  α=( 1 4 6 5 3 2 )Explanation:Step 1:

Q: Classify the following functions with respect to concavity and convexity. Please explain as detailed…

A: Ans: the function f(x,y)=(x2+y2)1/3is convex for all x,y=0.  Explanation:Solution: Let's classify…

Q: In(k5) k8 +2 converge absolutely, converge conditionally or diverge? Does the series k=2 (-1)…

A:

Q: 1 2 0 Determine if the matrix A: -1 1 3 is invertible or not. EXPLAIN! 3 -2 -8

A: Given matrix A is not invertible.Explanation:Step 1:Step 2: Step 3: Step 4:

Q: refer  to  image  below.

A: null basis is ⎣⎢⎢⎢⎡​3100​⎦⎥⎥⎥⎤​Explanation:Step 1:

Q: (-4)(-5) using number line model

A: The objective of this question is to find the product of -4 and -5 using a number line model. The…

Q: tions. Find the General solution of y" - 2y' + 5y = 4tet with Real valued func-

A: We have to find the general solution of the differential equation.

Q: Prove that the general solution to the differential equation with a variable term and a variable…

A:

Q: (x+2, x ≤ 1 (B)Test the continuity of the function f(x) = {4-x, x>1, at x=1. 6

A:

Q: “ジタル形式で段階的に解決 ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT SOLVE BY BERNOULLI dy-y - y = dx xy 5

A: Given differential equation is dydx-y=xy5Now dividing both sides by y5 we get ,1/y5dydx-1/y4=x.Let…

Q: Determine the local stability of equilibrium of the ODE d = x(t) = x² − y dt d y(t) = x(y = 2x). dt'

A:

Q: 2. Solve this system. State whether it has a unique solution, no solutions, or infinitely many…

A: We will solve the system of equations.

Q: Use the Linear Approximation to estimate Af = f(4.7)f(5) for f(x)=x -3x². (Use decimal notation.…

A:

Q: (Feb 21—27) Projected Actual Difference Food Cost $6,971 $7,842 +$871 (over)…

A: The objective of the question is to determine the adjustments that need to be made to the Food and…

Q: Sales Analysis The total sales S (in thousands) of a video game are given by S(t) = at² t² + b'…

A: The total sales S (in thousand) of a video game was given by Where,  and  is the number of months…

Q: Verify that this map f: R³ → M2×2 is one-to-one. (You do not have to also do onto.) a f(b a+2b…

A:

Q: 1. Suppose V is a finite-dimensional vector space with dim(V) = n, and that T € L(V) has n distinct…

A: Proof are in explanation sectionExplanation:Step 1:

Q: FNSACC321/FNSACC322/FNSACC421 Assessment Monarch Institutes

A: Here's a summary of the key points:1. Competency-Based Evaluation: Students are evaluated based on…

Q: EXERCISE | 6.1.3: Finding the transitive closure of a graph. Draw the transitive closure of each…

A:

Q: Use convolution to find f(t) = L¹{F(s)}. $2 F(s) = = (s²+4)(s²+16)

A: Final result:so, Inverse Laplace transform of the given function is:…

Q: Given is the graph for the second derivative of some function f(x) which has the domain of (-co, co)…

A: We have given a graph of as shown below:Now use the above description of in the graph, which has…

Q: Solve the given differential equation by variation of parameters. 3x2y" + 7xy' + y = x2 - x

A: y(x)=(c1/x)+(c2/3√x)+(x²/21)-(x/8)Explanation:

Q: For the DDS given by yn+1 = Ус -0.5y + 30, find the equilibrium value.

A: The equilibrium value for the given DDS is ye = 20.Explanation:The equilibrium value (ye) for the…

Q: (c) We want to find a three-point formula, [*^* ƒ (x)dx = w₁ f(x1) + w2f (x2) + wzf(xx) + E, -h…

A: Three-Point Formula for a Definite IntegralWe want to find a three-point formula for the definite…

Q: Suppose that f(x) = (x+4)(x-3)². (If an answer does not exist, enter DNE.) (a) Find all critical…

A: Note : As per our guidelines, we can answer the first three parts. Please repost the  remaining…

Q: Problem 1. Using the table of Laplace transforms or any other method, compute the Laplace transforms…

A:

Q: A lactory manufactures two products, A and B. Each product requires the use of three machines,…

A:

Q: Alexis found US$90 in her attic and sold it to a bank that charged her a commission of 0.85%. How…

A: Alexis received approximately C$117.41 from the bank after selling US$90 and accounting for the…

Q: Herold manages a company that makes and sells two kinds of speakers, the Boomer and the Rocker. Each…

A:

Q: Consider the graph G = ({1, 2, 3, 4}, E), where E = {12, 13, 23, 24, 34}. (a) Find the adjacent…

A: Dear Student,      As per our guidelines we can answer only first three subqustions. So kindly…

Q: 8y" +32y+8y = 3x a) What is the general solution for homogenous ODE (yn) b) What is the particular…

A:

Q: 2. The context of this question is linear transformations on the plane R². Let T: R2 R² be the…

A: is a function defined by first rotating the vector counter-clockwise by an angle of  and then…

Q: Find the solution of the given initial value problem 40y" + 13y" + y' = 0, y(0) = -1; y'(0) = −6,…

A: We will find the solution of the given differential equations.

Q: Question 2.7. Show that the following sequence is : convergent. (ii). a₁ = = 0.1, a2 = 0.12,...,a10…

A: The objective of the question is to prove that the given sequence is convergent. A sequence is said…

Q: 10.3.9. Let G be a group, and let N < G. Assume that |G : N| = m. Let x = G. Prove that xm Є N.

A: The proof is in the uploaded photo, kindly look at it. If you find any problem in understanding it,…

Q: If f(x, y) = xy, find the gradient vector Vf(3, 7) and use it to find the tangent line to the level…

A: Gradient vector (7,3)Tangent line is 7x+3y=42Explanation:Step 1: Step 2:Step 3:Graph 1 is the…

Q: Use the linearity property and the basic Laplace transforms to find F(s) = L{f(t)}. a. f(t) = 2t³ -…

A: ​(a) L{f(t)}=s412​−s2+4s​+2(s+3)1​​​(b)L{f(t)}=2s3​−2(s2+100)s​−s2+2510​​Explanation:Step 1:​ a.…

Q: Let A= -2-3-4 2 5 12 Find the third column of A without computing the other two columns. 1 2 5 How…

A: The matrix is :

Q: (C) Calculate the limits (1) lim 1-cos(x) (2) lim sin(x) x-0 x X1X x

A:

Q: In the figure, the circle of radius a is stationary, and for every 6, the point P is the midpoint of…

A: Let,      From given curve we have seen that