A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the equilibrium position, and the resulting motion takes place in a 7 medium offering a damping force numerically equal to - times the instantaneous velocity. (Use g = 32 ft/s2 for the acceleration due to gravity.) Complete the Laplace transform of the differential equation. s² L{x} + +(C _ )sL{x} + { Use the Laplace transform to find the equation of motion x(t). x(t) = [ ) L{x} = c 0

Q: Use the Divergence Theorem to find the flux of F = (xy², x²y, y) outward through

A:

Q: Use the inner product (u, v) = 2u₁v₁ + U₂V2 in R2 and the Gram-Schmidt orthonormalization process to…

A: If x1 and x2 are given vectors then orthonormal basis will be u1=v1v1, u2=v2v2where…

Q: Question 5. Find the general solution of t²x" + 3tx' - 3x = t² when t> 0

A:

Q: (5,0) Ax (X-2) Graph of f -10 810 (10.2) 10 Let f be a differentiable function defined on [-10, 10]…

A:

Q: Fill in the blank. (Enter your answer in terms of t.) 1 * 1{ -² = [ (s - 9)5

A:

Q: 3. Apply Taylor's series method of order p to the problem y'=y, y(0)=1 with h=0.1 and p=3.

A: Taylors Series Formula y1=y0+hy0'+h22!y0''+h33!y0'''+....... We have y'=y, y(0)=1, h=0.1, p=3

Q: Use the method of reduction of order to find a second solution of the differential equation 1²y" +…

A: I have given the answer in the next step. Hope you understand that

Q: Previous Problem Problem List Next Problem ( , The discriminant fxx fyy-fy is zero at the origin for…

A: The discriminant  is zero at the origin for each of the following functions, so the Second…

Q: Find the eigenvalues and eigenvectors for A = The eigenvalue a + bi = The eigenvalue a - bi = 15…

A:

Q: et f: R → R be a function satisfying |f(x) +2| ≤ 4|x - 6/5/³ for all x € R. 110ve that f is…

A:

Q: 4. Let f(x, y, z) = e² + zy² and let C be a straight line segment connecting the points (4,2,1) and…

A:

Q: Define a relation Ton the set of real numbers as follows: Vx, y ≤R, x Ty ⇒xy < 0 The relation is not…

A:

Q: Find the area of the region bounded by the parabola y² = 2x2 and the line y = x - 5. 16 17 18 19…

A:

Q: 1. Find all critical points of f. 2. Classify each critical point that you found in part (a) as a…

A: Given function is fx, y=2x2y-6xy-xy2+3   1. To Find: All critical points of f. 2. To Classify: Each…

Q: 27 7. Find a power series for the function f(x) = 3²-52-2 and its interval of convergence. 8. Given…

A: Consider the given function, fx=2x3x2-5x-2 Now for power series,…

Q: The vector field F = (y², 2xy + e³2, 3ye³z + x) is conservative

A:

Q: Investigate the stability of the region of the system -y, y--r-y(1-x²).

A: Given that : differential equation x'=y , y'=-x-y(1-x2) To find : Investigate the stability of the…

Q: 4).  Find an explicit formula an for the nth term of the geometric sequence whose first term is a1…

A: I have used formula for geometric sequence.

Q: Suppose A is a 3 x 3 matrix with real entries that has a complex eigenvalue 9-3i with corresponding…

A: If x+iy is an eigen value of a matrix then x-iy is also an eigen value of the same matrix. To find…

Q: What is the P(k+1) statement used in the proof by mathematical induction of the formula: Σ=¹² i(i +…

A:

Q: during typhoo Ambo, PAGASA tracks the amount of accumulating rainfall. For the first three hours of…

A: For first three hours, the rain fell at a rate of 25 mm per hour.  So for time 1≤t≤3 the rate was 25…

Q: [9] 6 and let W be the set of all x in R³ such that u x = 0. (a) Show that W is a subspace of R³.…

A:

Q: ( The discriminant fxx fyy-fy is zero at the origin for each of the following functions, so the…

A: 1 Given function is fx,y=x4y4. f0,0=0 In the neighborhood of 0,0, choose any a,b∈R2, a,b≠0. Hence,…

Q: Evaluate fff zz dV where E is the solid tetrahedron with vertices 0(0,0,0), A(1,0,1), B(0, 1, 1) and…

A: Given that E is the solid tetrahedron with vertices 0,0,0,1,0,1,0,1,1. Suppose, the equation of the…

Q: Answer true or false. The function f(t) = (et) ¹0 is of exponential order. O True O False

A:

Q: Provet is a core sequence of tournament the n

A:

Q: Let C be the boundary of the region x + y ≤ 1 and (x+y) ≤ 1 which is oriented counter-clockwise…

A: Given- Let C be the boundary of the region x2 + y2 ≤ 1 and x + y2 ≤ 1 which is oriented…

Q: Use the transformation x = u + (1/2)v, y = v to evaluate the iterated integral ry=2 x=(y+4)/2 y³(2x…

A: Let us consider the function x=g(u,v) and y=h(u,v) The Jacobina is obtained as J=∂(x,y)∂(u,v)

Q: has its largest value. a = Find two numbers a and b with a ≤ b such that b = ⠀⠀ (10+ 3x - x²) ¹² dx

A: To Find: Two numbers "a" and "b" with a≤b such that ∫ab10+3x-x21/3dx has its largest value.

Q: 6. Let and additionally we are given that -3 -5 A -3 1 20 1 1 3 A = 9][8 0 0 3 0 3 0 3 -1 -1 0 5 00…

A: Solution is given below:

Q: 5. Let P([0, 1]) be the space of polynomials on [0, 1] with the norm of uniform convergence, that…

A:

Q: Q2) Show that: The right side of the following equation is equal to the left side, by choosing any…

A: Matlab Code:

Q: Find all the eigenvalues (real and complex) of the matrix The eigenvalues are M = -9 -3 -12 12 6 12…

A: Given Matrix M=-9123-36-2-12126 Eigen value equation M-λI=0

Q: If your system has a subcritical bifurcation and your initial condition is too large, the solution…

A: As per the question we are given the following dynamic system : ẋ = μx + x3 - x5 Now we have to…

Q: 7. Let u and v be two vectors for which ||u||² + ||v||² = ||u + v||² From this information alone,…

A: Given that u2+||v||2=||u+v||2 consider ||u+v||2=u+v.u+v

Q: Consider the following system of differential equations à ý 2x - x² - y 1. The point (-2,-8), (0,0)…

A: As per the question we are given a dynamic system as : ẋ = x3 - y ẏ = 2x - x2 - y Having the…

Q: Given the triangle below, find the following: Note: picture is NOT drawn to scale, but ZB is obtuse.…

A: Here we can use sine formula to find missing side and angles. Sine formula for a triangle is  sin…

Q: Section 14.7: Problem 7 Previous Problem Problem List Next Problem has its largest value. a= Find…

A:

Q: Answer true or false. If L{f(t)} = F(s) and L{g(t)} = O True O False G(s), then ¹{F(s)G(s)} =…

A:

Q: Use the inner product (u, v) = 2u₁v₁ + U₂V2 in R2 and the Gram-Schmidt orthonormalization process to…

A: u1 = (2, 1) u2 = (-2, -5) v2 = u2 - u2, u1u1, u1u1v2 = (2, -5) - (2, 1), (-2, -5)(2,1), (2,1)(2,1)v2…

Q: 9. Let S₁, represent the given statement, and use mathematical induction to prove that Sn is true…

A:

Q: 9).  State whether the sequence, whose nth terms are indicated, is bounded and whether it is…

A:

Q: Is zero a rational number? Why or why not?

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Let A = (a) (b) (c) A :) Show your work. -1 0 6 -12 2 1 0 0 ) Find all eigenvalues of A. A 3) For…

A:

Q: A spring with an kg-mass is stretched by m from a natural length and has damping 1 4 9.8 64 constant…

A:

Q: Consider the graph with 6 vertices of degree 2, 4, 1,1, 6,3, 5. Does the graph exist? Graph does not…

A: NOTE: As given degree of 7 vertices , so we consider number of vertices as 7 ( otherwise question is…

Q: Find the centroid of the region bounded by the graphs of the equations given below. (Round your…

A: Introduction: The formula of centroid bounded by the curves is given by,…

Q: 1 A. Using convolution to find L¹ [(5+2)(s+4)].

A: Convolution Theorem : If L-1F(s)=f(t) and L-1G(s)=g(t) then L-1F(s).G(s)=∫0tf(u).g(t-u)du. (As per…

Q: A mass weighing 16 lb stretches a spring 3 in. The mass is attached to a viscous damper with a…

A: Solution :

Q: Answer true or false. If f is not piecewise continuous on [0, ∞>), then L{f(t)} will not exist. True…

A: