Use Laplace transforms to solve the initial-value problem. x'' + 4x = cos t;   x(0)=0, x'(0)=0

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Q: Find the solution. (D5 - 2D3 - 2D2- 3D - 2)y = 0. -3x y = (c,+c,x)e-*+c;e-+e*(c,cosx+c gsinxr) -2x A…

A: Given differential equation is (D5-2D3-2D2-3D-2)y = 0

Q: 1. Are the following matrices diagonalisable? Explain your answer. 2 0 50 1] a) A =-2 3 -1 -2 0 3 c)…

A: A matrix is diagonalizable if and only if for each eigenvalue the dimension of the eigenspace is…

Q: Define f:R → R by ƒ (x) = 5x if x is rational and f (x) = x² + 6 if x is irrational. Prove that f is…

A: Given :  f:ℝ→ℝ  defined by ;         f(x) = 5x,if x is rational.x2+6if x is irrational To prove :…

Q: What is the general solution to the differential equation (3 tan x – 2 cos y) sec?x dx + tan x sin y…

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Q: Which of the following statements is not true? 1) The graph of an odd function is symmetrical about…

A: 1. As when graph of a function is symmetric about y-axis then it is an even function. But in option…

Q: 1. Let n be a natural number with n > 1. (a) Suppose n is prime. Prove that if ab = 0 (mod n), then…

A: In 1)  (a) we need to prove that ab≡0 ( mod n), then a≡0 (mod n ) or b≡0 (mod n ).     In (b) We…

Q: 1. Consider a loaded mine cart weighing 3000 lb with 1500 Ib of high-grade ore from an underground…

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Q: sed betv la y = x² 2

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Q: Consider the following IVP: /" -10y' +9y = 5t, y(0) = -1, y'(0) = 2 %3D Find the general solution. 5…

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Q: Find the Inverse Laplace Transform of (s+4)3 A ³(2cos21 + - sin2t) e-2(cos21+ -sin2t) (2cos21 +…

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Q: Say z1=2+15i and z2 = 3-6i, find z1*z2

A: We have to find z1*z2 where z1=2+15i and z2=3-6i

Q: Enter the matrix P: Enter the matrix D:

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Q: Find the area of the shaded region. r = Vcos 20 r = 6 cos 0 NOTE: Enter the exact answer. A =

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Q: Example #4 MSE A component has the following linear hazard rate, where t is in years Extra Credit 10…

A: The solution provided above is correct.

Q: dan Elimination. 1. x1 + x2 - x3 = -2 2x1 - x2 + x3 = -5 -x1 + 2x2 -3x3 = -

A: We solve this system of equations using gauss jordon elimination .

Q: Tabulate the differences of Euclidean, elliptic, and hyperbolic geometry according to the four…

A: Given: To find the difference between Euclidean Geometry, Elliptical Geometry, and hyperbolic…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 2s + 3 Find the Inverse Laplace Transform of (s+4)3 A e"(2cos2t +- sin2t) 2 (cos2t+ -sin21) (2cos21+…

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: 2) If we know that y,(x) = e2* is the solution for the equation (2) xy" + (2x – 1)y' – 2y = 0 (2) a)…

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Q: Find the solution. y'-y =y2ex A y = с — х с +х B y = с —х y = D y = с +x

A: The solution is given as

Q: Find the solution. dy y dx A y = y = -x+ cx-8 y = y-2 -| 00 B.

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Q: When the insured knows more about their circumstances than the insurer, there is O propitious…

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Q: a. Write in your own words a definition of a complex numbers and Modulus of the complex number.…

A: This is a problem of complex analysis.

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y(t) =…

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Q: Which of the following is the general solution to the differential equation x + (1 +x)y = 6? dx xy =…

A: The solution is given as

Q: Complete the following Truth Table А в сD (A B) (АЛB) (сOD) (C+D) |0 0 0 0 Item 1 Item 3 00 1 0 0 1…

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Q: c) Find u (v x w) if u = [0,0, p], v = [0, q, 0] and w = [r,0,0].

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Q: You are given: (i) H; 1 for 0 Sx <110. 110-x (ii) 8= 0.05

A: We need to find average cost of life insuranceafor a person aged x after 10 years from now. Which is…

Q: 6. Given that z = u' + 2v – x + 3y; u = r´ - s', v = r´ + s´, x = 2rs, y = 4. Find 2 =r dz(r, s, h,…

A: Given, z=u2+2v2-x2+3y2u=r2-s2 v=r2+s2x=2rsy=2rsTo find: dz(r,s,h,k)

Q: [2 - 3 2 – 3 and be express as A = LU as below L4 1 c) Let A = 1 1 2 [2 3 1 1 [U11 U12 U13 - 7 l21 1…

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Q: A pulley and two loads are connected by inextensible cords as shown. Load A has a constant…

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Q: Find the area of the shaded region. Vcos 20 r = 2 cos 0 NOTE: Enter the exact answer. A ||

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Q: dy 1. The linear differential equation dx has the integrating factor equal to (Note: Simplify or…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: X(1) h(t) 2 t 4

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Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

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Q: When the centered difference approach of f (x) = sin r - a+1 is used to estimate the first…

A: When the centered difference approach of f(x) = sinx-x³+1 is used to estimate the first derivative…

Q: Let fcx)=X,XE [ar} Shaw that fe Riemann Loll and find Sede

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Q: Consider and remember that A = (0,4,2) , B = (6,-1,0), C = (3,0,1) 1 1) Determine the unit vector…

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Q: Decide if the statement is true or false. Assume that C#ø, U#Ø, and CCU. UCO

A: The sets C, D are non-empty sets. The set C is a subset of the set U. Therefore the set U contains…

Q: b) Determine whether the matrices L- ), M = [ - 3 - 2 2 4 3 ,and N = -2 2 are linearly independent…

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Q: In a Hardy-Weinberg situation, suppose that 249 out 400 individuals in a population express a…

A: Total individual = 400 Recessive phenotype individual = 290

Q: Consider the following IVP: y"+a?y = 0; y(0) = 1, y'(0) = 0 Find the general solution. A) y(t) = sin…

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Q: 2. Graph the function f(x) = Identify asymptotes and holes in the x2 – 4x +3 graph.

A: If f(x)=p(x)q(x) is a rational function, then (a) f is not defined at the roots of q(x). (b) f has…

Q: he line connecting PC to PT is equal to 125m. If this line makes an angle of 13.5 with the back…

A: Given step by step explanation below

Q: Let A = 2 1 4 so that A4(t) = (t–1)³. Define T : R³ → R³ by T() = Ax. %3D 1 0 3 1 by first (a) Find…

A: Given the matrix A=-10-4214103 so that △At=t-13 and define T:R3→R3 such that Tx=Ax (a) We have to…

Q: Consider the following IVP: у" + у'%3D -сos x; у(0) %3D а, у'(0) 3b Find the general solution. 1 1…

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Q: Find the solution. y' = y - xy3 e-2x A e=x?(y²+c) (A) (в B e2 =x²(y²+c) © e2» =y²(x²+c) e2x…

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Q: Using the Divergence Theorem, evaluate I= F-dS where S is the sphere of radius 2 centered at the…

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