A second order system with a single input and a single output is the state equation given below It is represented by. According to this; a) Explain whether the system is stable. b) Obtain the impulse response of the system.

Q: Sketch the graph of the function below and determine its Laplace transform. u(t-3)-u(t-8) Click here…

A: Given: ut-3-ut-8 To sketch: the graph of given function and find Laplace transform.

Q: Define the mapping 7: R²→R by π((x,y))=x. (Note that R is a group under addition with identity 0).…

A: Here we use the definitions of group homomorphism and the kernel of it . Which are given in solution…

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Q: Express the function below using window and step functions and compute its Laplace transform. 0,…

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Q: Let A be the matrix below. Find the singular values of comma-separated list. Use these to find a…

A: We find required Singular Values of A.

Q: K Three men and three women are waiting to be interviewed for jobs. If they are all selected in…

A: Required probability is 1/20. Explanation is as follows

Q: Determine the intervals in which solutions are sure to exist. t(t − 2)y(4) + e¹y" + 6t²y = 0 -

A: Find the singularities.Then form intervals avoiding them

Q: 2. Equip C[0, 1] with the inner product (f 1g) = f(x) g(1) dr. Define the func tions fi(1) = 1,…

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Q: Q4. Find the inverse Laplace transform of 2s+19 s²-6s+58

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Q: Use Stokes' theorem to calculate JJ (A) nds by A = 3yi-xzi+yz²k where S is the surface of the…

A: The given vector field is: A=3yi-xzj +yz2k The surface S is the paraboloid 2z=x2+y2 bounded by z=2.…

Q: Write the integral that would define the mgf of the pdf 1 1 π1+x² Is the integral finite? (Do you…

A: Solution :-

Q: 24. Let S denote the multiset {o e₁,00 e2, ∞ ek}. Determine the exponential where ho 1 and,…

A: Let us write  the multiset first...and name it as S Then we will define g(x) Given h0=1 n>=1…

Q: Let u= (1,-1,0,4) and = (1,-1,2,0). Find a vector WE R4 that satisfies - 2 w). 4u wü.v(u =

A: The explanation is as follows

Q: Let M₂ (Z) denote the set of all 2 x 2 matrices over the ring of integer. Let + and denote the usual…

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Q: 5. Is it possible to plant 10 trees in 10 straight rows, with 3 trees in each row? Hint: Desargues…

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Q: Consider the matrix [5 A = 1 LO 5 -1] 1 1 O 6 a) Diagonalize the matrix in the form A = SAS-1, with…

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Q: Given the basis B = the basisi B | {Q.B]} Find the change of coordinates matrix from the standard…

A: We find required matrix.

Q: 4. Set up a triple integral to find the volume of the tetrahedron that has vertices (0,0,0),…

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Q: B/ Given a polynomial function with following data points: Find x f(x) 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6…

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Q: {Q.B} 5 e change of coordinates matrix from the standard basis E of R² to the basisi B Given the…

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Q: Check if f (x) = 4x³ + 3x¹ − 12x² + 3 is irreducible in Q[r].

A: Note: As company policy, we solve only the first question. Please resubmit the rest of the questions…

Q: Find the present value PV of the given investment (in dollars). (Round your answer to the nearest…

A: Please find the answer in next step

Q: Determine whether each of the following matrices is positive definite. If it is not, give a…

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Q: 2. A contestant on a game show spins a wheel that is located on a plane perpendicular to the floor.…

A: Solution:- Let the total distance moved be x and the angle moved be θ then the angle moved will…

Q: Evaluate or simplify the following. Your answers should not involve any trig functions and they must…

A: Draw base,opposite and hypotenuse .Find unkowns using pythagoras.

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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Q: Use the Gram-Schmidt process to transform the following sequence of vectors into an orthonormal…

A: To Use: The Gram-Schmidt process to transform the following sequence of vectors into an orthonormal…

Q: Use the method of variation of parameters to find a particular solution of the differential equation…

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Q: Let a, b R and consider the function f defined by: (a) Suppose that we were asked to determine the…

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Q: Q5. Consider the following three functions: f: Z+xz+ →Z+ f(m, n) = mn g: Z → Z g(n)=n-9 h: RxZ+→Z+…

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Q: Let a11 a12 a13 A = a21 a22 a23 a31 a32 a33 3 x 3 real matrix and consider it as a linear map A: R³…

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Q: Example 0.5.1. Given the function g(x, y, z) = x² + 2y² + 3z². Find a unit vector u such that the…

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Q: (d) If F(x, y) = (4x² - y², -2xy), then f(x, y) =

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Q: 1. How many elements are there in Z 2. List all elements in Zis 3. Answer either'true' or "false"…

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Q: Use the Remainder Theorem to find the remainder when f(x)= 3x² + x³ -3x+1 is divided by x + 3 erify…

A: Given that fx=3x4+x3-3x+1 To use Remainder theorem to find the remainder when f(x) is divided by…

Q: Q7. Solve the following equations: 3.2. cos¹ 4x-sin' 4x+x

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Q: Find the value of (T) for a solution (x) to the initial value problem: y" + 25y = 10 cos 5x; y(0) =…

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Q: Find the solution of the given initial value problem. 7y""+154y' - 2436y = 0; y(0) = 10, y'(0) = 69,…

A: We have to solve the given system of equation using the given conditions.

Q: Consider finding the root of f(x) = e*(3.2 sin(x) - 0.5 cos(x)) on the interval [3, 4], this time…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Solve the initial value problem below using the method of Laplace transforms. y" +36y=72t²-72t +…

A: Introduction: Laplace transformation can also be used to solve differential equations. The equation…

Q: Determine the Laplace transform of the given generalized function. 31³8(t-3) 231³8(t-3)} (s) =

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Q: Find the present value PV of the given investment (in dollars). (Round your answer to the nearest…

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Q: Consider the following initial value problem. Determine the coordinates tm and ym of the maximum…

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Q: Let A = {-42, -7, -6, -2, 1, 10, 11, 29} be a set. Define a binary relation R on A as follows: For…

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Q: Use the method of variation of parameters to determine the general solution of the given…

A: Sol:- y''' +y' =tantThe general solution to anxyn+...+a1xy'+a0xy=gx can be written asy=yc+ypyc is…

Q: (a) Find x, y, z and B, where Го 3 A = 1 -3 y 4 4 ; A² = 1 ; c(4+1)+3BT = 2A and I: unit matrix

A: (a) To Find: x, y, z, and B, where A=0x31-3yz44;   A2=I;     cA+I+3BT=2A and I:unit matrix

Q: Solve the triangle. a = 65, b = 22, c = 47 A≈ B C≈ с (Do not round until the final answer. Then…

A: Introduction: The law of cosines describes the relationship between a triangle's side lengths and…

Q: Use the Definition to find an expression for the area under the graph of f as a limit. Do not…

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