Q3: Solve the difference equation: y[k] -y[k - 1] +y[k - 2] = ( using Z transform.

Q: d²p If 2 dq² dp 7- +4p = e³x, what would be the solution for the particular integral? dq

A: Given the differential equation, 2d2pdq2-7dpdq+4p=e3x

Q: 4. Prove that the following curves are intersecting with a right angle: 5y-2x+y²-x²y = 0 2y +…

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Q: What is an algebraic system?

A: Answer What is an algebraic system?

Q: Бxї Zet (x, г) бе space, then Co-countable тебя xis not Тз-брасе

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Q: Figure Y Part A Determine the moment of inertia of the composite area about the axis Set a = 250…

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Q: b) The system of nonlinear equations above has a solution near the point (x₁, y₁) = (1,1). Taking…

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Q: Problem 8: By integrating an appropriate branch of semicircle, show that S (In x)² x² + 1 dx 773…

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Q: 2. Produce the linear and quadratic Taylor polynomials for the following cases. Graph the function…

A: Given functions are 1)  f(x)=x,a=1 2) f(x)=sin(x) ,a=π4 3) f(x)=ecos(x) ,a=0 To Find : Linear and…

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: A child bought 4 pears and 3 apples for 90 cents. The next day they bought 3 pears and 4 apples for…

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Q: A line OP makes equal angle with coordinate axes then find its direction cosines...???

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Q: By using Laplace transform to solve y" - y = et with y (0) = 1 and y′ (0) = 0 , what would the…

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Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given : x'=1-40-201006-12-1-60-40-1x  ; x1=e-t1001  ; x2=e-t0010  ; x3=et010-2 ; x4=et 1030 (a) To…

Q: Construct a niche overlap graph for six species of birds,where the hermit thrush competes with the…

A: Given That : There are six species of birds  The hermit thrush contends with the robin andwith the…

Q: List all subsets of {a, b, c, d, e}, containing a but not containing b.  

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Q: as a definite integral. Express lim 81x i=1 2 - n In(1+ 2i n

A: What is Definite Integral: Definite integral is the sum of areas of all possible rectangles over an…

Q: let T be a linear operator on a finite- dimensional vector space V, and let f(t) be the…

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Q: Evaluate these complex numbers: (a) _2 – j] (b) 6 30° + j5 –- 3 + e45°

A: To find- Evaluate these complex numbers:  j31 + j2 - j2 6∠30° + j5 - 3 + ej45°

Q: 10 69 8 7 6 5 ST 3 2 1 2 3 4 5 6 7 8 9 10 Consider the (x,y) coordinate grid above. The grid also…

A: Hint: It is given that (5,6) is placed on the graph facing southwest.

Q: Three sets have 5, 10, and 15 elements, respectively. How many elements can their union and their…

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Q: Calculate the following double integrals and draw the region of integration.

A: Given: The integral is ∫12∫yy3exydxdy. To find: The value of the given integral. To sketch: The…

Q: Find the sum of the degrees of the vertices of each graph in Exercises 1-3 and verify that it equals…

A: We know that, Degree of vertex is the number of edges passing through that vertex. We need to…

Q: Determine the velocity vector of the given path r(t) = (6 cos² (t), 2t - t³, 3t)

A: What is Velocity Vector: The velocity vector of a given path is nothing but the rate of change of…

Q: Explain Special Linear Group is a Normal Subgroup of General Linear Group?

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Q: he figure shows the flow of traffic (in vehicles per hour) through a network of streets. (Assume a =…

A: We creat equation of the flow of traffic X1 = 400 + X2 X1 - X2 = 400.............(1) X4  = 200 +X2…

Q: The graph of 7 is shown on the coordinate plane. Selected values for g are shown in the table. Graph…

A: Given : x-value -2 0 5 6 g(x) values 1 4 3   limit values of g(x) limx→-2 gx=5 limx→-1 gx=4…

Q: the values of the elements of an RLC circuit are given. Solve the initial value problem di - i(t) dr…

A: Given: The initial value problem is Ldidt+Ri+1C∫0tiτdτ=et and the condition is i0=0. The given…

Q: Using steepest descent optimization method, determine a minimum of: f(x) = x² + 3x² Starting from…

A: The function given is as follows: fx=x12+3x22 We are asked to find the minimum of the function using…

Q: P(3, 1), Q(6, 5) and R(x, y) are three points such that PRO is a right angle and the area of ARQP is…

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Q: Energy Savers, Inc., produces heaters of types S and L. The wholesale price is $40 per heater for S…

A: The linear function(cost function or the profit function etc.) that needs to be optimized(maximize…

Q: Suppose that p(t) is a differentiable function with $'(1) S kø(1) (k > 0) for 1 2 a. Multiply both…

A: Given: Suppose ϕ(t) is a differentiable function with ϕ'(t)≤kϕ(t) (k>0) such that ddtϕ(t)e-kt≤0.…

Q: c1x1(a) + c2x2(a)+ . . . +cnxn(a) = x(a). Let X (t) be the n x n matrix with column vectors x1, x2,…

A: Given : Xt be any  matrix of n×n           : c be column with component c1 ,c2 , . . .  . . .  ,cn…

Q: In this worksheet, you will be defining 30 unique matrices denoted by the letters of the alphabet.…

A: 2) D , E , F are 4×4 matrice. D=2460-1817325-42560 E=12-432504329-376705818-8335570-67…

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Given : x'=-32-34x     ;  x1=e3t3e3t   ,  x2=2e-2te-2t To Find : (a) Verification              : (b)…

Q: find the number of vertices, the number ofedges, and the degree of each vertex in the given…

A: We know that , In a graph vertex is node of a graph. Degree of a vertex is known as number of edges…

Q: explain the nature of mathematics with exaple

A: Hint: First explain the nature if mathematics then given an example of nature of mathematics.

Q: [cos 20-i sin20cos 30+ i sin301² [cos 40+ i sin40 ]³[cos 20-i sin2015 using De Moivre's theorem?

A: We have to solve given Questions.

Q: In the following problem apply the eigenvalue method to find a general solution of the given system.…

A: The given system is x1'=5x1-9x2x2'=2x1-x2 So, the matrix is A=5-92-1 We find the eigenvalues.…

Q: 3. Let R be the region bounded by the following curves. Use the washer method (slicing method) to…

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Q: A line OP makes equal angle with coordinate axes then find its direction cosines.

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Q: Let g(x)= Find the domain of g(x).

A: The domain of a function is the set of all possible inputs for the function

Q: (2) Consider a thin plate, which occupies the region D in the xy-plane bounded by the curves = y²…

A: We will find limits for boundary region and then integrate it to find area and mass of the region

Q: Eliminate the arbitrary constants from y = method and determinant method. C₁e* + c₂e-* by the…

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Q: In the following problem apply the eigenvalue method to find a general solution of the given system.…

A: Given: The system of equations are  x'1=3x1+4x2  x'2=3x1+2x2 ;   x1(0)=x2(0)=1 To find: The general…

Q: Prove that if every subgraph of G has a node of degree at most d, then G is (d + 1)-colorable.

A: We know that G is itself a sub graph of G, so G has maximum vertex degree d. A standard result in…

Q: Explain Proper and Improper Nodes?

A: To explain: Proper and improper nodes. A vector that is associated with the set of linear equations…

Q: Problem 2) a) Write a function to factorize a matrix A into A=LU with Doolitle's method (not use the…

A: Given That : component Metal plastic  Rubber 1 15 0.30 1 2 17 0.40 1.2 3 19 0.55 1.5…

Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: write these numbers in polar form for the complex setup: (1,-1,i,-i)

A: We know that , Complex numbers are of the form z=x+iy, where x and y are real numbers. Also Polar…

Q: Describe and graph the regions in the first quadrant of the x1x2-plane determined by the given…

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