1. Obtain 10 samples of x(t) = 2 cos (10t) from t = -0.3s at a sampling frequency 10Hz. Plot a.) x[n] b.) x[n +3] c.) x[n - 5] and find X(z).

Q: b) The function y(x) satisfies the inhomogeneous second order linear differential equation d²y dy…

A: Variation parameter method

Q: Problem 25. Find the Laurent expansion of f(z) = 1/[2(2-1)(z-2)] in i) 0< < 1 ii) 1 < x < 2 iii) 2 <…

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Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Consider the given parabolas, 2cy-x2=0 and x2-4cy=c2 The graph of the curves in the first quadrant…

Q: 1. Determine the angle between v and the vector w = 2. Solve for an equation of the plane which is…

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: 3. Evaluate Iffa a x dV, S is the tetrahedron bounded by the S planes x+y+3z = 6, x = 0, y = 0 and 2…

A: We have the that S is bounded by the planes : x+y+3z=6x=0y=0z=0 So, from x+y+3z=6 we get z=6-x-y3…

Q: III. Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: As per our policy, we are allowed to attempt the first part of the question. kindly post remaining…

Q: 3. Let 7 and w be vectors such that 7= (2,2, -1), ||w|| = √2, 7-3, and x = (2,-1, 2). a. If u =…

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Q: 4. Let X be a set. Let A, B be the elements of the power set of X, P(A). Define the symmetric…

A: When we collect one or more well defined object and keep them together, it forms a set. The theory…

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂:r = 2-2 sin (in red) and let R be the…

A: Given,C1 : r =3C2 : r =2-2sinθand r &gt; 0 , θ∈[ 0, 2π )

Q: Find the Laurent expansion of g(z) = (2-1)/[23+322 +22] in i) 0 < 2 <1 ii) 3<|2| iii) 0<z +2 <1

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Q: Inverse of a Matrix II. Solve the following 1. Find (1,3) entry of G-¹. 2. Find (3,2) entry of G-¹.…

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Q: Q3: Use finite difference method to solve Laplace equation in the red domain illustrated below. Ax =…

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Q: 6) Let f(z)=(2²-z-1)7. If a²+a+1=0 and Im(a)>0, then find f(a). a) 128a b) -128g c) 128g² d) -128g²…

A: Note: As per our policy, we are allowed to answer only first part of question kindly post remaining…

Q: Allow A be the point with Cartesian coordinates (6, 9), and D be the plane curve with parametric…

A: The slope of the tangent to the curve: y=fx at x=a is f'a. The point-slope form of a line that…

Q: x² T +3y² = z + 3. Consider the surface T with equation 3 1. Find the equation for the trace of T on…

A: Solution

Q: c) y (3) - 54 (²) +254² - 1254 x(esx 125)+25

A: The solution for the asked part is given as

Q: 4.1. Find a power series representation for the function 8 using summation 2x-15 sign, 4.2.…

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Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

Q: 5. (4xdy + 3ydx) + x³y² (xdy + ydx) = 0 Ans: 6x³y4+x6y6 = c

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Q: (d) The Cauchy problem u, + 2 uy = 0, u(x, y) = x² on y = r has: (A) a unique solution (C)…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan x)…

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Q: d) y'= 4y-3x 2x-y

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Q: 10. Determine the value for k for which the two lines are parallel and the value for k for which the…

A: The given lines are       L1: x, y=3, 2+t4, -5   and      L2: x, y=1, 1+s7, k

Q: E be a Euclidean space of dimension (E(1, f)) = dim(Ker (f- id)), then s minimal.

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Q: Find the Laurent expansion of g(z) = (2-1)/[2³3 +32² + 2z] in i) 0 < 2 <1 ii) 3<|2| iii) 0<z +2 <1

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Q: 4. Which of the following is a Legendre's equation? a. (1-x²)y" - 2xy' + 3y = 0 b. (1-x²)y" + 2xy' -…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. y" - 4y + 5y = g(x); y(0) = 1, y'(0) = 0 where g(x) = x if 0 < x < 1, and g(x) = 0 if x ≥ 1

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Q: nonhomogeneous system tY' = 2-2 Y + -2t (₁-²₁).

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Q: Find the Laurent expansion of g(z) = (2-1)/[23+322 +22] in i) 0 < 2 <1 ii) 3<|z| 0<z +2 <1 E

A: As per guidelines we experts are allowed to solve three sub-parts at a time. Please reupload the…

Q: Set up the integral which yields the arc length of the portion of C2 traced counterclockwise from B…

A: This is a question from the application of calculus.

Q: Please choose the right answer for the statement below: Suppose V1,V2,V3,V4,V5 are five vectors in…

A: given 5 vectors in ℝ3

Q: Sky Property cc, a real-estate developer is planning a new apartment complex consisting of 1-bedroom…

A: Consider a system of three linear simultaneous equations with three unknowns.…

Q: Consider the polar curves C1 : r =  4 + (3√2)/(2) cos θ and C2 : r = 2 − (√2)/(2)  cos θ as shown in…

A: Given: C1:r=4+322cosθ  C2:r=2−222cosθ To find: a) Area b) Perimeter

Q: Let S be the quadric with equation 4x² - (y - 3)² + 4z² = 4. What type of quadric is S? Find an…

A: The trace of the surface: f(x,y,z)=0 on any plane is the projection of the surface on that plane.

Q: 4. ( i) Consider the function f(x) = x²-7x+12 x-4 a) Determine the key features of the function: i)…

A: (a) We have f(x) = x2-7x+12x-4 We know x2-7x+12 = x-4x-3

Q: If mx = 1 (mod n) has a solution, then nx= 1 (mod m) has a solution. Select one: O True False

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Q: The logistic growth equation is represented by the equation: dN Nrmox (1-7) dt =

A: Introduction: There are many different types of population models. All the models are based upon the…

Q: Provide a hand-drawn sketch of S using the traces obtained in (1). Label all important points found…

A: As per the question we are given a 3d surface S defined as : 4y2 + 4z2 - x2 - 16 = 0 And we have to…

Q: For what value of a, we have 0= . You may explain your answer below if you like (optional). Give…

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Q: Let f be a function which has an inverse and let f(-1) = 2. If Q is the surface of revolution…

A: As per the question we are given an invertible function f such that f(-1) = 2 And Q is the surface…

Q: ● Considering R(t) is a differentiable vector function for t > -1 with R' (t) = (₁+₁'11²,1 + t²) and…

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Q: 5. Consider the following function: f(t)= Find the Laplace transform of this function. Lis odd -1 is…

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Q: f(x) = sin (2x)| -T≤x≤0 0<x<*

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Q: Find a solution to the given IVP using Laplace and Inverse Laplace Transforms y" + 3y' + 2y = 4t²,…

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Q: 3. Magkano ang nominal wage? Real wage = P10,200.00 CPI = P180.20

A: Here given  Real wage =10,200.00 CPI =180.20

Q: Find the volume of the solid generated by the region bounded by -x + y² = 8, x = -2y and y = -2…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E³r = g(0) = 1/2 500 € C D: r = 3 the…

A: (1)C : r =f(θ) =3-3cosθ,E : r =g(θ) = 32secθSo,C0 : r =f(θ) + g(θ) =3-3cosθ +32secθ⇒r =3-3cosθ…

Q: Find a set of parametric equations for the curve of intersection of the given paraboloid and plane:…

A: Solution:-

Q: 5. D = 2 5 3 4 00 3 0 24 2 1 Evaluate D.

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Q: Lett: V→ V' be a linear transformation. Then (1) Ker (t) is a vector sub space of V, and (ii) im (1)…

A: The solution is given as