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Q: t) = y"+y= √2sin(√√√2t), y(0)=9, y'(0) = 0

A: Given,        y''+y=2sin2t, y(0)=9, y'(0)=0

Q: DERIVATIONS PROVE THAT THESE ARGUMENTS ARE VALID no truth tables ((PVT)-(SR)) + (-S-P) 1.…

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Q: 1o₂ = 2 · (² x (+) · cos (nwot) at O 11 2 1 = 2 25+ (1-1) cos (2nrrt) dt = 21- - [² (1-t) d 2 Los (n…

A: Using the integration by parts can be stated that: ∫udv=uv-∫vdu.

Q: "The auxiliary equit of the given diff- is m² +6m +8 = 0 2 m² tym + 2m +8=0 2 m (m+4) +2 (m+ 4) = 0…

A: The auxiliary equation , m²+6m+8=0 ⇒m²+4m+2m+8=0 ⇒m(m+4)+2(m+4)=0 (by, taking common m from m²+4m…

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Q: For the curve x³ + y² + 2xy = 4x Find all the x-intercepts of the curve. Then for each x-intercept…

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Q: F, (w) -1 a+jw -8 7 a + jw

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Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: jw)²x1 w) = - w2x/w) = 21 A (b-a) 24 (b-a) sin (bw) - sin(aw) 120)] [sin (bw) - sin(aw)

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Q: (jw+4) (jw+3) (jw+2) (jw+3) + B (jw+2) A(jw+2)+B(jw+3) (jw+3) (jw+2) Ajw+2A+Bjw+3B (jw+3) (jw+2)…

A: Introduction: The partial fraction decomposition is a method to simply a fraction that is written as…

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Q: 2. Given that F(x, y, z) = (e, xey + e², ye²) is a conservative vector field. a. Find a potential…

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Q: Suppose U = {1, 2, 3, 4, 5, a, b, c) is a universal set with the subset A = {a, b, c, 1, 2, 3, 4).…

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Q: S In x (a² + x²)2dx.

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Q: Show that the function y1 = 1 / t is a solution of the first order Riccati differential equation…

A: Given differential equation is y'=1t2-1y2- 1t2-1 Rewrite it,  y'=1t2-1y2-1  ------(1) Also, given…

Q: . (a) How many quadratic residues are in the residue set Z₁9? (b) Determine if 4 and 9 are quadratic…

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Q: Given't fltje [ The Fourier Series f(t) = findi 1 a b 17750! 27751 a + b + = 2 I sin nit Ž b TT n…

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Q: f told that |A| = 18 find the possible value(s) for x                                3x        x…

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Q: Use the Midpoint Rule and Simpson's Rule to approximate the given integral with the specified value…

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Q: 39. y (0, 3) C.4 D. 7 R What is the length of RL? A. 6 B. 5 L (4,0) X

A: In the given problem Length of the line is RL=5 Hence option (C) is correct.

Q: Find a general solution for the given differential equation with x as the independent variable.…

A: Given differential equation is y''' + y'' - 6y' = 0

Q: X 3. Solve the equation y'+ xy = with the Bernoulli substitution method. y

A: To solve the following problem, we use the Bernoulli substitution method. Then the problem convert…

Q: By the Mean Value Theorem, we know there exists at least one c in the open interval (-4, 4) such…

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Q: Find the critical numbers of the function f(x) At x = At x = At x = = 12x5 + 15x4 - 20x³ – 6 and…

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Q: PROBLEM SOLVING: Evaluate the following integrals | 1. Jdx/(x-1) ² 2. JV (4-x) dx 3. (9-x) ¹/3 dx…

A: Since you have posted multipart question we'll do first three parts of the question. If you want any…

Q: Solution Given that, and F.T X(t) = y(t) = x (2+-1) ēst x(w) and x(w) 1. F{y(t)} = Y(w) = (y(t) =…

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Q: Find a basis for the subspace of RA spanned by S. S = {(2, 5, -3, -5), (-2, -3, 2, -2), (1, 3, -2,…

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Q: 10. Consider the initial value problem y" +ay+y=k8(t-1); y(0) = 0, y(0) = 0, where k is the…

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Q: Compute the volume of the solid bounded by the hemisphere z = = √4c² - x² - y² and the horizontal…

A: The given problem is to evaluate the volume of the solid bounded by given hemisphere z=√(4c2-x2-y2)…

Q: 1. 2. (2y³ +42) dx = (62-2xy²) dy 1 yy" + (y)² = yy' y(0) = 1, y'(0) : 11 2

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Q: Prove that at a party where there are at least two people, there are two people who know the same…

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Q: (a) Test the convergence of the series given by (r+1)! Σ r!(er) r=1 . G C M . 2

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Sketch the motion of a particle with position as: x = 5 sint y = ²/-nstsn - St≤n as tvaries in the…

A: We need to plot the motion of the particle, whose position is defined as: x=5sint, y=t2 in the…

Q: Question 13 Write a system of equations to model the problem. Be sure to define your vairables.…

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: 8 A LTI system is described by the D.E. ÿ + 6 ý +8y -2t find h(t), then find y(t) if X(t) = te²t…

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Q: How did he get the 2t1 = x (zt-1) = d* value inside the circle 2 dz 11 인(豐)(x(z) 한(豐)로 e dz j(엘) x(t…

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Q: Let TE B(H) be a self-adjoint operator on a Hilbert space H (a) Use the continuous functional…

A: Given that: T∈BH be a self-adjoint operator on a Hilbert space H. The objective is to show that: a…

Q: dy__=1 with the homogenous substitution method. Solve explicitly. 7. Solve the equation dx x² X…

A: Introduction: If the degree of both f(x,y) and g(x,y) is the same, a differential equation of the…

Q: Write the given system in the matrix form x' = Ax+f. r(t)=9r(t) + cost e(t)=r(t)-20(t)-4 Express the…

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Q: (Note: since the determinant is unchanged by row reduction it will be easier to calculate the…

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Q: IA LTI system is described by the D.E. y +6 Y+8y=2 -2t find h(t), then find y(t) if X(t) = te²t tro-

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Q: Use Euler's method to make the graph of the following functions on the given interval. a) dx/dt = t…

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Q: 7) Write the quadratic function, f(x)=x²-2x-8 in vertex form and then find all of the following: a.…

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Q: Describe the steps in words that you would use to show that (x-a) is a factor of x" - a". Your…

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Q: (e) Second order differential equation 3. The nontrivial analytical solution of (a) 3-et dx x + dt…

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Q: If r is an independent variable and r with a subscript (like ,,,, etc.) represents given data points…

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