y" + 3y' + 2y = 12x²; y(0) = a, y'(0) = b

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Q: Laplace A H(s) %3D s2 –9 s2+9 B H (s) s2-9 s2+4 3 3 C H(s) + s2-4 s2+4 6. H(s) + s2+4 s2-4 2.

A: Given function is h(t) = 3sinh(2t) + 3sin(2t)

Q: MO22. A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has…

A: We use the p-value formula.

Q: Evaluate the following double integral 1 V- 2' (r° + y°)* dydr. -1 0

A: First we convert the integral into polar coordinate and then we solve the integral.

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A: Draw a rectangle ABCD and join the points A and C. Note: Opposite sides of a rectangle are equal.…

Q: contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per gallon is flowing…

A: Given that a tank contains 60 gallons of pure water. A mixture consisting of 1 pound of salt per…

Q: Find the Laplace transform of f(t) = 6e +e* + 5t² -9 16 4 F(s) = - +- S-5 9. A + S-4 5 F(s) = - S+6…

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Q: VI. Instruction: Write the truth table for each of the following compound statements and determine…

A: First we construct the truth table

Q: An airline offers coach and first-class tickets. Fo the airline to be profitable, it must sell a…

A: This is the question of LPP and optimization.

Q: 10. M OM = %3D PN = %3D ON = MN = %3D N *LN = 46

A: 10 Consider the given figure. Given figure is a square Here, LN=46 From the property of square, we…

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Q: 1. 43y こ。 It ex

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: IF F= 3yI - Xy I+ 9ZK and s is the Surface of the Pasabolied 2X =x2 fy Bounded By Evaluate %3D I=2…

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Q: What could be the general solution to the differential equation dx - xcot(2y) = x³csc(2y) ? dy 1 =…

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Q: The accompanying table shows the number of bacteria present in a certain culture over a 4 hour…

A: Given The table show the number of bacteria present in a certain culture over a 4 hour period where…

Q: apply stok's Theorem to evaluate (Ydz +7dy+ xdz) whereCiB the curve of intersection of x²+ y²+z² =…

A:

Q: 1. Find the Taylor series polynomial expansion of degree 5 of the function cos x at a == 2

A: We want to find Taylor series of f(x) = cos(x) at a = π2

Q: Determine whether the lines Lj and L2 are parallel. L1: x = 1 – 2t, y = 2 + t, z = 5 – t L2: x = 4 –…

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Q: Question 24 Find the Inverse Laplace Transform of s2+4s +4 A te D le -2 2.

A: Inverse Laplace transform

Q: 相 3. Let S = and T = be ordered basis for R. Let v = 5 (a) Find the coordinate vectors of v with…

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Q: Match the graphs on the left with the correct equations on the right.

A: The value of sine function  and cosine function is given as x 0 π2 π 3π2 2π y=sinx 0 1 0 -1 0…

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A:

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

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Q: Which of the following is the general solution to the differential equation (х — 4у — 3)dx — (х — бу…

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Q: Jompute the line integral | (yzev +y? + z - 2r) dr + (rze"ys + 2ry) dy + (rye*v= +x +32?) dz, where…

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Q: 2 2 A = 1 2 1 1 1

A: Solution:-

Q: For the system below, find the critical points, sketch the direction fields in the phase plane and…

A: The solution of the problem is given in the next steps.

Q: 1. y' = et ; y(0) = 2

A:

Q: Question 4 The parametric equations for a line L1 are as follows: x = 4+2t y = -1-6t z=-3-4t Let L2…

A: Introduction: In three dimensional geometry, a line can be represented in any of the three different…

Q: Lone Divider Method|| Use the lone divider method to solve the following problem. 5. There are 3…

A: The Lone Divider method works for any numbers of participants. There is one participant called…

Q: When the ratio test is applied on the power series > Cn(x – 4)", the resulting limit is Which of n=0…

A: Here we use ratio test formulas.

Q: Find the area to the

A: Given, the left of z=-1.96 or to the right of z =1.96.

Q: Find the Laplace Transform of (t? +4t + 2)e* 2 (A (s – 3) 3' (s- 3)² 's-3 4 2 B (s – 3) 3 (8 – 3) 2…

A:

Q: the physical dimensions of an object?

A: To define: Physical dimensions of an object.

Q: L = {cos (–5t)} L = {e-3t sin (5t) } 5 s2+25 (s+5)+9 s2– 25 (s+3)+25 s2+25 (s+3)–25 s2+5 (s+5)+25

A:

Q: Show that if f: A-> B is continuous and A is compavt then f(A) is also compact

A: Let , f : A →B be continuous function. Here , A is compact set. We need to prove that , f(A) is also…

Q: (2.3) Let pi = 2-x+x²,p2 = 1+x, p3 = x+x². Show that S = {p1. P2, P3} spans P2. Conclude that S is a…

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Q: What is the general solution to the differential equation dx + (4) dy = : ) 2x²y²dy ? 2x3 – y3 = Cx…

A: Given differential equation is dx + 2xydy = 2x2y2dy

Q: 3. Let P be a projection on a Banach space X. If ace, then these are closed linear subspačes of X .

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Q: Find dy/dx for y = J_1P+4 t2 dt t2+4 X. 3

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Q: Let f(n) = n and g(n) = log2 n. Show that g e O(f) but f ¢ O(g).

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Q: A regular pentagon has sides of 20 cm. An inner pentagon with sides of 10 cm is inside and…

A: We have to find the area inside and concentric to the larger pentagon but outside the smaller…

Q: Which of the following is the general solution to the differential equation (2х + 3у — 1)dx + (2х +…

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Q: 4. ".p>-1

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Q: 3. Find the solution of the heat equation = 0 if the boundary conditions are = 0 %3D and the initial…

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Q: Answer each question correctly. Show your complete solution The complex number 2 + 4i is one of the…

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Q: Let f : R? → R be defined by f((x, y)) = 8y – 5x + 8. Is f a linear transformation? a. f(x1, Y1) +…

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Q: | (3z + 4) dy 2.

A:

Q: (1.3) Using part (1.2), find the "negative" of C): Explain clearly.

A: Introduction: In a vector space, zero vector is very significant. Under the operation addition, zero…