1. Find the general solution of the given differential equation using MUC: y(4) – 4y(3) – 21y(2) + 104y(1) – 80y = x² e2* + 3 – 5 cos 3x.

Q: Find the volume of the solid of revolution generated by revolving the region in the first quadrant b...

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Q: . Show that x2 + 3 and x2 + x + 1 over Q have same splitting field.

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Q: schools’ enrolment this year increased by 20%. What was last year’s enrolment if there are 4,800 stu...

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Q: Find the solution of the given initial value problem using Method of Variation Parameters (MVP): (35...

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Q: In which one of the choices below is the given triple integral not equal to II dxdzdy? Select one: O...

A: Using the limits of integration, following result can be concluded.

Q: A trucking company transports goods between two cities that are 960 miles apart. The company charges...

A: Given:   Total miles 960 $0.55/mile  1st 100 miles $0.35/mile  100 - 400 miles $0.25/mile  400 - 800...

Q: A point in the complex plane with both coordinates rational is called a rational point. The set of r...

A: Please find the answer in next step

Q: Suppose that consumer has the following utility function: U(X,Y) = X2 + Y2. Which of the following i...

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Q: =-rگت( (1+ V5) )(n- 2) < fn (п— 2) Use induction to prove that 2 ((1+ |(n–1). for all n 2 3.

A: Introduction: One of most important sequences in mathematics and number theory is Fibonacci sequence...

Q: YA 10 Translate image MATH -9 -8 -7 3-2-1 0 1 345 6 7 8 9 10 -1 -2 -3 -5 -6 -7 prelim image -8 Descr...

A: The pre-image is represented in blue color, and the transformed image is used in yellow color.

Q: Determine the surface area generated when a portion of the curve in the first quadrant of y? = 4 + i...

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Q: Question 5 Flog question Find the volume generated by revolving the area bounded by x2 – 4x – 4y + 4...

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Q: x/2 1. Let F(x) = | f(t) dt and G(x) = | g(t) dt, where the graphs of f(x) and g(x) on [0, 6] are be...

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Q: Given system of linear equations: х+у—3z %3 4 2х + 4у — 4z %3D 5 —х + у + 4z %3D —3

A: Solve using Cramer's Rule. Show complete solutions.

Q: Let A = [aij] given by a x bij = (i-j)^3 is a: * Anti-Symmetric matrix Symmetric matrix Identity mat...

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Q: Consider the function f (z) = ²-sin z z3 The Laurent series of f (z) around 0 is : 1 z2 a) 3! 5! 7! ...

A: Given: f(z)=z-sinzz3

Q: Question 4 Find the volume generated by revolving the area bounded by x² + 4x + 4y + 8 = 0 and y = -...

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Q: 9. Test the following for convergence (p and q denote fixed real numbers): (a) Σ1P"n"; p > 0

A: Please specify which subpart is to be solved. Here is the solutions of subparts. (i) The given serie...

Q: Let Ax = b be a linear system whose augmented matrix has a reduced row echelon form given by: 1 0 -1...

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Q: (3) If today is Thursday what day of the week will it be 31 days from today? (4) If it is currently ...

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Q: 10. Find the polar form of -4 + 4i.

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Q: (;) x-(; )* 1 2 K1 = X' = (cos2t + C2 cos2t (cos2ty sin2t. X = c (o) e cos2t X = c; () e' + cz () te...

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Q: graph. Find the area common to the circle r = 3 and the cardioid r = 3(1 – cos 0).

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Q: Find the moment with respect to x = 2a the area bounded by x = 2y and x? = 4ay. %3D %3D

A: Given the region bounded by the curves y=x2 and y=x24a. We need to calculate the moment of inertia a...

Q: Let y sin(5x). If Ar 0.3 at z 0, use linear approximation to estimate Ay %3D Ay = = Find the percent...

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Q: A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population ...

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Q: Use a truth table to determine whether the argument below is valid or invalid. pA (q V r) ... ~pV ~ ...

A: Given argument p∧q∨r~q∨~r

Q: Use finite approximations to estimate the area under the graph of the function f (x) = x³ between x ...

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Q: -2 2 1 -3 6. -1 1 -7 10

A: We have to reduce the following matrix 2-221-360-11-7102 to Row Echelon form and then reduced row ec...

Q: Consider the function of two variables defined by: f(x,y) = (x3 - y4) / (x-7210)2+(y-9245)2 What p...

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Q: Question 7 Find the volume of the solid generated by revolving the area bounded by x – y? + 6y – 9 =...

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Q: Find the volume generated by revolving the area bounded by x2 + 4x + 4y + 8 = 0 and y = -2 about the...

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Q: Stati lue or talse eilh neces ons The Green's function does not exist for the boundary value problem...

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Q: Given the matrix and its eigenvalues 28 -8 52 - 12 Find the eigenvalues for this matrix, then use th...

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Q: The variables m and n satisfy the differential equation: dn (2n — т) ——3 n; т > 0,п > 0 dm SHOW that...

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Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs o...

A: See below for the solution.

Q: min 4a1 + 5xз subject to 2x1 + x2 – 5x3 -3x1 = 1 + 4xз + х4 — 2 Ti > 0,і — 1,2, 3, 4.

A: As per Bartleby guidelines we're supported to answer only first one question when two or more questi...

Q: 7. Let T : V space W. Prove that the range of T is a subspace of W. → W be a linear transformation f...

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Q: ー0 Let A = -3 -8 %3D そ 14 Label the colmn vectors C ,s,C3, and Cy respeutively. let b. be a linear C...

A: The given matrix is ;                     A =  577-10-311-86713914 If  C1 , C2 , C3  and  C4  are th...

Q: 4. A solution curve with initial values F(0) = 5 and H(0) = 10 is sketched in the figure on the left...

A: Introduction: The slope field or direction field visualizes the nature of the family of solution cur...

Q: Find the area of the region bounded by y = x2 + 2x - 1, y =+x- , x = -3, x = 1.

A: As per our guidelines, we are supposed to solve only one question. Kindly repost other question as n...

Q: 1-z Let C: z-il=9. Then ſ. dz = z(z+1) а) 0 b) 2ni с) —2лі d) 4ni e) — 4пі f) 2п

A: Multipart:    We have , gz = 1 - zzz + 1 gz = 1zz + 1 - zzz + 1 g(z) = 1zz + 1 - 1z + 1 We need to f...

Q: 3. Which of the following is the Laplace transform of sin (2t) - 2tcos (2t) ? A. s^2 / (s^2 + 4) ^2 ...

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Q: A car sales agent sold a car for P280,000 and he received a commission of P35,000. His rate of commi...

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Q: An object of mass 20 kg is released from rest 4000 m above the ground and allowed to fall under the ...

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Q: -3x1 + x2 + 12x3 = 50 6x1 – x2 – x3 = 3 6x1 + 9x2 + x3 = 40

A: Here we consider X1=x,  X2=y, X3=z (for Easier to solve) .  So, 

Q: Question 2 Find the area bounded by the parabolas (x – 1)² = 4ay and y² + 4a = 4ax. %3D

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Q: — 3x1 + х2 + 112х3 %3D 50 бх1 — х2 — х3 %3D 3 бх1 + 9х2 + х3 %3D 40

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Q: 3. The Cartesian coordinates of a point are given. (i) Find polar coordinates (r,0) of the point, wh...

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Q: A cylindrical tank of radius 5 ft and h.

A: Given, a cylindrical tank of radius 5 ft and height 6 ft is two-thirds filledwith water.