Obtain the genral solution to (D5-15D³+10D² +60D-72)y=0 y=e²x(C₁ + C₂x) + e-³x(C4+C5x) y=e²x(C₁+C₂x + С3x²)+e³x (C4+ C5x) y=e-2x(C₁+C₂x + C3x2)+e-3x(C₁+ C5 Oy=e²x(C₁+C₂x + C3x²) + е-3x(C₁+C5X

Q: Solve: си ch= -|P I/2 (1) 2012/0 dt

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Q: # of Aqua-Spa hot tubs to produce = # of Hydro-Lux hot tubs to produce X 350x₁ + 300x₂ x₁ + x₂ ≤ 200…

A: # Solving by Simplex The given LPP is Max Z= 350x1+300x2 x1+x2≤2009x1+6x2≤156612x1+16x2≤2880x1,x2≥0…

Q: IV. Approximate the following up to 4 decimal places using Maclaurin's series... 1. sin (110) 2.…

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Q: The expression dy/dx = x(cube root^3 y) gives the slope at any point on the graph of the function…

A: Consider the differential equation dydx=fx,y with the initial condition yx0=y0. Substitute the…

Q: |3z +48z = 5 cos(4t) |3z +53z5 cos(4t) |3z +25x' +48z = 5 cos(4t) ✓3r |3x +22r' +48z = 5 cos(4t) |3z…

A: solution is given below:

Q: 2) For the vector field F(x, y, z)=(xz²-x²y)i + (xy²-y³2²)] +xy²z³k, find the following: a) Find the…

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Q: Find the inverse of AB if 5 -1 A-¹. and B-1 = -5 -5 5 4 [84] 0 -1 (AB)-¹ = E

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Q: Example 10: Define T: R" → R", x = (X1, X2,...,xn) → (X2, X3,..., Xn, 0), with the Euclidean norm.…

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Q: Let F be a commutative ring with identity and let f(x) € F[x] be a polynomial of degree 4. Which of…

A: It is given that F be a commutative ring with identity and f(x) ∈ Fx be a polynomial of degree 4.…

Q: Create a truth table for the statement: r⇒ (p^q)

A: Answer :- Truth Table can be formulated as given below:-

Q: From which we have (a₁ + a₂) D+ (a3 + α4 + α5) d−(1 − A) (B₁ + ß₂) D² = (1 − A) (B3 + ß4 + 35) Dd…

A: given  D=AD+α1D+α2D+α3d+α4d+α5dβ1D+β2D+β3d+β4d+β5d simplify the terms…

Q: Answer True/False   D) The zero vector is always an eigenvector for a linear transformation. E)…

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Q: Find the critical numbers of f (if any). Find the open intervals on which the function is increasing…

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Q: ·[²₁₁-²² Compute (a) Trapezoidal rule de using the

A: Given integration is I=∫-11e-x2dx here f(x)=e-x2 For n=2 subinterval step size is h=1-(-1)2=22⇒h=1…

Q: дгу ду дх2 5- · + 4y = 0 дх In

A: Given differential equation is y''−5y'+4y=0.....1. We have to find the solution of the expression…

Q: Find the area of the region bounded by the curves y = sin (7x), y + 1 = x², 3x = -2y on the interval…

A: 1st we will draw the solid of rotation and then use cylindrical/shell method to find volume of the…

Q: A tank full of water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide, and 25 ft…

A: The total work done by pumping part of the liquid in the container to any point P above it's top is:…

Q: Let a graph have vertices i, j, k, l, m, n and edge set {{i, j}, {i, m]}, {i, n}, {j, k}, {j, m},…

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Q: Two hundred fifty-eight TCC faculty members were surveyed regarding their plans for the upcoming…

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Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: to itself. Show all your work to recei

A: given as,

Q: A 5 1 -3 9 7 -5 5 Apply Gram - Schmidt process to columns of to make matrix Q, Whose columns are…

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Q: The temperature at a point (x, y, z) is given by T(x, y, z) = 300e-x²-3y² - 9z² where T is measured…

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Q: max f(x, y, z)=x+2z s.t. x+y+z=1 is (x. y. 2) = (0. - 12/2) with Lagrange multipliers equal to ₁ = 1…

A: Solution of First question is given below:

Q: 6. Find complementary function and particular integral of the following differential equation: (D-…

A: 3

Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: V ). I) For any linear transformation T : V → V , ker(T ) ≤ ker(T2).

A: Please find the answer in next step

Q: * finel fx, fxx, by

A: Note:- As per our guidelines, we can answer first three sub-parts of this problem as exactly three…

Q: a) Draw the corresponding Venn Diagram. b) Find the following: 1)n(A) 5) n[(AB) C] 6) n[(A' B') C]…

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Q: Solve: си -|P TE I/2 22 (1) 24 ( он То dt

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Q: Show justifying that if A and B are square matrixes that are invertible of order n, A-¹BA then the…

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Q: Write down the first five terms of the following recursively defined sequence. a₁ = -2; an+1 = -2an…

A: In the given problem it has been given that  a1=-2 an+1=-2an+7 the aim is to find the first five…

Q: • Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…

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Q: (2x + y - 3z = -9 | x + 5z = 14 | −3x + 2y - z = 4). From 3 (three) equations, what is the value of…

A: Solution :-

Q: 3 Consider a linear transformation To R₂ [x] → R² whose matrix relative to the bases B = {x ²₁ x, 1}…

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Q: Consider the following function. f(x) = x6/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2 (a) Approximate f by a…

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

Q: (b)Solve 9 ax Z+9 dz ду = 4

A: Given partial differential equation is 9∂z∂x2z+9∂z∂y2=4......1. Equation 1 an be written as follows…

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Q: 5. Supposen converges. Prove that %n converges. n=1 6. Calculate the Taylor series of f(z) 7. Write…

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Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral. Let n…

A: The end points of the subinterval are x0 = 1, x1 = 2, x3 = 3, x4 = 5.

Q: = (k₁) be an m x n matrix with scalar entries. For x € K", let Mx € K™ be defined as n Mx(i) = Σkjj…

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Q: Find the polynomial of degree three for the following data. Also find P(-2). X 0 y 1 4 6 1 -1 1 -1

A: This is a problem of Numerical Analysis.

Q: Convert the following English sentences into WFF in First Order Predicate Language. All frogs are…

A: (i) The given sentence is " All frogs are green ". To convert: the given sentence in First Order…

Q: (a) Use differentiation to find a power series representation for f(x) = co f(x) = Σ n = 0 What is…

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Q: Set-up the integral that of revolution when given region bounded by the y-axis (x = o) and the…

A: This is a problem of the Volume of rotation.

Q: 4. T(n) = 4T() + n 5. T(n) = 7T()+n²

A: We use here, Master's Theorem

Q: 1. (a) Find the Fourier series of the function f(x) = 1 |x|, -2<x≤2 (b) Hence prove that 1 + 3/2 +…

A: 1. (a) Given,                 f(x)=1-x, -2&lt;x≤2

Q: The weather in Columbus is either good, indifferent or bad on any given day. If the weather is good…

A: Given that: If the weather is good today, there is a 60⁒ chance the weather will be good tomorrow, a…