Use separation of variables method to solve the partial differential equation: du d²u du(x,0) = +u where u(0, y) = 0 and = sinx . dy ax² dy

Q: ) Find the derivative: d cos(x) (1 dx √1-t²dt

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Q: A 2nd degree palynomial passes through the points (1,-1); (2,-2); (3,-1) and (4,2) Find the…

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Q: The personnel department of a particular company has observed that 20% of the people the company…

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Q: (32) Find the derivative: cos(x) de (1.060 V₁ - Pdt). 1 dx

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Q: Use Laplace transform to solve the partial differential equation: o'y dy ox² at +xl where y(x,0) =…

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Q: Can you help me solve this Question? Derive the formula to get the third forward finite difference…

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Q: (1) Using Legendre polynomials, find linear least-squares approximation to f(x) = In|xl.

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Q: Find the Laplace transform of t², -8+ 3t, g(t) = - (t-6)² + 2 cos (1-²), 6 0 2

A: Firstly using heavy side function to write the function and then  taking laplace transform .

Q: Based on known series, give the first four nonzero terms of the Maclaurin series for this function.…

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Q: Exercise (1-3): By Charpit method solve the following PDE (3): p²-q²y = y²-x² (4): (y² +4)xpq −2=0

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Q: If u = f(y + ax) + (y-ax), then to №² u №² u (a) a² (b) dy² 2 Əy² 2 (c) - a². (d) a №²u น 2 Əy² №² u…

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Q: Showing your working, use Shanks' Baby-Step Giant-Step algorithm to find a power x such that 3x = 11…

A: I will first write down the algorithm used in the above question.  Baby steps: Suppose we want to…

Q: 3+3=

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Q: An n×n magic square is a square array of numbers (n > 1) such that the sum of every row, of every…

A: Consider the 5*5 magic square using the consecutive positive integers from  391 to 415 given in the…

Q: Question: Find the mass of a plate bounded by one arch of the curve y = sin x, and the x-axis, if…

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Q: Make example about  matrices and determinants method

A: Solution:- Matrices are the ordered rectangular array of numbers, which are used to express linear…

Q: 1. Find the zero-divisors of Z6- 2. Let D be an integral domain. Show that if a E D such that a² = a…

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Q: Establish the following set theoretic relations: a) AUB=BUA, AnB = BnA (Commutativity) b) AU (BUC) =…

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Q: If A = 3ai +4j-k and B = 4i+j-3k, find the value of a if A normal to B.

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Q: Use Laplace transform to solve the partial differential equation: dy dy +xt where y(x,0)= 0,…

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Q: Consider sets A and B with |A| = 7 and |B| = 4. How many functions f: A → B are surjective?

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Q: (32) Find the derivative: (cante), 1 d cos(x) dx √1-t²dt

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Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Transformers for underground works were planned to be provided. Type A has an initial cost of…

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Q: 35040 MOD 76397. Explain how and why Pollard's p - 1 factorisation method works.

A: Given: p-1 To find: Pollard method

Q: 4 Find the eigenvalues of A, given that A = -6 0 ,02= -2 and 3 = and its eigenvectors are v1 = The…

A: Given matrix  A is ,                                                         A =     4    0    0-6…

Q: Normal subgroup 2. Endomorphism of group 3. Field 4. permutation.

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Q: = 13² 1² for Consider the ordered bases B=( a and C= a. Find the transition matrix from C to B. TB =…

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Q: Before the election, you want to determine the number of possible president/vice-president…

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Q: (B) Explain the relationship between any three of the following a) Ideal and subring. b) Prime ideal…

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Q: T/3 (29) Evaluate the integral: 73 - csc? rdr. π/4 (30) Find the derivative of the integral…

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Q: Suppose that A is an nx m matrix of rank 3, the nullity of A is 4, and the column space of A is a…

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Q: 3. Calculate the polarizability a(wo), the scattering cross-section scatter (wo) and the absorption…

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Q: Turn the following differential equation into a system of first order equations suitable for…

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Q: 6. For any n x n matrix A over C, there exists a positive semi- definite matrix H and a unitary…

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Q: Consider the differential equation: 1+ y² xy+y³+y dz This differential equation is not linear in y,…

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Q: The amount, in milligrams, of a medicinal drug in the body t hours after it was injected is given by…

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Q: 5. If u = f (y + ax) + ( (y - ax), then to อิน น อน (a) ay (b} 2 ay (c) −a? (d) a สิน 2 ay? 2 a อน…

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Q: Q4: (A) Prove or disprove each of the following 1. Every prime ideal is maximal. 3. The cancellation…

A: Each and every option is false. We disprove them by giving appropriate counter examples. The…

Q: Find the general solutions to the following differen (3.1) Un+1=un +7 (3.2) un+1=u-8, u = 2 (3.3)…

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Q: 1. The blood glucose level (L units) of a patient t hours after the injection of a certain kind of…

A: please comment if you need any clarification. if you find my answer useful please put thumbs up.…

Q: 3. Find the area of the region bounded by y = x², y = 8 - x² and y = 4x + 12.

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Q: Which are true?

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Q: :True or False 1. Every ring is a group. 2. Every subset of a ring is also a ring. 3. Any ring must…

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: find an approximate value of y 1

A: Given,        dydx=xy12 and x=1, y=1

Q: 18. ( .) Answer the questions for the following functions. The leading coefficients are only +/- 1…

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Q: - Let R=(Z9,+9,9). Find 1. Char(R) 2. Nilpotent ideals of R 3. Prime ideals of R.

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Q: The matrix has eigenvalues -4, 1, and 3. Find its eigenvectors. The eigenvalue -4 has associated…

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Q: Prove that, there is no simple group of order 200.

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