Q2: Show that u = ln(x² + y2) is harmonic function and find the conjugate harmonic v = (x. y) and from an analytic function f(z)= u(x. y) + (x.y)

Q: 1. From a corridor of VNHSain building 50 m above the ground level, the angle of depression of I…

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Q: Q3/A-(12 degree) If the A-¹ = 0 -1 1 11 13 25 11 -3 11 31 11 11 11 51 , Find the value of A.

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Q: P6.3 Simplify the following Boolean expression using Boolean algebra laws: (a(a+b))' + ba'

A: Given Boolean expression is aa+b'+ba'. We have to simplify the given Boolean expression using…

Q: (laplace transform) 3u If L (e³t) = ¹, then L( e³u du) is... S-3'

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Q: Convert the following Linear Programming problem into Standard LPP form.       Minimize P = 5x1 –…

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Q: Use the given information to find the exact function value. 63 Given sin a = = and <a<, find cos. 65…

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Q: Prove that the product xy of two real numbers x and y is nonnegative if if and only if the absolute…

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Q: Consider the function G below: G a b d Y e Z Select all statements below that are true: □ Rng(G) =…

A: Range of G is { V,X,Y,Z}. Image of a and e is V , so G is not injective.

Q: 7. Calculate each of the following. [from #22, 4.5] b) 971321 (mod 765) a) 2557341 (mod 5681)

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Q: 1. Legendre functions for n = 0. Show that (6) with n = 0 gives Po(x) = 1 and (7) gives (use In (1 +…

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Q: As preparation for designing a new line of business wear, a clothing manufacturer asked a large…

A: Part(a) Pink color has the smallest slice out of all colors. So, pink is approximately 1/8th of the…

Q: Question 9 Use your value of x to calculate a value for e* from the first four terms. Compare the…

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Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

Q: 1 Use your given sequences to answer the questions Series A 1, -1, -3, -5, -7 ... Series B 4, 2, 1,…

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Q: Verify that the given function u is harmonic. u(x, y) = 8xy3 - 8x³y + x The function u(x, y) has the…

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Q: Consider curve C which is the intersection of the surfaces shown in the attached figure. y + 3x = 2…

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Q: Solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of…

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Q: How can the unit circle help us find the exact values of trig expressions involving special angles?…

A: To show how trigonometric expressions can be found using Unit circle.

Q: If two statements are logically equivalent You can rearrange one to get the other the columns for…

A: Introduction: Two expressions are logically comparable if all conceivable combinations of truth…

Q: . Error and Q Functions 1. Use the definition of errar function, prove that 1₁ ( ² ) = √ T

A: Using definition of error function we have to prove that

Q: Given that F = xz i − 2yz j + x2yz k. Find the followings at (1, 1, 3): (a) div F.  (b) curl F.  (c)…

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Q: Hand written plzz : Find the Laplace transform F(s) = {f(t)} of the function f(t) = (8t) [U(t− 4) –…

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Q: (x+y)² Prove: x = y if and only if xy: = 4 here: the "if" and the "only if" part. Note, you will…

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Q: 11. Consider the equation dy/dt = ay - y³ = y(a − y²). (a) Again consider the cases a 0. In each…

A: Given differential equation, dydt=ay-y3 =y(a-y2) The objective is to find the critical point for…

Q: 3) Consider the curve C which is the intersection of the surfaces shown in the attached figure. If…

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Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: Ten international students who include four males and six females are friends. Each of the four male…

A: If choices are independent we can fill n places with p things in p*p*.......p (n times)=pn ways.

Q: Find the determonant of the matrix A 1 2 1 -21 -1 -2 -1 4 2 1 3 2 L-2 1 2 -31

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Q: Simplify the complex number 7 (²+1) ³ - 5 (¹)² and express it in the standard form.

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Q: Determine the solution of the differential equation using Laplace and Inverse Laplace Transforms.…

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Q: What is the optimal solution for the following problem? Maximize P = 3x + 15y subject to 2x + 4y ≤…

A: The given linear programming problem is                     Maximize P = 3x + 15y subject to 2x + 4y…

Q: Use Euler's method with step size 0.1 to estimate y(0.4), where y() is the solution of the problem ₁…

A: Use Euler's method with step size 0.1 to estimate (0.4), where y(x) is the solution of the problem…

Q: 너 S 2 (5²+4) 2

A: We need to find the value of L-1{ss2+42}

Q: Q2

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Q: create a polynomial p that has the desired characteristics. You may leave the polynomial in factored…

A: Consider a polynomial px with solution px=0 are, x=±3, x=-2, and x=4 It is known to us that if x=c…

Q: Q6. The points A(3, 4, 2) and B(3, 7, 2) are on a plane. If the plane also passes through the y axis…

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Q: 1. If a= (-8, 2) and b=(-1,-7) the projection b on to a C-1 ******** .

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Q: After the Northwest Corner Rule, how much is the initial total transportation cost? Town A Town B…

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Q: For the two leaf rose r = 1 + cos(20) and cardioids r = 1 + sin(0) and r = 1 - sin() shown in the…

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Q: Prove the following: If m is an even number and n is an odd number, then n 2m is odd. Hint: start…

A: We prove that if m is an even number and n is an odd number , then n-2m is odd .

Q: Q₂: A. Re-write the double integral dydx in the form: (draw the region of integration) (1) ff dxdy…

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Q: 6. List every generator for the subgroup of order 8 in Z32.

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Q: See the points D(4,-2,5), E(-1,3,5), and J(4 + 2√3, −2 − 2√3, 5+ 2√2), and the line / with symmetric…

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Q: What is the difference between convergence and stability of parabolic PDEs? How is Galerkin’s method…

A: While numerically solving a p.d.e. we replace each derivative term by a Taylor series. Rearranging…

Q: Nx - My xM - YN has an integrating factor of the form a(zh Find an integrating factor and solve the…

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Q: If g € ([a,b] and g(x) € [a,b] for all x € [at] then g has only one fixed point in[a, b] true O O…

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Q: Use the Squeeze Theorem to show that  lim x→0 x2 cos(16?x) = 0.

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Q: 1. If a= (-8, 2) and b=(-1,-7) the projection b on to a =......... 2. The inverse Laplace Transforms…

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Q: (B) Solve the differential equation:- y"-3y' +2=0, y(0) = 1, y'(0) = 1, y" (0) = 0

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Q: Find f(3.67) from the next table X 3.50 3.55 3.60 3.653 3.70 Y=f(x) 33.115 34.813 36.593 38.475…

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