Q1: The Hamiltonian is represented by the matrix H = 0 Where is positive real number. (a) Find the eigenenergies for the Hamiltonian. (b) Calculate the eigenvectors corresponding to its eigenenergies. 100 20 002

Q: Find 0, given sin'0 - 0.2 sin0 -0.01. (Give your answers correct to 2 decimal place).

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Q: Convert the integral from the CARTESIAN COORDINATE SYSTEM to the SPHERICAL COORDINATE SYSTEM. S-s √…

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Q: Determine the point on the curve y = 19x² closest to the point (0, 5) with x>0. What is the slope of…

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Q: Solve the following heat equation = ut (x, t) u(0, t) = t, u(1,t) = 0, u(x,0) = x². Uxx (x, t) + x…

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Q: 5. Prove that the set of points at which sequence ef measurable real-valued functions converges (to…

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Q: 1. Given an initial value problem y' = y² sin(t) with y(0)=-3. π a. Approximate y using Euler's…

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Q: Let C be the curve y 12 11 10 9 8 -7 6 15 || 2 4 + 25 1 3x for 0.6 ≤ x ≤ 3.7. Find the arc length of…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 4 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: Determine the form of a particular solution for each differential equation 2 2. ""4" +4y' = 5x² - 2x…

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Q: 3. Suppose Par = $10,000,000; PO = $7,500,000; T = 3; d = 0.006; m = 0.7 and π = 0.5. Then what is…

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Q: How many years if the compounded total conversion periods is 99 when compounded monthly?

A: Solution: Given, Total conversion periods = 99

Q: 1. Given an initial value problem y'= y² sin (t) with y(0)=-3. a. Approximate y using Euler's method…

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Q: 8) Let a 3-2 +45 for n-0, 1, 2, 3, ... If we write an as a recursive relation, it is Hint: calculate…

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Q: (6) Given A 2 2 -4 1-4 2-4 2-1 S B = O 234 2 then find BA and use this to solve the system of…

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Q: Solve for the two positive values of x that satisfies the equation e* = 3x² Using the following…

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Q: Q4: Show if the series is convergent or divergent cos(n) n√n n=1

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Q: 4. For the below ordinary differential equation, state the order and determine if the equation is…

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Q: Aluminum Eal = 10(10³) ksi AAB=0.09 in² 2.00 kip A 18 in.- Copper Ecu=18(10³) ksi ABC = 0.12 in² B…

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Q: Evaluate the given integral along the indicated contour. 6 z² dz, where C is z(t) = 3t+2it, -2≤sts 2

A: The given problem is to evaluate the given complex counter integral of the given function z2 over…

Q: The first five rectangular numbers are shown: 2 .. 3 a. Make a sketch to represent the eleventh…

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Q: H.W: Evaluate the integral 3 0 [ [(x²y - 2xy)dydx 0-2 1. 3. 3 1 ss 1 -1 (2x - 4y)dydx P

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Q: Q: Use Lagrange's Formula to Prove that : 1) Y₁ = Y3 0.3 * [Y5 - Y-3] +0.2 * [Y-3 - Y-5].

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Q: Q2. Use the Stokes' Theorem to find fF.dr where F(x,y,z) = and C z=9-x²-y² on the xy plane oriented…

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Q: In Problems 10-8, the auxiliary equation for the given differential equation has complex roots. Find…

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Q: Use properties as completely of exponents to simplify the expression as you can.

A: Given: a) 2x9·8x1 b) z9·z8 Property of exponent: Law of product is given by, am·an=am+n To simplify:…

Q: 7. 8. Show that T(x1, x2, x3) = (3x₁ − 6x3, x2 + x3, X1 X2 - 2x3) is a linear trans- formation by…

A: We use definition of linear transformation and properties of linear transformation.

Q: If 4 p and q P крса are conjugale exponent a measure X a measure space, p р. f₁g:x [₁₂+] measurable…

A: Given P and q are conjugate exponent and f,g are measurable function and let p,q∈(1,∞)

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 15 x³ 1 + 4 3x 25 for 0.6 x ≤ 3.7. Find the arc length of…

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Q: Problem A. Consider the linear transformation T : R₁[x] → R₁[x] given by (A1) Is T cyclic? (A2) Is T…

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Q: Determine the Inverse Laplace transform for 2s +9) 5² +9) L-

A: Here we have to find the inverse Laplace transform of  L-1{2s+9s2+9} Applying property…

Q: 2. For the quadratic function y = -6x² + (K + 4)x+9, find the following: The Axis of Symmetry of the…

A: Introduction: Standard form refers to the quadratic function f(x) = a(x - h)2 + k, where an is not…

Q: 1. Consider the graph below. Find the betweenness of the following edges (a) AB (b) BC B (C) DE…

A: Solution :-

Q: Use any of the results in this section to evaluate the given integral along the indicated closed…

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Q: What is the main equations of Kalman Filter Recursive Algorithm.

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Q: Using the following method, determine the smallest positive value of x that satisfies the given…

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Q: 4. Draw the graph of the linear equation: 3x + 4y - 7z = K + 8.

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Q: Using Lagrange's interpolation formula to fit a polynomial to the data -10 2 3 BBBBH y -83 1 12 And…

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Q: Consider the point P(-2, 1, 4) and the vectors Question 2 a = and b =. (a) Find the unit vector u…

A: Explanation of the answer is as follows

Q: Use the table of Laplace transforms to find the Laplace transforms of the following functions. cos²…

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Q: 3. 1 1 1 SSS √√(x + y -1 -1 -1 (x+y+z)dydxdz

A: Sol:- ∫-11∫-11∫-11x+y+zdydxdz

Q: Use the method of reduction of order to find a second solution of the differential equation t'y" -…

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Q: How long will it take for an initial investment of $ 133000 to reach a balance of \$1,000,000 ,…

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Q: 2. Find the area of the region inside the cardioids r = a(1+cos), a>0

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Q: Let C be the curve y = 12 11 10 9 8 7 6 5 15 x³ 1 + 4 3x 25 Find the arc length of C shown above.…

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Q: 1. XYZ, Inc., is a small firm that produces a variety of chemical products. In a particular…

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Q: A ladder, with its foot in the street, makes an angle of 30 with the street when its top rests on a…

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Q: 1. Given an initial valuc problem y'= y² sin (t) with y(0) = -3. 6) 2 a. Approximate y using Euler's…

A: Sol

Q: 29. Evaluate (a) 2π (b) To 5² 2л (c) T Jo (d) the following integrals. 1 + cos 0 -do 2- sin 0 sin² 0…

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Q: Many patients get concerned when a test involves injection of a radioactive material. For example…

A: As per the question we are given a the following data base : t(hrs) 0 1 3 5 7 9 R 1.000 0.891…