Q1) Solve the wave equation: at? ax? dU(x,0) Where: U(0,t) = U(1, t) = 0,- = 0,U(x,0) = 2(sinx+ sin3x) dt %3D

Q: 4. z = tan-'(y/x), x = e', y = 1 - et

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Q: If the electric potential at a point (x, y) in the xy-plane is V(x, y), then the electric intensity…

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Q: a. Find a parametrization of the curve x = (y* – 3)e2y.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: solve the given wave equation utt(x,t) = uxx(x,t) u(0,t) = u(1,t) = 0 u(x,0) = 0  ut(x,0) = 1…

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Q: Let C be the line segment from [1 – i,2+ 2i). (a) Parametrize C. (b) Integrate 2 over C.

A: According to the given information, Let C be the line segments from [1-I,2+2i]. For part (b) it is…

Q: from wave equation  ∇2u(r,t) + 1/c2 (∂2u(r,t)/∂t2) = 0, get the Helmholtz equation. Using that…

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Q: A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t> 0…

A: Here, the position vector is given as R→(t)=cos t+ t sin ti^+sin t- t cos tj^+t2 k^. (a) The tangent…

Q: 1. Find a parametrization for the line segment from (2, 1, 3) to (4,3, 2). 2. Find the velocity and…

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Q: The monkey saddle z = x³ - 3xy² can be intersected with the cylinder x² + y² = 1 to produce the…

A: Given monkey saddle is z=x3-3xy2 and the cylinder is x2+y2=1. The given curve is the intersection of…

Q: An elastic string is stretched between two points 40 cm apart. Its center point is displaced 1.5 cm…

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Q: Q4 (a) Define Gauss's theorem and Stokes' theorem.

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Q: Show that f(x, y) =(Aekx + Be-kx )(Ce2ky + De−2ky) is a solution of the wave equation ∂2f/∂y2−…

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Q: Write the equations in cylindrical coordinates. (a) 7x + 5y +z 2 z-2-(5 sin(0) +7 cos(8)) (b) -3x-3y…

A: To convert the given equation to cylindrical coordinates we have to put the value., x = rcosθ y =…

Q: Consider the one-dimensional wave equation Fu 00 u(0, t) = u(1,t) =0 u(r. 0) = 3 sin(27z) %3D (r,0)…

A: u(xi,tj) The CTCS scheme stands for central time central space difference scheme. In this scheme, we…

Q: An elastic string which is fixed at both ends is governed by the wave equation a²u a?u 0 0, at2 əx²…

A: Let us consider the wave equation ∂2u∂t2=∂2u∂x2, 0≤x≤1, t≥0 and L=∆x=0.25; K=∆t=0.1 Consider x=ih…

Q: Q1- The divergence of the function f= (r cos 0)e, in spherical coordinates is..........

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Q: 8. Describe the motion of a particle with position (x, y): x = 3sin (t),y 4cos (t)

A: To describe the motion of a particle for below curve. x=3sint, y=4cost

Q: Solve the wave equation in two dimensions Utt = v²u u (x, y, 0) = sin 4y U (x, y, 0) = cos xcos3y…

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is...

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Q: Use Gauss' Law to find the charge enclosed by the cube with vertices (±1,±1±1) if the electric field…

A: Given The given electric field is Ex,y,z=x,y,z and the charge enclosed by the cube with vertices ±1,…

Q: Show that ¥(x,t)= Asin(wt+kx) describes a wave motion

A: Given: ψx,t=Asinwt+kx

Q: 25. A particle is located at (1, 1,0) at time t = 0 and it follows a path whose velocity vector is…

A: Let's find.

Q: A string of length 15 cm is stretched between two points as shown in Figure 1. A point P on the…

A: Given a string of length 15 cm is stretched between two points. We have to obtain the differential…

Q: Solve the wave equation by Laplace transtelm %3D ax² ulet)=1 ...d.......

A: Solution

Q: Solve the wave equation on the half line with the Utt – cʻuxx = 0, x> 0, t > 0 и, (0, 1) %3D h(),…

A: Given the wave equation is                     utt-c2uxx=0,   x>0, t>0ux(0,t)=h(t),…

Q: The motion of string deflection u, can be expressed by the one-dimensional wave equation, shown in…

A: Given that: ∂2u∂t2=c2∂2u∂x2   ...1 c2=Tp, Where T=Tension in string p=mass per unit length of string…

Q: au %3D ax at u(x, 0) = 0 ди (x, 0) = 0 at u(0, t) = sin? t u(1, г) — 0,

A: Given,           ∂2u∂t2-∂2u∂x2=0                       for 0<x<1, t>0      ...(1)u(x,…

Q: Express the given parametrization in the form y = f(x) by eliminating the parameter. x = 5t + 2, y =…

A: Given

Q: 3. Verify that u(r,t) = sin(r - at) satisfies the wave equation:

A: To verify that ux, t=sinx-at satisfies the wave equation ∂2u∂t2=a2∂2u∂x2

Q: sin(t) et, X2 sin(t)- cos (t) and X3 D sin(t) + cos (t)] 0. Given that X, cos(t) sin(t) + cos (t)|…

A: The problem is wrong, three vectors are not linearly independent.

Q: Obtain the solution of the wave equation u 12 under the following conditions (i) u(0, t) = u(2, t) =…

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Q: Use Gauss's law to find the charge enclosed by the cube with vertices (±2, ±2, ±2) if the electric…

A: The net charge enclosed by a closed surface S is given by Q=ε0∫∫s E.dS We can divide S into 6…

Q: 4. Compute the directional derivative of f(r, y) = at the point (1, 1) in a direction normal to the…

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Q: Uo (r² + a?) cos 0. u(r, 0) = ) Hence show that the velocity components of the flow are ди Ur = ax…

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Q: 4. Consider the closed curve C, which is the image of the path 7(t) = (a cos t, b sin t), t E [0,…

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Q: Solve  using wave equation: u(0, t) = u(π, t) = u(x, 0) = 0, du/dt | t = 0 = sin(x)

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Q: u(0,t)=0 2. Consider a piano string of length L = 50cm that satisfies the wave equation Utt81Uxx, 0…

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Q: Q1- The divergence of the function f = (r5 cos 0)e, in spherical coordinates is.. .

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Q: Q1- The divergence of the function f (r5 cos 0)e, in spherical coordinates is...

A: The given problem is to find the divergence of the vector function in spherical coordinates.

Q: For the particle in a box, show the wave functions w, NTTX sin - for n=3 and n=6 are normalized and…

A: Note that the question has a typo. Since, The function sin(nπx/l) is of period 2l/n.

Q: 2. Find the complex potential function f(z) = u + iv, given that 2u +3v = e*[cos(y) - sin (y)]. Also…

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Q: Find the acceleration of a particle having position function r(t) 6 sin ti+ 9t j+ 2 cos t k

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Q: 5- Find the solution of the following wave equation using the method of separation of variables.…

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Q: F(x, y) = (3x-4y2i+6yj by the force in moving a particle in the positive direction once around the…

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Q: Solve the normalized wave equation 0 0, %3D u(0, t) = 0, u(T, t) = 0, u(x,0) = sin x, du (r, 0) =…

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Q: Consider the wave equation Pu Pu 0<I<2, t2 0, with boundary conditions u(0, t) = 0, u(2, t) = 0,…

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Q: Use Gauss's law to find the charge enclosed by the cube with vertices (±2, +2, +2) if the electric…

A: The given Electric field: E(x,y,z)=xi+yj+zk The given vertices of cube is (±2,±2,±2) The expression…

Q: Consider a vibrating guitar string of length L = 648mm that satisfies the wave equation Uxx = Utt, 0…

A: Given below clear explanation

Q: A particle at (1, 0, 0) starts moving in space in such a way that its position vector at any time t…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.