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

Q: Find an equation of the normal line to the parametric surface given by R(u, v) = ((2+ cos v) cos TU,…

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Q: Evaluate the line integral / Vxy° +3 dx +6xy" dy, where C any curve joining (1, -1) to (16, 1).

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Q: Solve the follo wing in itial Value problem by using laplace trans formi- 9y =0 ; yl0) =0 and…

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Q: Let R(t) = et+e be a particle position moving in the plane Then the acceleration at time zero is

A: We have the position vector given in terms of time t.                  Rt=et i+e-t j To find the…

Q: Find the open interval(s) on which the curve given by the vectorvalued function r( ) = 2 cos3 i + 3…

A: Consider the given vector-valued function: Here the objective is to find the open intervals on…

Q: Prove that fe, r*dx + rydy = 0 where Co is the line segments from (0, 1) to (0,0) by using…

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Q: 2. Find the r-component of the acceleration for the velocity field of a flow given by v(r, y, z,t) =…

A: NOTE: Hi! Thank you for the question. As per the honor code, we'll answer any one question in case…

Q: ди ди ду ду Find the cauchy-riemann equations of, f (z) = | z | sin z. əx' dy'dx' ðy,

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1. In…

Q: Let z = e* sin(y+a), show that %3D ôx? oy?

A: Given, z=e-xsiny+a, then we have to show that ∂2z∂x2+∂2z∂y2=0.

Q: When body is an equilibrium ,the net force is not vanish

A: False. The given statement is false. We know that: There are two conditions that must be met for an…

Q: If F= represents the flow of a liquid through a parabolic cylinder S: y=x, 0sxs2, 0szsl. That is…

A: If F→=y2,-x2,z2 represents the flow of a liquid through a parabolic cylinder S:y=x2,0≤x≤2,0≤z≤1.…

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

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Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t) i + sin(t)j + tk…

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Q: determine the magnitude of the force exerted by block Y on block X during this acceleration.

A: In this question, we need to find the force exerted by block Y on block X.

Q: The velocity field for a fluid is given by V=(X2t3)i+(2XYT)j. The convective acceleration in the…

A: Given, V=x2t3i^+2xytj^ Here, u=x2t3 and v=2xyt Convective acceleration in y-direction is given by:…

Q: A slender rod of constant density lies along the line segment r(t) = tj + (2 - 2t)k, 0≤ t ≤ 1, in…

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Q: By using two methods, find the work done by the force field F(x, y) = ysin xỉ + xe³ ĵ to move a…

A: Given: To compute:  ∫C F.dr=?F→(x,y ) = y sin x i^…

Q: Use a scalar line integral to find the length of the curve r(t) = (20 sin , 20 cos ,5), for 0 < t <…

A: Given

Q: Let X, Y be jointly Gaussian, standard, and Cov (X,Y) = y. Find pdf of Z = X +

A: Answer:-  Given that, X and Y have jointly Gaussian distribution.

Q: Find the tangential and normal components of accelerationfor a particle moving along the circular…

A: We know that, tangential and normal components of acceleration for a particle moving along the…

Q: consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b…

A: Consider a particle moving on a circular path of radius b given as, rt=bcosωti+bsinωtj Where ω=dudt…

Q: Find the Nork do ne against (x,Z)ih muving a particle 11 along the curve parametrized

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Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) : equi-…

A: The formula to calculate the vector which is normal to the equipotential  line of the potential…

Q: Use the full differential to calculate an approximate modulus value. of the vector (5, 8 ; 3, 1 ; 2,…

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Q: Calculate the work done by the force F(x, y) = y?î+ xyj in moving a particle along the line which…

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Q: Compute the vector line integral: x – 4 dx + (x – 4)² + y² -y dy :- 4)2 + y² where C is the circle…

A: To find the below vector integral. ∮C−yx−42+y2dx+x−4x−42+y2dy

Q: Calculate the area under y = x2 over [0, 1] using Eq. (11) with the parametrizations (t3, t6) and…

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Q: When body is an equilibrium ,the net force is vanish ulgn O İhi O

A: when body is an equilibrium the net force is vanish

Q: Let the the position vecor be R(t) = (e' cos(3t) , e' sin(3t),0). Compute the unit tangent vector

A: The given position vector is R(t)=etcos(3t),etsin(3t),0 . compute the unit tangent vector T(t)=?

Q: dt dx2 dy , ди u(0, у, 1) dx (1, y, t) = 0, и(х, 0, г) %3D ди - (х, 1, г) %3D 0, dx и(х, у, 0) %3D 2…

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Q: 2. Integrate f(x, y) = sin /x2 + y² А. over the closed unit disk.

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Q: Use the Chain Rule to find az/ðs and ôz/dt. z = arcsin(x – y), x = s² + t?, y = 2 - 2st as az at II

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

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Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: What is Gradient of a Scalar Function: The gradient of a scalar function is vector quantity. It is…

Q: 8) Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x = y - y?…

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Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: A body of mass n: moves along Y such that at time t its position is y(t) = at3/2 - bt + c, where a,…

A: a) Given the position of the body at a time t is given by yt=at32-bt+c where a,b,c are constants.…

Q: Evaluate /|/ (x² + y² + z²)² dV where E is the solid ball centered at the origin with radius 2.

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Q: A curve in the xy-plane is defined by the vector valued function f(t)= (x(t), y(t)), d'y in terms of…

A: Given : x(t)=2ln(t)y(t)=2sin(-5t)   To find : d2ydx2

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: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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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: 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: A particle is accelerated along a curved path of lengthl = 4.0 m under the action of an applied…

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Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…

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Q: Find the coordinates of the centroid of the curvex = cos t + t sin t, y = sin t - t cos t, 0 ≤ t≤…

A: Given, the curve x = cost + t sint, y = sint – t cost, [0,pi/2].

Q: (2x + y)dx + (x + 2y)dy

A: Given integral is:  where C is any curve that joins the point (1,1) with the (2,2).

Q: 4. Use Stokes Theorem to find the circulation of the vector tield F around any smoo th, Simple…

A: Stokes theorem ∫CF.dr→=∫∫Scurl F.N→ ds Curl of the vector point function Ff1, f2 f3…

Q: Find the coordinates of the centroid of the curve x = cos t + t sin t, y = sin t - t cos t, 0…

A: Given,