Under suitable assumptions derive one dimensional wave equation.

Q: Define the term binormal vector?

A: Question:- Define the term binormal vector?

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (8y – 4xy) Give your answer in unit vector…

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Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: Rit +1 ,2it ait -| = î7 e +iz (1-iz)eit 1+iz %3D iz

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Q: Wave mechanics are often employed for

A: Given,              ∂2u∂t2=16∂2u∂t2  for all  0≤x≤10 and t≥0.             ...(1)

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: What is meant by a tangent vector?

A: To Explain:  a tangent vector

Q: name another different type of 3-D curve from vector valued functions

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Q: Describe 2-dimentional vector addition for any scenario? Put your best example over here.

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Q: Explain the term scalar.

A: Explanation: Given that, term scalar.

Q: Define the term Change of basis?

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Q: A vector s has initial point (0, 0) and terminal point (-3, -2). Write s in component form.

A: A vector s has initial point (0,0) and terminal point (-3,-2).

Q: A velocity vector of variable magnitude of an object can have a constant direction. O True False

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Q: wing vector fields is not con

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Q: Find the derivative of f at the point P( – 3, – 2) in the direction of = ( – 1, – 1) | -(– 3, – 2) =…

A: Given, f(x,y)=-0.02x2y3   (b) The directional derivative for a function f(x,y) in the direction of…

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

A: Solution

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: Find the vector in component form with initial poi

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Q: What is the relationship between Stokes’ Theorem and the Fundamental Theorem of Calculus?

A: Solution: Stokes Theorem: Stoke's theorem states that ''the surface integral of the curl of a…

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: a horizontal vector has initial point (-4,1) and has a magnitude of 7. What is the terminal point?…

A: The initial point of the vector is (-4, 1) and the magnitude of the vector is 7. Since it is a…

Q: Apply Gram- Schmidt process to the vectors 3

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Q: Derive three-dimensional heat equation in cylindrical polar coordinate system.

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Q: Detemine the lineality over a full langth in the a-direston of he wave Sine Curve y- Asina

A: We know that the wave length of y=A sin x is 2π.  Note: The linearity over a full wave length of the…

Q: According to the function in image 1.1, we can say that its gradient vector at point (1,1,2) is (in…

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Q: (a) What is a parametric curve?

A: If  x  and  y  are continuous functions of  t  on any interval I , then the equations: x=x(t) and…

Q: Consider a partially polarized light whose Stokes vector is given by [5,4,0,0]. Obtain the output…

A: Here a partially polarized light whose Stokes vector is given by [5,4,0,0]. We have to calculate its…

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (4y² – 5xy) Give your answer in unit vector…

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Q: I need to get the parametric equation for a line between the points (0,1,2) to (3,0,-1). I have the…

A: Line passing though the points 0, 1, 2 & 3, 0, -1. Now let, x0, y0, z0=0, 1, 2 & x1, y1,…

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

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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: A vector t has initial point (0, 0) and terminal point (4, 1). Write t in component form.

A: Write vector, terminal point minus initial point

Q: 1. Convert point P(2,3,-1) and vector A ya,-xaytza, into cylindrical coordinates.

A: Given - Point P2, 3, -1 and vector A = yax - xay + zaz To find - Convert the point P and vector A…

Q: A force of (2i - j+k) Newtons acts on a line through point P having coordinates (0, 3, 1) metres.…

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Q: Find out the general solution of one-dimensional wave equation in spherical polar coordinates by…

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Q: Describe the particle's acceleration

A: Given s(t) = t (2t - 1)2 and t = 2s The velocity v(t) = s'(t) = 12t2 + 1 - 8t The acceleration a(t)…

Q: Chapter 13, Section 13.7, Question 005 Find an equation for the tangent plane and parametric…

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Q: Using vector Calculus, Parametrize the circle of radius 5 having centre (8; -3) and hence and a…

A: Solution:-

Q: Find the angle between the vectors (-5, 4) and (-3, -1). Carry your intermediate computations to at…

A: Solution:

Q: Find the displacement vector with initial point A(-3,4) and terminal point B(1,1) and determine the…

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Q: Find the nature of the second-order wave equation O a. Hyperbolic/ elliptic O b. Parabolic ос.…

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Q: Define Gauss's theorem and Stokes theorem.

A: We will define first the Gauss's theorem then we will define the stokes theorem.

Q: A vector s has initial point (5, - 2) and terminal point (1,-3). Write s in component form. S =

A: Let, A = (5, -2) be the initial point and, B = (1, -3) be the terminal point.

Q: Chapter 11, Section 11.2, Question 025c Find the component form of the vector v in 2-space that has…

A: We know that  ||v||=x2+y2=r||v||=8x2+y2=8=rso r=8   Component of vector v  can be written as…

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

A: Given below clear explanation