3- Derive Lagrange's equation in Cartesian coordinates in one dimension?
Q: Q2 (i) Evaluate ,7 dz, where C is the positively oriented circle lz - 1| 1.
A: Here we have to integrate the complex integral I=∮(z¯)2 dzalong a circle z-1=1, x-12+y2=1 ;this…
Q: Q5 Given a volume of the inverted hemisphere bowl "dome" of radius R, resting on the xy plane and…
A: According to the problem,we need to construct hemi sphere "dome" using spherical coordinate system…
Q: Ql: Show that: sin e sin o -cos e cos o cos e sin o -sin e cos o A, A, A. sin 0 cos o Cos A A %3D…
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Q: Q2:- Enumerate the possible polar diagrams forl= 3, and the seven possible values of m i for this…
A: Required : Possible polar diagrams for l = 3
Q: 2. Solve the following Laplace equation analytically PDE: Uz + Uyy = 0, u = u(x, y), 0 < x < 2, 0<y…
A: Laplace's equations are the fundamental equations satisfying by the potential energy φ due to a…
Q: Jse Cauchy's theorem or integral formula to evaluate the integrals.
A: If f(z) is analytical function within and or on the closed contour and a is any point of…
Q: 4) Solve F.dr using Stokes' theorem for yzi✦ zi‡ yk„where S is the cylinder x² + y² = 4 between -3 ≤…
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Q: 4. Proof using integration in Spherical coordinates that the volume of the sphere is: V= Using dv =…
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Q: The unit sphere 8 ha e' is a regular polyg
A: Consider square ABCD, and O be the center of the square on the unit sphere. Lets take OAB and the…
Q: 4. Given vectors A, B, and C below: B (80.0 N) 30.00 Å (100.0 N) 30.0° 53.0°O (iii) Find E where E =…
A: Given, Three vectors
Q: Explain the significant of the Curl of a vector and discuss what exactly is the essence of the del…
A: Have a look?
Q: Q5) Given H = sina in free space where, r = 3, 0≤0 ≤90, 0≤ ≤ 90°. Evaluate both sides of stokes…
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Q: (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and…
A: Given Parameters in term of t x=sinty=cosec t
Q: . Water at the top of Horseshoe Falls (part of Niagara Falls) is moving horizontally at 9.2 m/sm/s…
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Q: 11. Use the divergence theorem to evaluate F-N dS. where F = (ry, yz², zr²), and N is the the unit…
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Q: Calculate the spectral line wavelength λ using the equation d sin 0 m X and its uncertainty X using…
A: the uncertainity in position Δx that is approximately equal to the particle's wavelength. In other…
Q: Problem 3) Prove Stokes's theorem for the following field of E=3sino/2âgfor a hemispherical open…
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Q: 4) No matter what Ả and B are, prove algebraically that Ả · (Ả x B) =
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Q: Calculate dS where S (3xy², xe², z³) and S is the surface of the solid bounded by the cylinder y? +…
A: From the given equation of cylinder, the projection of the cylinder on the yz-plane is a circle of…
Q: Find the area of the specified region. Shared by the circles r= 5 cos 0 and r= 5 sin 0 O A. (2-12)…
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Q: Q4) Consider an arbitrary vector A = Agâg + Agâo+A„â„ in spherical coordinates and express in…
A: Given,A=AR aR^+Aθ aθ^ +Aφ aφ^
Q: IT V2=18.9377 will V1 be 31.759???? 18.9377 V2= Bernoulis Equation P₁+ = V₁² + pgh₁ = P₂ + V₂ + pgh…
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Q: 4. Vectors A,B and C form a triangle, as shown in the figure. Prove the law of cosines, |C|? = |A]?…
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Q: се free space.
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Q: 4) Estimate the surface energies of PE and PET using the Zisman approach. Hint: plot cosine of the…
A: 4) To estimate the surface energies of PE and PET using the Zisman approach. Hint: plot cosine of…
Q: 4. Evaluate the surface integral [[ f dS where, = xz and E is the boundary of the region D in R3…
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Q: 1- (Exercise) Given the vectors A= 7i-2j, B=i-3k, and Č = 21 –23+3k, calculate the fol- (1) lowing…
A: Given: The three vectors are
Q: 2) Transform A=y“ ax +xzay +4a- from Cartesian to spherical system. Then evaluate vector A at point…
A: See attached picture
Q: 2. Gradient of the cyllindirical coordinates Drive gradient of the cyllindirical coordinates as we…
A: Derive gradient of the cylindrical coordinate.
Q: 3) Simplify (vf – v.)(vf + v.) = ()(at) so you can solve for vs. (Note: you should not need the…
A: Since you have asked multiple questions in a single request, we would be answering only the first…
Q: 3. For x[n] = {1, 1, 0, 0), y[n] = {1, 0, 1, 0), evaluate circular convolution z[n] = x[n] Ⓡy[n] (b)…
A: Solution:- The circular convolution of the given signals…
Q: 3. Region 1 (z0) is characterized by &2= 4. Let E, = -30ax + 50ay+70a, V/m, find: a) E2. b) D2 c)…
A: Given: E1→=-30ax+30ay+70azεr1=2.5εr2=4
Q: Choose the plot of V(x), with the condition V(3)=0, that best corresponds to the plot of E vs. x…
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Q: Given: Three forces act on particle P. Force A has a magnitude of 15 N and acts 60° CCW from the…
A: a) Draw the free-body diagram of the system of forces.
Q: Given the vectors d = i-+ k and b = 2i - - 2k, determine the following: a. the scalar projection and…
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Q: Determine the coordinate of a 3D point P(100.0, -60.0, 80.0) after rotating 60 degree across…
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Q: Find the distance between the Earth and the planet Venus at the point of maximum elongation B ?! The…
A: Distance between Earth and Sun, x1 = 15×1010 m Distance between Venus and Sun, x2 = 10.8×1010 m…
Q: Determine the tangent to the curve 3y2 = x³at (3,3) and calculate the area of the triangle bounded…
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Q: 5. Given: Three forces act on particle P. Force A has a magnitude of 15 N and acts 60° CCW from the…
A:
Q: 2) Consider the two vectors Ā = A,î + Ayĵ and B = B,î+ Byj. If î · î = ĵ · j = 1 and î·j = ĵ · î =…
A: Write down the given values using suitable variables. Here A signifies the 1st vector, and B…
Q: Electric charge is distributed over the triangular region D shown below so that the charge density…
A: Total charge over a region is given by the double integral of charge density over the region that…
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