92 that the elect ric potential prove -5x V = e Cos 13y sinh 12 Z achieves the Laplace equation اثبت ان الجهر الكهرباي الممهى :v لحق ق معادله لابلاس

Q: Find the laplace of  f(t) = cos(root2)t + sin (3t)

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Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: Find Laplace 2 2 [sin(34) + 65inh czt) ]

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Q: +4y= 16t (Laplace)

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Q: Rotate 90° clockwise about the point (1,1). + 2344 Rule New coordinates P(₁) S(,) R(₁) Q(₁) ➖➖➖➖➖➖…

A: Given

Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: A point moves along a right-circular helix C, which is the curve of the path 7 :R → R³ given by,…

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Q: find inverse Laplace 2s-11 s²-4s+ 8

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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: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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Q: Find parametric equations for the tangent line to the given curve at the point (30, 135, 469). The…

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Q: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: (b) Prove that 1+ cosh x + cosh 2x coth x sinh x + sinh 2x 1+ cosh 2x + cosh 4x dx Hence evaluate…

A: 4b. Given,

Q: Find an arc length parametrization r₁ (s) of the curve r(t) = (7 cos(t), 7 sin(t), ³/²), with the…

A: Given Data: Let us consider the given data, r(t)=7cost, 7sint, 43t32 To Find: The arc length…

Q: The position vector of a particle moving along a helix is = = 4TT. c(t) = (cos(t), sin(t), t²). (a)…

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Q: Sit/ If r(t) = cos(t-1) i + sin (t-1) jitzo Does the particle have constant speed? If so, what is…

A: given position vector is

Q: b) A particle moves in simple harmonic motion according to the equation, s = 0 x Acos(wt)+ 0 ×…

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Q: Given a velocity field: V = 1.8 ( rz (1-sin²(0))) er + 2.8 (1-cos2(0)+ rz) eg +1.8 ( rz tan(0)…

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Q: laplace{sin3t sin8t}

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Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

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Q: Given A¹¹'(-4, - 6) and are the coordinates of A? 3/092103/talu = Ro 180°(Ry - axis(T (5. s>(A))),…

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Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…

Q: 1. Use formulas (2)–(5) to find the Laplace image of the given function (c) 5e²t - 2t3 (f) 1+ sin…

A: Laplace transformation of the functions

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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Q: Find the length of the curve T=e* 30 T<0<T given in polar coordinates. a) V10 sinh(37) b)2/10…

A: Power rule ddnxn=nxn-1 Length of a curve with equation r=fθ , a≤θ≤b is given by  L=∫abr2+[drdθ]2dθ