Example 28: If u is moment about origin, prove the rth that r-1 Σ H-j Kj; where Kj is the jth cumulant. i = 1

Q: Q: Prove the trans ferm; formula's by definition of Laplace t a) B(t) j(t-t) dt = F(S)GS) %3D

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Q: et a =i- 2j + k and b= 2i+j +k. Show that la + b| s lal + b|

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Q: Show that the followIng function satlsfles the twa-dimenslanal Laplace's equation. z = In(x? + y2)…

A: Given: z=ln(x2+y2)+2 tan-1(yx)

Q: Suppose that r(t) = cos³ t i+ sin³ tj+et k, show that d dr (r.- dt dt d?r X at2 dr d'r. r.at at3…

A: Given: rt=cos3t i+sin3t j+e-t k we have to show that ddtr·drdt×d2rdt2=r·drdt×d3rdt3

Q: 7) fouo momEUT THE Mss, THを momet Adout X-4XIS, Aんの 2 A BOLT Y-AXTS of RLJOU Boun DEp By THE メート…

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Q: a) +++ where C is the helix r(t) = cos(t) i + sin(t)j +t k, Osts2T

A: Note:- As per our guidelines, we can answer the first part of this problem as all the sub-parts are…

Q: Wer: 1088/3) 3. Compute the moment of inertia of the plate of constant density p described by -a <r…

A: Here is the moment of inertia of the plate of constant density ρ described by -a≤x≤a and -b≤y≤b…

Q: ECR 9s a sordon Area cvol CE) =V0ICE) ean Yntegraole on E Sand 主 After thet desariptron. 1ntegroble…

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Q: In the absence of a damping mechanism, the deplacement, go, helners cons tant k suspended oloject°…

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Q: Find the Lyplace tiangern f (t) = sin Ct+a) of cor (t-a) usng S e-e f (t) dt f Ct) dt .

A: The given problem is to find the Laplace transform of the given function using integral method.

Q: 9. Consider the equation d?x + q(t)x = 0, (A) di? where q is continuous on a stsb and such that 0 <…

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Q: Example: Find the torsion of the r= (cos t i + sin t j + tk)

A: We use the formula to find the torsion :-

Q: Show that the following function satisfies the two-dimensional Laplace's equation. z = In(x² + y²) +…

A: The given function is -  z = ln(x2 + y2) + 2tan-1yx We have to test whether the above function…

Q: 1. Let u be a smooth harmonic function inside the unit ball B(0, 1) in R? so that |u| < 1. Prove…

A: To prove this we will use the following tools : Solution of Laplace's equation in polar coordinates…

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

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Q: itegal 10. Find he Vadue anf P which the ntegral Caverges, absolutely Condlitionally". r Sin olu

A: Here we that sin function has modules less or equal 1.

Q: Suppose a spaceship of length Lo is traveling at a high speed v relative to an observer. To the…

A: topic - functions

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

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Q: What is the laplace of L(f"(t))? A s2F (s) – sf (0) – f (0) B sF (s) - f(0) Osf (0) - f(0) D s2F(s)…

A: as per our company guideline we are supposed to answer only one question. kindly post remaining qs…

Q: Consider the slope field shown. (a) For the solution that satisfies y(0)-0, sketch the solution…

A: The solution curve that satisfy the condition y(0) = 0 can be drawn as follows:

Q: If the density of the frame element (shown in the figure) is given as p(x, y)=b+cy where a-9, b-1.2…

A: Given  Density μx,y=b+cy Where a=9, b=1.2, and c=3.1

Q: Consider the cune C: (x-8)+ 4-7) When parametneing C, A tungent veotoar is i O a) r (0) = (8 +3…

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Q: Let f(r, y, 2) = 2ry + 2. Evaluate f(1, y, 2) dz where C is the portion of the helix r(t) = cos ti+…

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Q: Show that the process X(t) = A cos At + B sin At (where A and B are RVs) is wide-sense stationary,…

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Q: If D = 15p sin 2øa, + 10p² cos 2pa, C/m², evaluate both sides of the divergence theorem for the…

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Q: 10. Show that the function f(x, y, z) = e3z+4y cos 5z satisfies the Laplace equaton. Good Luck.

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Q: Write a in the form a = aT+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i +…

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Q: W Q4. a) Without using the shift formula prove that Laplace of f(t) = e¯ª sin wt is (s+a)² +w?

A: The laplace transform of ftLft=∫0∞e-stftdtLet ft=e-at sin wt∴ L e-atsin wt=∫0∞e-st e-at sin wt dt=…

Q: Let W(t) be Brownian motion. Using Ito's lemma evaluate | (4w (t) – 124W (t))dW(t)

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Given the field D = 6p sin 124 ap +1.5p cos 12 a, C/m2, evaluate both sides of the divergence…

A: field D=6ρsin12ϕ ap + 1.5ρcos12ϕ aϕ C/m2 here ∇ = aρ ddρ + aϕddϕ+azddz Divergence = ∇·D ∇·D=…

Q: yi + aj 2. Find the flux of F = across the curve C given by r(t) = a cos(t)i+a sin(t)j, ²+y² for 0…

A: ∵ Given thatF=-yi^+xj^x2+y2;           0≤t≤2π r(t)=acosti^+asintj^ As we know that Flux=∬ F·nds…

Q: If V V30 everywhere then the resuiting flow is c O rotational O dynamic Osteady Pirrotational

A: The general form of a vector-valued function in three dimensions is given by F→=F1i^+F2j^+F3k^,…

Q: Let T(r,s,t) = (r cos(s) sin(t), r sin(s) sin(t), r cos(t)) Find the Jacobian of T at (3, π/4, π/3)

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Q: A velocety field f giren by by: -y 2. Does 9 xepser Pnt Find the Cquation ot the ut& eam lineu Find…

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Q: The signal (t) = tan(t) satisfies the Dirichlet conditions. O True O False

A: False

Q: L{cos3t} fonksiyonunun Laplace dönüşümünü bulunuz

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Q: What is the laplace of L(f"(t))? A SF (s) f(0) (в B s2F (s) – sf (0) - f'(0) © s2F(s) - sf (0) -…

A: Use the definition of laplace transformer and derive the required solution.

Q: Laplace for following L(3cosht t) V3 12 4s2 - 1 O 3 A otherwise s - 1 12s s2 3(s? - 1)

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Q: (7) Let w(x, y, z) = xy cos z, where x = t,y = t², and arcsin(t). %3D dw Find dt

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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: Q: Given a r.v.*=2, 3,4,5, then O Evalute (e) the ond 2 non Centeral moment ofx. nod

A: Given , a r.v. X = 1,2,3,4,5 We need to find, 1st and 2nd non central moment of X. i.e. E(X) and…

Q: Choose an appropriate form for a panticular Soln of y"+ qy =f8cos@t) evaluate the constants in the…

A: To find - Choose an appropriate form for a particular solution of y'' + 9y = t2cos(3t) and then…

Q: Q2/ Use Laplace properties to find L{S e3u (2sin? u - 1)du } .

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Q: Let X and X, independence r.v. have same moment generating function (-) where tsa, let Y=aX+bX, ,…

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Q: Let D-f2-2i 2す 0,e4 +1, と + ±i) md f: D-e f(e) = + e 1/1 -2) 2-2 True oY False for f(z) ? True Zo =0…

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Q: 2.1 Evaluate la Im(z – i)dz where C is the contour from z = 1+ 2i to z = i and from z = i to z = -i.…

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Q: Without using the shift formula prove that Laplace of f (t) = e**-atcos wt is w**2/((s+a)**2+w**2)

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Q: find enit vect in the d a most ropidly at in which f increase P and find the yoate of charge of f at…

A: The objective is to find a unit vector in the direction in which F increases most rapidly at P and…

Q: (c) The region between the loops of the limaçon r = 1 + cos 0.

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