X=r sinø cose y=r sinø sine z=r cosø p² = x² + y² + z² Determine a, y ,əz , ə, ,dg,dg

Q: Angular speed Consider the rotational velocity field v = ⟨0, 10z, -10y⟩ . If a paddle wheel is…

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Q: %3D In this exercise we want to us I sin(z) cos(c) dr Tp (I)SO Hint: Preview My Answers

A: Topic:-: integration Let I=∫xsinxcosxdx.

Q: F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x), Cis the triangle from (0, 0) to (0, 6) to (2, 0) to…

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Q: A hang glider is spiraling upward due to rapidly rising air along the curve r(t) = (3 cos t, 3 sin…

A: Given the position vector: rt=3cost,3sint,t2 Rewrite it: rt=3cost i+3sint j+t2 k

Q: Po PDE: ar'r dr' ² do² 1 do 0 = do BCs: v, = dr at r=a v, = U„ cos 0 at r= 00 1 do Ve = -U„ sin 0 r…

A: The Laplace equation in polar coordinates for two dimension is given by, ∂2ϕ∂r2+1r∂ϕ∂r+1r2∂2ϕ∂θ2=0…

Q: A particle moves with acceleration a(t) = 10 sin t + 3 cos t, s(0) = 1, v(0) = 2. Find s(t).

A: We have to find s(t)

Q: y" + y + y = 0, y(0) = 1, y (0) = 0 Oet(fcos 1 + sin ) O e (cos t+ sin t) e (cor sin 뿔) cos 5 O e…

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Q: a2u, a2u = -2; 0<x< 1, 0 < y<1 condition u(x,0)= u(x, 1)= u(1,-x) u(0,y)= 0, u(1,y)= sinh(IT) sin…

A: Given: ∂2u∂x2 + ∂2u∂y2 = -2   0&lt;x&lt;1, 0&lt;y&lt;1 ---------(1) with boundary condition…

Q: A hang glider is spiraling upward due to rapidly rising air along the curve r(t) = (3 cos t, 3 sin…

A: Given:          r→(t) = &lt;3 cost, 3 sint, t2&gt;   To find:           The time when the glider's…

Q: u(0, t) = u(2, t)=0 u(x,0) = r sin(rr)

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Q: %3D In this exercise we want to r sin(z) cos(z) dx I)SO ( UIS I Hint: Preview My Answers

A: Let I=∫x.sinx.cosx dx.

Q: Qi find Laplace Tranform for the fllowing functivas e f 4)= t ést sinzt - 34 -t ® PCt) = t e %3D

A: Note- As per our company guidelines, we are supposed to answer only first 3 sub-parts. Kindly repost…

Q: + COS I etan sin z – cos I cos2 7 Find: a cot r dr b S cot(3r) dr c csc² r dr dsecr tan r dr ecsc r…

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Q: 20. Which of the following expressions are false? I. u(x, y) = e² is a harmonic function. %3D II.…

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Q: u =u, +u ,u(0, y ) =u(1, y ) = 0, u (x ,0) = sin 7.x ,0<x <1, %3D

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Which of the following expressions are false? I. u(x, y) = e is a harmonic function. II. u(z, y) =…

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Q: 5. r(t) = (t°/3) i + (12/2) j, t>0 %3D 6. r(t) = (cos³ t) i + (sin³t) j, 0<t< a/2 %3D

A: This question is about finding vectors   k, b &amp; t

Q: Laplace equation is called a harmonic function. Let the functions u = u(x, y) and v = v(x, y) be of…

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Q: Cos t sed 2. (cos t) (cos t) sin(t) Cos t sin t cot t %3D

A: Conversion of cosecant to sine is, cosecθ=1sinθ Conversion of secant to cosecant is, secπ2-θ=cosecθ

Q: e integral be 'solvable' using trigonometric substitution. What is the correct choice of u given J…

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Q: (a) x, = a+bZ, +cZ,- • (b) x, = Z, cos(ct)+Z-1 sin(ct). (c) x, = Z,Z, •

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Q: ++.Usethechain.Rule.t.find. DZ and..Z b.. Z e cos@. rEst. 2 2.. S+t?

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Q: QI by the chain rule iplakdy 订 =(sin x)cox x = sin-ly+ cos(er) %3D and Find dy

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Q: Let R=[a,b]×[c,d]. || e*sinyda = e*dx S siny R. C Select one: O True False

A: This is a problem related to double integration. Based on the general formula and concept we will…

Q: Use Stokes's Theorem to evaluate JCF• dr. Use a computer algebra system to verify your results. C is…

A: To evaluate the integral ∫CF→·dr using Stokes's theorem, where F→=6xzi^+yj^+6xyk^, and S :…

Q: 3) ft)= (t+リ sin (t+z)= t sinけtz) + sint +2) Asin(よ)+ - Cole) ds s Sin(2) +1- Gd ニ (8+1) - sind -…

A: We have to find the Laplace transformation of f(t).

Q: (1) sin (z + y) com ( z + v) (2) COS

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Q: Use Stokes's Theorem to evaluate JcF•dr. Use a computer algebra system to verify your results. C is…

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Q: sinxcost ; 00 = 0, u(pi/2,t) = 0 ) =0, ut(x,0) = 0 %3D 00 = u. - sin x cos t, : u(0, t) = 0, E u(x,…

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Q: 10. Show that the function f(x,y, z) = z arctan satisfies the Laplace equation.

A: We have to cheek

Q: Use Stokes's Theorem to evaluate Jc F. dr. Use a computer algebra system to verify your results. C…

A: Formula is in the solution part

Q: Torsion of a helix Compute the torsion of the helixr(t) = ⟨a cos t, a sin t, bt⟩, for t ≥ 0, a &gt;…

A: Position vector - r(t) = acost, asint, bt Formula for finding the torsion is given by - ζ =…

Q: theorom J f E Riemann La,b] and feas>o for xE Ľ q,bJ then a

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Q: PDE: uf = 2ихх, 0 0 0 0 ВС: и (0, t) — —1, иx(1,t) — 1 3πχ IC: и (х, 0) — х + sin - 1 2

A: Claim: solution for the heat equation: Let us use separation of variables. Let u(x,t)=X(x)T(t).…

Q: ez - w = tanh z = ez + e 1 w = coth z: tanh z 1 w = sech z cosh z 1 w = csch z sinh z Example: prove…

A: Since you have asked the multiple question as per our policy we will solve first one for you if you…

Q: 1) Solve U = Uz + U, u(1,t = 0) = sin(e¯² ) cos z, COS T, %3D %3D

A: Given,             and

Q: I am studying for a quiz and do not understand the substitution rule. can you help work the attached…

A: Hey, since there are multiple questions posted, we will answer third question. If you want any other…

Q: r(t) = ( 2- sin(t), 2·cos(t), 2 t) from the point (0, 2, 0) to the point (0, 2, 47).

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Q: Describe the motion of a particle with position (x, y), where x = 6+ sin t, y = 3+ cos t, as t…

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Q: r = 3sine b) r = sin30 c) r= |3D r = cos20 f) r = 0 g) r = r = 1.5 – 1.5cos0 i) r:

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Two transverse waves y1 = 2 sin(2nt - x) and y2 = 2 sin(2rt - Ix + T/2) are moving in the same…

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Q: Consider / sin'x cos?x dx. If we let u=cos x , the integrand can be transformed to A (u²+ 2u* +u6)…

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Q: I x=rsin p cos 8, y=rsin g sin8,2=r cos.0s0s 2n,0spsn then the value of Jacobian/.

A: Given: x=r sinφ cosθ, y=r sinφ sinθ and z=r cosφ. The value of Jacobian is given as J=∂x,y,z∂r, θ,…

Q: A variable force f(x) = sin Tx (in Newtons) moves a particle along a straight line from the origin…

A: The given force function is  f(x) = sinπx    Newtons Partical moves from x = 0, to x = 2 m

Q: (i) p²(sin?(4) sin² (0) + cos² (4)) = 9 (j) 0 <0 <T/2; r< z < 2 in cylindrical coordinates (k) 0 <0<…

A: (i) Given that, Distribute left side, Consider special co-ordinates x = ρsin(ϕ)cos(Θ), y=…

Q: Which of the following expressions are false? I. u(z, y) = e² is a harmonic function. II. u(z, y) =…

A: Harmonic function is a function that satisfies the Laplace equation that is where u is a function…

Q: Laplace inverse of L is |(8 – 4)2 + 6² e ot sin 4t O ebt sin 4t O et sin 6t O e 4t gin 6t

A: L-16s-42+36 Apply inverse transform rule: if L-1fs=ft then L-1Fs-a=eatft Noe for 6s-42+36⇒ a=4,…