sin? Of + cos? 0i F = A pn where A is a real constant. Compute the flux of F through a spherical surface centered on the origin. How does the flux depend on the radius of the sphere?

Q: az Let z=xy-e'siny, x-uv, y=7Vu?+v?. Then at (u,v)=(7T,0) is du

A: Given that z=xy-exsiny, x=uv, y=7u2+v2find ∂z∂u at u,v=7π,0

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: #21 2D Describe the motion of a particle with position as tvaries in the given interval

A:

Q: 9 cos r+j9 sin 24 cos r+j24 sin + võ cos T+ jv6sin T+ V15 cos – j/15 sin T COS what would this be…

A: This is a problem of complex analysis.

Q: When a particle is located a distance meters from the origin,a force of Cos(πx/3) newtons acts on…

A:

Q: 3. For what value of K the velocity field in plane polar coordinates given by v, = tion of…

A: 3. The given values are,vr=K36r2-1cosθ and vθ=k36r2+1sinθ

Q: Find the area Inside the cardioid r=2 cos (6/3) and outside the circle of radius r = vZ centered at…

A:

Q: ((2- sec?r) ! sec(3A – x) eIn (ale) secx dx to be integrable using the formula What should be the…

A:

Q: 5. On the rectangle 0 < x < n, 0 < y< 1, show that |sin z| is maximal at the point z = 5 + i. (Hint:…

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Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

A:

Q: Show that the spherical harmonics 1 3 sin 0 e-iº, 2V 27 Y1,+1 and 3 1 Y1,0 2V V cos 0, %3D | are…

A: Given: The given harmonics are Y1,+1=1232πsinθ e-iϕ and Y1,0=123πcosθ  are orthogonal over the…

Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: a) Find the relationship between Ju(x) cnd je(x) by comparing the invariont forms of [x;, x, x- r?]…

A:

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: Given r1t=costi+sintj+5tk, r2t=4i+tk

Q: Evaluate the integral. 1/2 | [6 cos ti-3 sin tj+ sin 3t k] dt 1/2 | (6 cos ti- 3 sin tj+ sin? 3t k]…

A:

Q: Use Gauss' Law to find the charge enclosed by the cube with vertices (±1,±1±1) if the electric field…

A: Given The given electric field is Ex,y,z=x,y,z and the charge enclosed by the cube with vertices ±1,…

Q: Given the acceleration and initial velocity of a body moving along a coordinate line at time t, find…

A: The acceleration of a body moving along a coordinate line at time t is given by: a(t) = 8 sin(4t)…

Q: A- Find all values of z such that sinh(z) = B- Are |z, Img(z) analytic? Give reason. C- Choose the…

A: We have to solve the given questions

Q: OSolve where y (0, t) = 0 = y (5, t) and y (x, 0) = 10 sin 4Tt x.

A:

Q: x = a(0 – sin 0), y = a(1 – cos 0). %3D %3D urve followed by the particle as a function of 0.

A: The given parametric equations are, x=a(θ-sinθ)...............(1) y=a(1-cosθ) .............(2)

Q: i? た(uパ) : tan ニ u= X Cosy V= X siny JR Determine Jf to 24 つメ

A:

Q: (a) Suppose that a black hole has magnetic field F = (2a* + e" sin(2), y³ + xe*, 2z³ + e" cos(z) +…

A: TO FIND: Magnetic flux across the black hole

Q: 5. For a vcctor Á written in spherical coordinates, A = A,f + A,® + AøØ, the spherical coordinate…

A: The answer is in below steps.

Q: ige view Nead ai oud 8. Determine the constants a and b such that sin x + cos a = a sin (x + b) .…

A: As per the company guidelines we are supposed to answer first question. Kindlyrepost the other…

Q: 1 27 1+sin(0) 2r dr d0 dz -1 0

A:

Q: -yi + xj 2. Find the flux of F across the curve C given by r(t) = a cos(t)i+a sin(t)j, VI² + y² for…

A: F=-y i+x jx2+y2,    r(t)=a cos(t) i +a sin(t) j 0≤t≤2π x(t)=-a sin(t) ,     y(t)=a cost    ,  F=-y…

Q: Dircetional desivalive :- unut veetor giren flay)= e* siny by' ongle at (0,0) i) Q = ズ find Du f(do,…

A:

Q: The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1 + cos? 0) de = 0. %3D

A: In order to obtain the differential equation for the family of curves, we must eliminate the…

Q: se method of Laplace Transforms to solve y"+2y +y = ecost, y(0) = 0, y (0) = 0. %3D

A:

Q: a. Show that If z=x+iy where y >0 Then: 0 < |e*|<1 b. Evaluate cos (i z) – sinh?(z)

A: Using De Moivre's Theorem

Q: The degree of the homogeneous function f(r.y) = sin--tan- is Enter your math answer

A:

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: Show that z- sinh z Rcs :* sinh z

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Q: Describe the motion of a particle with position (x, y) as t varies in the given interval. x = 3…

A:

Q: 2 A force of F(x)=4cos (2x)-7 sin(x), x is in meters, acts on an object. What is the work required…

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Q: 3. Use integration to determine the formula for the "equatior: given that : F(t) = ( 2t , 12e" , sin…

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Q: 7 Jlgull sin(2) = e-e- 2i eiz-e-iz 2 et +e-iz 2i e -e-i: 2i

A:

Q: Show that z - sinh z Res i | 2 z sinh z z=ri

A:

Q: (a) If f(x,y) = e" siny – e" sinx then verify that fry = fyz-

A: This question is related to partial derivatives.

Q: r(t) = (-2 cos (2t), 3 sin (3t), ln (2t)), then the fr(t)dt is equal to 3 -cos (3t), tln (2t) - t) +…

A: Here we find the correct option,

Q: 65. The function z(u, v) = u cos v satisfies the equation dz cos U- ди sin v dz = 1. и до

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Q: find the flux of 3 – e")i+ (y³ + sin z)j+ (z³ – unded above by z = V4 – x² outward orientation.

A: We have to find the flux using the divergence therom according to the given information

Q: 3. Solve the Laplace equation inside a 60° wedge of radius 1 subjected to the boundary conditions…

A: The Laplace equation is given by: r2∂2u∂r2+r∂u∂r+∂2u∂θ2=0 The boundary conditions are: ∂u∂θr,0=0,…

Q: 2. Find the complex potential function f(z) = u + iv, given that 2u +3v = e*[cos(y) - sin (y)]. Also…

A:

Q: 17. Suppose F = V × A, where A = (y + Vz)i + e»²j + cos(xz)k. Determine the flux of F outward…

A:

Q: 29-32 Use double integration to find the area of the plane re- gion enclosed by the given curves.…

A: Solution is in step 2

Q: A uniform and stationary magnetic field Ris perpendicular to the plane containing a circular…

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Q: uate the erihite integrai. 1/4sin(t) dt Cos (t) COS

A: Follow next step

Q: A particle travels along the helix C given by 7 (t) = cos ti + sin tj + 2tk and is subject to a…

A:

Q: 74. A particle moves in the xy-plane along the elliptical path x = 2 cos t, y = sin t, where x and y…

A: