Only Pulley A has friction. O F(x) = +] A boundary from x=1 tox = 2 2.25 m m 0-90* μ-0.1 3 m- 3 m k= 200 N /m- 3 m -2 m 1 m- |-2m-F1m 3 m 3 m- 3 m F(x) = N boundary from x=1 to x = 2 3 m 3 m Activate V Go to Setting

Q: Integrate f(x,y,z) = x + √y-2² over the path from (0,0,0) to (4,16,4) given by C₁: r(t)=ti+t²j,…

A: The objective is to integrate the given function f(x,y,z) .

Q: A clamped cubic spline S(x) on interval [0, 2] is defined by 1+ax + bx2 – 2x³ 0<x<1 1+ c(x – 1) –…

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Q: f ay) =xy(3-x=y) what is the absolute maximum and Minimum absolite of the funtion R reğion in

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Q: Q1. Given the functional t2 I(x, y) = (9x²y 2y²x) dt t1 where i dx/dt, y = dy/dt, t and t2 are…

A: According to Euler Lagrange's equation, and . The equation of that satisfies these equations will…

Q: Find the maximum and minimum values attained by f (x,y, z) = xyz on the unit ball ² + y² + z² < 1.

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Q: Consider f(x, y) = x2 + 4.xy + y? subject to the constraint x2 + y? < 49 (a) Find all critical…

A: The function is fx, y=x2+4xy+y2. Differentiate f partially with respect to x: fx=2x+4y Set the…

Q: Consider the pendulum x' Y, y' = -vy - sinx, - where 0 is a friction parameter and (x, y) E S¹ x R…

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Q: 0.1 at c 5, use linear approximation to estimate Ay Let y 2x + 8x + 4. If Ar Ay =

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Q: 1. Verify that (t) = et, y(t) = e' satisfies the system %3D dx 3y3 dt dy y, dt %3D

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Q: 1. Show that the problem may be formulated in terms of the velocity potential o(r, 0) satisfying 6,…

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Q: (b) 6xy dV, where E lies under the plane z=1+x+y and above the region in the xy-plane bounded by the…

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

Q: The solution of Laplace equation du + = 0, where 0 < x < 3 %3D dx and 0 < y< 2 with boundary…

A: Given equation is  ∂2u∂x2+∂2u∂y2=0 Where 0≤x≤3 , 0≤y≤2 with boundary conditions…

Q: The solution of Laplace's equation Urx + Uyry 0 < r < 3, 0 < y< 4, subject to the boundary…

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Q: 1. If F= (y,z,x), the outward flux through a smooth closed surface (a) depends on the surface. (b)…

A: Given, F=y,z,x We know,  Flux by the Gauss divergence theorem. ∬F.ds=∬∫divF.dvF=yi+zj+xk If you…

Q: Solve Laplace’s equation uxx + uyy = 0 on the unit square with boundary conditions • N: u (x, 1) =…

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Q: 2) let f(x,g r.Z) =x?yt x Jit z g Fincd thedirectiuncal cdecvative aff t at the point(42,3) Mthe…

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Q: The first step in using the Hamilton-Jacobi-Bellman equation 0 = J*(x(t), t) + min {g(x(t), u(t), t)…

A: Given Hemilton-jacobi-bellman eqn: Jt*(x(T),t) + minu(t) {g(x(t),u(t),t) + Jx*T(x(t),t)[a(x(t),…

Q: Consider the finction f(x, y) = 6y² + 4x² – 12xy- 4y. Then: (1,1) is a critical point and f has a…

A: The given function is f(x,y)=6y2+4x2-12xy-4y

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Find the rates at which the volume, surface area, and interior diagonal are changing at the instant…

A: Volume of rectangular box (V) = xyz Take derivative with respect to t, we get…

Q: Which of the following is not a homogeneous function? h(x,y)= xª − 3xy³ + y¹ − x² cos Option 1 b(x,…

A: Let's solve.

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A:

Q: Find the bounded solution of âyở y x> 0, t>0 where y (0, t) = 1, y (x, 0) = 0.

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Q: 11. The solid bounded by the surfaces S : 1-1= y? S2 : y+z = 2 S3 : 1 = 0 S4 : y = 0 S5 : z = 0…

A: We will use triple integral to find volume of solid bounded

Q: Solve Laplace's equation u +u, = 0, 0<x< 5, 0 < y< 4_for a rectangular plate %3D subject to the…

A: Laplace equation: uxx+uyy=0 For a rectangular plate 0≤x≤a, 0≤y≤b With boundary conditions: u(0,y)=0,…

Q: . Use the separation of variables, u(x, y, t) = X(x)Y(y)T(t), to solve the following vibrating me…

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Q: f(x.y)= are ) = arccos( x² +y² – 3 )+In(x²+y² –3) fonksiyonunun tanım kümesi aşağıdakilerden…

A: Given function is fx,y=arccosx2+y2-3+lnx2+y2-3. We know that the range of the cosine function is…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Let the required path be γt=xti+ytj . Then the velocity vector in the direction of maximum…

Q: B- Solve the Laplace equation for steady heat conduction in the semi-infinite region 0 < y< 1, x 2…

A: The given problem is to solve the given Laplace equation for steady heat conduction in the given…

Q: Consider the Hamiltonian flow on R² associated to H(x, y) = }y² + x(x – 1)(x + 1). Show t (11 2 0)…

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Q: Suppose that the temperature in degrees Celsius at a point (x, y, z) of a solid E bounded by the…

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Q: Find the maximum and minimum values attained by f(x,y,z) = xyz on the unit ball x2+y2+z2 ≤ 1

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Q: 7.* Give the candidates to local extrema (maximum or minimum) of f(r, y, z) = 2z – y – r under the…

A: The solution to the given question is as follows.

Q: 0 0 0

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: (b) || 6xy dV, where E lies under the plane z 1+x + y and above the region in the xy-plane bounded…

A: A triple integral involves the integral with respect to x,y, and z. In this problem, we have to…

Q: Hand written plzzzzz...will rate

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Q: 1. Show that the problem may be formulated in terms of the velocity potential (r, 0) satisfying r dr…

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Q: 4) a) Find a potential function f (#, y, z) with Vf = F(r, y, 2) = yz? 7 + (xz² + 2z) + (2.ryz + 2y)…

A: Conservative Vector Field and Line integral:

Q: 4. (a) Use the trapezoidal rule to numerically integrate from a = 0 to b= 2 /(z)-0.2+25 +3r

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Q: A string of length 1m attached with two points. The deflection in the string is given by y" + Ay =…

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Q: A 3 cm length silver bar with a constant cross section area 1 cm (density 10 g/cm³, thermal…

A: The equation is u t…

Q: Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a…

A: We use langrange multiplier method

Q: 2. Sketch the streamlines for the flow u = ax, v = -ay, w = 0, where a is a positive constant. Next,…

A: Given the velocity is u=αx, v=-αy, w=0 and Lagrangian description is x=Xeαt, y=Yeαt, z=Z

Q: Solve ut = upx in the interval [0, 5] with u(0, t) = 0, and u(5, t) = 1 for t > 0 and u(x, 0) = 0…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to other then…

Q: Consider a potential problem in the half-space defined by z 0, with Dirichlet boundary conditions on…

A: The green function solution to the potential problem with this boundary for Dirichlet boundary…

Q: Solve the problem with Neumann boundary conditions, 0, x, t>0 u, – Ugg = u(x, 0) = f(x) u;(0, t) = 0…

A: we have ut=uxx ux,0=fxux0,t=0 Fcut=Fcuxxdu¯dt=-su⇒u=Cse-s2tNow, ux,0=fx⇒us,0=f^cs=Cs⇒u=f^cse-s2t Put…

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

A: Consider the given function, Tx,y=100-x2-2y2 the differentiate partially, ∇T=-2x, -4y the slope at…

Q: A 3 cm length silver bar with a constant cross section area 1 cm" (density 10 g/cm, thermal…

A: