Use spherical coordinates to find [[[, z2 dV.

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Use spherical coordinates to evaluate f (ử+y° +z°)* dydzdx. 3/2

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Q: 2² dz dx dy By converting to spherical coordinates, evaluate

A: Given:  ∫02∫04-y2∫x2+y28-x2-y2z2dzdxdy we need to find following integeral by using spherical…

Q: Find the velocity and acceleration vectors in terms of u, and ue en r=6 sin t and 0= 9t

A: The velocity is given by            v = r' ur +rθ' uθandThe accerleration is given by        a =r"-r…

Q: Q3//A:- Verify that dV = p² sin p dp d0 do when using spherical coordinates.

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

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Given  a t=4t,5 sint, cos 3twe know that,v→t=∫a t dt +C1r t=∫vt  dt  +C2 ∴v→t=∫4t, 5 sint, cos 3t…

Q: Use cylindrical coordinates to evaluate d V when

A: The given integral is ∭RxdV where the region R is defined by R:x2+y2≤1, x≥0, y≥0, 0≤z≤2. Converting…

Q: Calculate the velocity and acceleration vectors and the speed at the time indicated.r(θ) =〈sin θ,…

A: Consider that: rθ=sin θ, cos θ, cos 3θ at θ=π3. Velocity vector denoted by vθ is vθ=r'θ.  Calculate…

Q: Express the following points in cylindrical and spherical coordinates: (i) P(l, -4, -3); and

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

A: To Find a parametrization of the tangent line at the point indicated. r(t) =〈4t, 5t, 9t〉,t = −4

Q: Use spherical coordinates to evaluate -VE 0 Vx? + y? +z? dz dx dy

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Q: Find the unit tangent vector for the parameterized curve: r(t) = 2ti + 2cos tj - 2 sint k

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Q: Find the unit tangent vector T(t) and a set of parametric equations for the tangent line  r(t) =…

A: The given space curve rt=e2ti+cost j - sin3t k. Its derivative is r't=2e2ti-sint j - 3cos3t k. At…

Q: Find the unit tangent vector of the curve: 7(t) = (3 cos t , 3 sint, t2) at t = 0. %3D

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Q: The position of a particle is defined by the vector r(t)=⟨sint,cos2t⟩. Find the maximum speed of the…

A: r(t) = ⟨sint,cos2t⟩ Hence, v(t) = ⟨cost,-2sin2t⟩

Q: z = In(x²y*) + / x² + y²

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Q: consider a particle moving on a circular path of radius b described by r(t) = b cos(ωt)i + b…

A: Consider a particle moving on a circular path of radius b given as, rt=bcosωti+bsinωtj Where ω=dudt…

Q: Find the divergence of the function in spherical ? coordinates f = (r* sin 0)e,r

A: Divergence of a function in spherical coordinates is                  ∇.F = 1r2∂∂rr2Fr + 1r sin θ…

Q: Find the velocity and acceleration vectors in terms of u, and ug- de = 5t, where a is a constant r=a…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 20 and 5t, where a is…

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Q: Compute the tangent vector to the given path. c(t) = (4t sin(t), 6t) %3D

A: The tangent vector for a vector r→t is r→'t.

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Finding the Position Vector for a Particle: The integration of the acceleration vector is the…

Q: find the acceleration of a particle whose position function is x(t)=sin(2t)+cos(t)

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Q: The vector parametric form of the tangent line to r(t) = (3t², ¿, t – 1) at t = -5 is

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Q: Evaluate the spherical coordinate integ A1 8 sin o | ? sin d dp dɖp de do de 0 0 512 2 O A. -

A: Here we have to calculate I= ∫0π∫0π∫08 sinϕ ρ2 sinϕ dρ dϕ dθ

Q: Transform the vector C = cospâ – sinpô + cospsinp2 into spherical coordinates and then evaluate it…

A: Given cylindrical co-ordinates system as                                               we know that…

Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

A: Let's find.

Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

A: Given, ellipse x^2+2y^2=6   point=(2,1)

Q: 它们也称 Use spherical coordinate to evaluate Vr² + y² + z² dz dy dx. 0,

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Q: 8. Given the vector r(t) = (sint,cos?, In(cos?)), find the equation of the tangent line in…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. r= a(7 - cos 0) and de =7, where a…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(3t))…

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Q: c) Use spherical coordinate to evaluate x dz dy dr 4-x²-y²

A: Sketch the region and find range of variable

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a(7 - cos 0) and = 6, where…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: We have to find position vector

Q: Find the position vector for a particle with acceleration, initial velocity, and tinitial position…

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Q: Evaluate | xz dz dy dx by changing to spherical coordinates.

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Q: The unit tangent vector of a(t) =cos 2t e, +stn 2t e, - tez at t = is

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: Find T(t) and a set of parametric equations for the tangent line to the helix given by 7(t) = 2…

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Q: Ex6:compute 4Cメッッ) du where: 4(メy)4 メサ by using spherical coordinates system.

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

Q: fund the laplace of Cos it CoS Bt dt

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Q: Convert the following function into Spherical Coordinates. f(x,y,z)=3z

A: Convert cartesian to spherical coordinate :                Put x=r cos(θ) sin(ϕ)       y=r sin(θ)…

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: what is the laplace equation for a sphere

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.