dr dt dV dt 1 4πr 2 1) In terms of a sphere, what does 4 represent? 2) Explain how the size of 47.² impacts 1) 2) dr dt

Q: Qi) Let ū =2 5 , and w=-5 ニ|+ フ find Scalars and b such that a ū - aū t bū

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Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: The following parametric equations x = 1 + 21, y=-3+5t, represents line L, and is parallel to a…

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Q: 2. a) Find the line of intersection of the two planes. (answer in parametric form) π₁: 4x-5y-2z=1…

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Q: Use spherical coordinates to evaluate 2π FT S 2-r r+z 0 (r² +2²) ³/ rdz dr de.

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Q: V18-x2-y Convert (x² + y + z?)dzdxdy into spherical coordinates. 2n/3 3V2 4 p* cos pdpdpdO /2 -n/2

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Q: 1) Use spherical coordinates to evaluate 4-x² -y² 4-x2-y2 4-y² LaSNa- y²/x² + y² + z² dzdxdy

A: The given problem is to evaluate the given triple integral using spherical coordinates, We have to…

Q: 16-y Convert (z² + y² + z²)dzdrdy into spherical coordinates.

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Q: Let S be a sphere or radius a. (a) Compute ff(² + y² + ²)dS. (b) Use symmetry and part (a) to find…

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Q: 5. Find u-dr for a unit square in the first quadrant with vertex at the origin by Stokes's C theorem…

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Q: 21. Let Sech u = 3/5 , determine the values of the remaining five hyperbolic functions.

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Q: Convert the following lines to parametric equation. a) l₁: = (1,0,1) + t(1,0,−2), t = R Z-3 b) 1₂: x…

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Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: Convent Cartesian equation to Parametric a) x² - y² = 4 b) y= ex et

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Q: Evaluate the double integral 1+ 4x² + 43²&A where D is the bottom half of the circle x? + y? = 16.…

A: In polar coordinates,                                   and

Q: Describe and sketch each surface in the specified coordinate system; identify free variable(s). (a)…

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Q: -> learn.vccs.edu/courses/262120/quizzes/2377480/t Apps M GmailN Netflix MyReynolds Canvas- Reynolds…

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Q: 2. Use polar coordinates to evaluate √9-1² 2 L √4+x² + y² dy dx.

A: This is a problem related to integral of polar curves. Based on the substitution in cartesian…

Q: 1. Find a parametrization of the line segment L from -2 to -2 + 2i. 2. Find the image of L under the…

A: We will find the equation for L and the image of L under w

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2.…

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Q: 5 25- y² 50-g² –y² Convert (x² + y² + z²)dzdædy into spherical coordinates. ²+y² 5/2 pª cos ødpdød0…

A: Answer:We have to convert∫50∫25-y20∫50-x2-y2x2+y2x2+y2+z2 dzdxdy into sphercal coordinates∵0≤y≤5…

Q: A find tke shuntest istanee betwen the points (a,b,e) and plane Ax + By + Cz =D

A: Equation of plane is Ax + By +Cz = D  Point is P(a,b,c)

Q: (a) (b) (c) r(u, v) = (u cos v, u sin v, v); u € [0, 2], v € [0, π]. (*) Find r, and r. (**)…

A: Surface integral of a function f(x,y,z) on a parametric surface r(u,v) in the region D  ∫∫Dfx(u,v) ,…

Q: Please solve asap: 9. Give a parametric description of the form r(u,v) for the equation 6x - 3y +…

A: To obtain a parametric description of the equation 6x−3y+2z=18, write it in terms of two variables,…

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: 24) Consider line L of parametric equations x =t, y = 2t, z = 3, t E R. a. Find parametric equations…

A: The given line is: x=t, y=2t, z=3 and t∈R Now, consider the angle θ between two intersecting plane,…

Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

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Q: 3. Use cylindrical coordinates to evaluate 3 √9-x² [² [³²*² [√²²+³ (2² + y²) ³¹ dzdydz 0 Jo

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