O Spherical coordinates O Jacobian Transformation O Rectangular coordinates O Cylindrical coordinates

Q: Arc length: Find the length of the space curve with vector equation r(t) =(4, 3cost, 3 sint ) over […

A: We have to find the arc length.   According to our guidelines we can do only one question so please…

Q: A curve Cis given by the parametric equations z = 2t –2 and y = (t- 2) where t > 0. 1. The curve has…

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Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 < 0 < 2n.) (a) (-7, 7, 7) (147,…

A: Given that  The rectangular coordinates  To convert the rectangular coordinates in to cylindrical…

Q: Cylindrical coordinates Evaluate the Jacobian for the transformation from cylindrical coordinates…

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Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 se s 2n, and 0 so s T.) (a) (0, -2,…

A: x, y, z=0, -2, 0. Now, ρ=x2+y2+z2=02+-22+02=2 θ=tan-1yx=tan-1-20=tan-1-∞=3π2…

Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 sos 27.) (a) (2, –2, 3) (b)…

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Q: A lamina occupies the part of the disk x2 + y2 < 4 in the first quadrant. Find the center of mass of…

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Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: The parametric equations x = x1 + (x2 − x1)t,    y = y1 + (y2 − y1)t where  0 ≤ t ≤ 1  describe…

A: To find the parametrization

Q: The parametric equations x = x1 + (X2 - x1)t, y = Y1 + (Y2- Y)t where 0 stsidescribe the line…

A: Step:-1 Given that x=x1+(x2-x1)t,  y=y1+(y2-y1)t  where 0≤t≤1  And vertices of a triangle is A(1,…

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 < 0 < 21, and 0 s¢ s n.) (a) (2,…

A: To change the coordinate from rectangular to spherical we can use these formulae:…

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 < 0< 21, and 0 s o < n.) (a) (0,…

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Q: genuy. Registration number = 026 II: Consider rx + y+ 4z = 8 and x + ry – z = -1 %3D Find the acute…

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Q: Minimizing polar inertia A thin plate of constant density is tooccupy the triangular region in the…

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Q: 2. Given point P(1, -2,4) and vector à = zā¸ + (x+y)ā. Express Pand A in cylindrical coordinates.…

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Q: Change from rectangular to spherical coordinates. (Let p≥ 0, 0 ≤ 0 ≤ 2, and 0 ≤ y ≤ n.) (a) (0, 3,…

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

Q: Change from rectangular to cylindrical coordinates. (Let r2 0 and 0 s 0 s 2n.) (a) (-1, 1, 1) (b)…

A: The solution of both the problems is given below. r=√(x^2+y^2)

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 < 0 < 2n, and 0 s p n.) (0, 2 3, 2)…

A: Formula for the converting rectangular coordinates to spherical coordinates.

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

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Q: Convert the point from rectangular coordinates to cylindrical coordinates. (6, –6, 9) Step 1 In the…

A: To convert the below point from rectangular coordinates to cylindrical coordinates. 6,−6,9

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0 s 0 s 2n, and 0 s ø s .) (a) (0, -7,…

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Q: urface S is parametrized by equations x = u + v, y = 3u², z = u – v; The point P (2, 3, 0) lies on S…

A: In this question, the concept of the derivative is applied to find out the equation of a tangent…

Q: Change from rectangular to cylindrical coordinates. (Let r2 0 and 0 s 0 s 2n.) (a) (-3, 3, 3)…

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Q: Change from rectangular to spherical coordinates. (Let ρ ≥ 0, 0 ≤ θ ≤ 2π, and 0 ≤ ϕ ≤ π.) (0, −7,…

A: Given Part a) coordinates  (0,-7,0) Part b) coordinates (-1,1,-2)   To convert:  From rectangular…

Q: Change from rectangular to cylindrical coordinates. (Let r 0 and 0 < 0 < 2n.) (a) (9/3, 9, –8) (b)…

A: The rectangular coordinates (x,y,z) are converted into cylindrical coordinates (r,θ,z) by using the…

Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 s 0 s 27.) (a) (-3, 3, 3) (b)…

A: Cylindrical coordinates are (r, θ, z)

Q: The parametric equations x = x1 + (x2 − x1)t,    y = y1 + (y2 − y1)t where  0 ≤ t ≤ 1  describe…

A: To find the parametrization

Q: Convert the point from rectangular coordinates to cylindrical coordinates and spherical coordinates.…

A: We have to convert the rectangular coordinates to cylindrical and spherical coordinates.

Q: The cylindrical coordinates (r, 0, z) of a point are given. Find the rectangular coordinates (x, y,…

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Q: Change from rectangular to cylindrical coordinates. Select such set of cylindrical coordinates as 0…

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Q: NIM Let line l: x = = and point P(1,0,1). 2 Find the parametric equations of the line parallel to…

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Q: The Line whose eduation is (X + 2y +Z=!) > Cx -y + 2Z +7 =0) intersecks X Z plane. write equation of…

A: The line represented by the equation x+2y+z=1 and x-y+2z+7=0 intersects the XZ plane.

Q: Change from rectangular to spherical coordinates. (Let p 2 0, 0o s0 s 2n, andos oS n.) (a) (4, 4/3,…

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Q: 18-z-y? Example 3 Convert + y² + z² dz dx dy into spherical coordinates.

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Q: Using spherical coordinates calculate ſezsqrt(x²+y²)dV where E={(x,y,z) | x²+y²+z²0,y>0,z>0}

A: To find- Use spherical coordinates calculate ∭Ezx2 + y2 dV where E = x, y, z | x2 + y2 + z2 ≤ 4, x…

Q: Find parametric equations for the line. (Use the parameter t.) The line through the origin and the…

A: Find parametric equations for the line. The line through the origin and the point (6,4,-1). Find the…

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. Y = 3√x ,…

A: We have given a curve; when we cube both sides, we get; On differentiating this function we get;

Q: Convert the rectangular equation to an equation in cylindrical coordinates and spherical…

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Q: Eliminating the Parameter Convert to rectangular coordinates. I=1+ sin t, y = 1+ cost for t in 0, 27

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Q: Cartesian Polar (positive radius) Polar (negative radius) (-3,3) (-2,0) (V3, 1)

A: The given cartesian coordinates are

Q: A lamina occupies the part of the disk x^2+y^2<16 in the first quadrant. find the center of mass of…

A: Find the centre of mass of following function:

Q: a. Show that when you express ds2 = dx2 + dy2 + dz2 in terms of cylindrical coordinates, you get ds2…

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Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 s 0 s 2n.) (a) (-3, 3, 3) X*…

A: a) Compare the coordinates with the form, x,y,z. x=-3y=3z=3

Q: (x – 1)² + (y – 2)² = 6 A) B) Center: (-3, 1) Center: (1, 2) Radiu: Ve Radiu: ve O A в D) Center:…

A: (x-1)2+(y-2)2 = 6

Q: Change from rectangular to cylindrical coordinates. (Let r 2 0 and 0 s 0 s 2.) (a) (-1, 1, 1) -,1 4…

A: a) We use the rectangular to cylindrical coordinate formula r2=x2+y2r2=(-1)2+12r2=2r=2…

Q: 2) Rotate this curve around the X-axis. Find the sur face Crea f the sur face. what is the sur face…

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Q: [4pts] Consider a point in Cartesian coordinates given by (3√/3, -3, -8). a.) Find a corresponding…

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Q: -1, -/ä, 1ị.

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Q: 33. The wave function is evaluated at spherical coordinates (r, 0, p) = (V3, 45°, 45°), where the…

A: Here we have to only use the conversion formulas.

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.