Over x-axis (x, y) Over y-axis (x, y) Rotation Rule (about the origin) Clockwise 90° (х, y) - Clockwise 180° (x, y)- Clockwise 270° (x, y)-

Q: Angular speed Consider the rotational velocity field v = ⟨0, 10z, -10y⟩ . If a paddle wheel is…

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Q: A particle moves on a circle of radius 4 cm, centered at the origin, in the xyxy-plane (x and y…

A: Consider the following: The particle at t =0 at A (0, 4) rotates counter clock wise in 11 sec, Find…

Q: F(x, y) = (y cos(x) – xy sin(x), xy + x cos(x), Cis the triangle from (0, 0) to (0, 6) to (2, 0) to…

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Q: x^2+y^2=4 The part of the circle in the first region is rotated around the line x + y = 2.…

A: When a surface S is revolved around any line Ax+By=C then the surface area is S=2π∫t0t1rtdswhere, rt…

Q: Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.

A: Use the Gauss’ Divergence theorem,: Use the Gauss’ Divergence theorem,

Q: Find the equation for the tangent plane and the normal line at the point Po(1,2,1) on the surface 3x…

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Q: roțațion 90° counterclockwise about the origin K(-4, 2), L(-4, 5), M-3, 5), M(-3, 3)

A: Please refer to the image below

Q: SOLUE USING LAPLACE TRANSTORMS y" - coy" + By' - 2car St i y(o) = -1, Y'(0) = 2

A: Given y'''-6y''+8y'=2cos5t, y0=-1, y'0=2

Q: ABC to A'B'C'. A' B'. A O a) 90° clockwise O b) 90º counter clockwise rotation rotation O c)…

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Q: roțațion 90° counterclockwise about the origin

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Q: You are in charge of erecting a radio telescope on a newly discovered planet. To minimize…

A: Given that  a spherical planet with a radius of 3 units and let its origin is centered at (0 , 0, 0…

Q: a2u, a2u = -2; 0<x< 1, 0 < y<1 condition u(x,0)= u(x, 1)= u(1,-x) u(0,y)= 0, u(1,y)= sinh(IT) sin…

A: Given: ∂2u∂x2 + ∂2u∂y2 = -2   0&lt;x&lt;1, 0&lt;y&lt;1 ---------(1) with boundary condition…

Q: 2) rotation 27e about the origin. (-y,x) ら s'( )フu V(, ) v' ( 4) rotation 90" about the origin

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Q: orthogonal trajectory   The trisectrices of Maclaurin (a + x) y² = x² (3a –x)

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Q: Non-exacr or first order linear DE

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Q: Zero component of the curl For what vectors n is(curl F) ⋅ n = 0 when F = ⟨y, -2z, -x⟩?

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Q: PLOT THE IMAGE PRE-IMAGE Transformation COORDINATES b) Pre-Image Points Image Poìnts A'L A (1,-4) в…

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Q: Pentagon ABCDE is rotated 90° counterclockwise about the origin to form pentagon A'B'C' D'E'. What…

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Q: y = ex,    y = 0,    x = 0,    x = 3 Find the exact coordinates of the centroid. (x, y) =

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Q: solute value of the Jacobian ) for the chang Ə(s,t) I = s -ť, y =t sin(s).

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Q: roțațion 90° counterclockwise about the origin U(0, -2), V(-1, 2), w(1, 3), x(4, 0) A) U(0, 2), V(1,…

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Q: Yt + ayx = 0, y(0, t) = t, y(x, 0) = 0. 0 0

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Q: uestion 1 dz az Find and on the surface (-5z + 2)4 – 72° - y3 + 6y- 23 + 2y4 . z = 9 - 7z in terms…

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Q: Use Stokes's Theorem to evaluate JCF• dr. Use a computer algebra system to verify your results. C is…

A: To evaluate the integral ∫CF→·dr using Stokes's theorem, where F→=6xzi^+yj^+6xyk^, and S :…

Q: Parabolic dome H(x, y, z) = x2√5- 4z, over the parabolicdome z = 1 - x2 - y2, z ≥ 0

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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: Designing a gondola The designer of a 30-ft-diameter spherical hot air balloon wants to suspend the…

A: Given information:

Q: The helix r,(t)= (1+cost,- sint,t) intersects the curve (2,0,0). Find the angle of intersection. i,…

A: Given,           Both intersects each other at the point (2, 0, 0). We have to find the angle of…

Q: 1. Suppose the x- and y-axes are rotated through an acute angle to produce the new X- and Y-axes. A…

A: Consider the following: Suppose the x-axes and y-axes are rotated through an acute angle  to produce…

Q: 2. Reflection over the y-axis (x, y) → (x − 6, y) 4. 180° rotation clockwise about the origin…

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Q: A particle moves on a circle of radius 6 cm, centered at the origin, in the ry-plane (x and y…

A: Given,  A particle moves on  a circle of radius 6 cm, centered at the origin in the xy-plane.  It…

Q: nares of the image points. Identify and describe the transt 3. M: (x, y)-(X,-y) 4. M: (x, y)-(3x,…

A: We have to find new coordinates of polygon

Q: F = in the displacement The work done by the force along the path C:y=x from the point (0,0) to…

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Q: Torsion of a helix Compute the torsion of the helixr(t) = ⟨a cos t, a sin t, bt⟩, for t ≥ 0, a &gt;…

A: Position vector - r(t) = acost, asint, bt Formula for finding the torsion is given by - ζ =…

Q: Find the volume of the solid

A: Given,

Q: Circular Disk Method 1. R: y = √?, y = 4, y- axis               axis of revolution: y = 4

A: 1 Given that R:y=x, y=4, y−axis and axis of revolution is y=4. We have to find the volume of the…

Q: iv.y %3D cot1 (x), у € [0, п] v.y = sec-1 (x), y e |-1, – u|0, vi. y = csc=1 (x) , y € [-T, – U [0.…

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Q: A triangle is graphed on the coordinate plane. Two of its vertices are located at (-10,3) ar…

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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: ht plane to th t the point where (x, y) = (2, 2) has the equation z = ƒ (x, y) = ln (4x4 y+1) OSP

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Q: CENTROIDAL X AND Y (Xc AND Yc)

A: If a  composite areas  can be decomposed to a finite number  of simpler subareas, and If centroid of…

Q: Rotation 270° counterclockwise around the origin Translation (x, y) (x + 15, y + 1)

A: In the given graph, coordinates of the corners of ∆XYW are given as X-12, -7, Y-9, -13 and W-9, -4.

Q: 4. x = 9 - y?, x = e-y, y = 0,y = 3, rotated about the y-axis 1)Sketch the planar (2D) sketch in the…

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Q: curves 1 1 1 1 y = -x+ 1, x =-jy+2, y=-i* x = --y+2, 1 y = --x (u= 2x +y. v= 2y +* v = 2y +x Use the…

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Q: 3 (z- i) +1 dz, - (z – i)? where C is a closed contour traversed once in the counter-clockwise…

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Q: rotation 180° about the origin U(-3, 2), V(-3, 3), w(-1,3), x(0, 1) 本y

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Q: Inverse Laplace of [ 0.9s / (s^2 + 0.1s -0.02)]

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Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (1,2,0) on the…

A: Let,  ϕ=-8cosπx+3x2y+exz+5yz-15∇ϕ=i∂ϕ∂x+j∂ϕ∂y+k∂ϕ∂z…