Use the parametric equations of an ellipse, x = a cos(0), y = b sin(0), 0 s 0 s 2T, to find the area that it encloses

Q: What is the surface area of the three dimensional solid formed by rotating the following parametric…

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Q: Зл The parametric curve x = 7 sin 2t and y = 9 cos 2t, where , traces the ellipse 49 = 1 81 a. 3…

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Q: Consider the parametric equation of the shifted ellipse 9 45 x = 4 cos 0, y = 16 sin e Evaluate the…

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Q: Find parametric equations for the line tangent to the helix

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Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: Find the parametric equation of x, y, z where : . z2 = x2 + y2 p. 9 = x2 + y² Nhat is the name of…

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Q: 4. (i) Use the parametric equations of an ellipse, x = a cos (t) , y = b sin (t), 0 < t 2m, to find…

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Q: Set up but DO NOT EVALUATE the integral to find the length of the curve described by the parametric…

A: We have given parametric equations  xt=cos2t,yt=sin5t  for   0≤t≤π.

Q: Show that the parametric equations x =a sin u cos v, y =b sin u sin v z=c cos u 0&lt;u &lt;pi  0 v…

A: Here,

Q: Find the surface area of the solid that is obtained by rotating the graph of the parametric curve…

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Q: Determine the number of cusps for the hypocycloid described by the parametric equations x(t) =…

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Q: - [[s sin(a2+y2) dA D where D is a disk of radius 2 centered at the origin. 14.

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Q: Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi]…

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Q: Find the length of arc of the curve given by the parametric equations x = t°, y=t² from the point…

A: Arc length is given byL=∫abdxdt2+dydt2dt

Q: Consider the parametric equation  x = t2 - 1 and y = t2 + 2t. (a) find (dy)/(dx) and (d2y)/(dx2).…

A: Given parametric equations - x = t2-1t2 = x+1t = x+1         .................(1)y =…

Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

Q: 3. Evaluate (sin r +y cos r)dr + (sin r + z cos y)dy + sin ydz), where C'is the ellipse 36.r + 4y =…

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Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: Cylindrical co-ordinates of the point P are (r,θ,z) rectangular co-ordinates of the point P are…

Q: Find the length of the parametric curve C = {(x(t),y(t)) : t E I} x(t) = cos (t) , y(t) = sin³ (t),…

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Q: Find for the parametric curve x= 2e', y= sin(1+ e') dx

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Q: (c) . sin (92? +4y?) dA D where D is the region in the first quadrant bounded by the ellipse 9a?…

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Q: Use the parametric equations of an ellipse x = 10 cos 0 y = 22 sin 0 0 ≤ 0≤2T to find the area that…

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Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

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Q: 3. Find the exact area of the surface obtained by rotating the curve described by the parametric…

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Q: The position of a particle moving in the xy-plane is given by the parametric equations x(t) =…

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Q: a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: . Find a cartesian equation for the given parametric equations: a) x = t2 – 4 and y =t+1 b) x = 2…

A: Eliminating t

Q: tind the area of the parametric curve X = t ,4=9t-73

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Q: 4. y = sin2r, 0 sa Find the area of the surface of rotation obtained by rotating the curved segment…

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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: Evaluate sin(x) dx + z cos(y) dy + sin(y) dz where C is the ellipse 25x2 + 9y2 = 225, oriented…

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Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

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Q: Consider the parametric equations below. x = t sin(t), y = t cos(t), 0 ≤ t ≤ ?/3 Set up an integral…

A: To set the integral

Q: What is the Cartesian form of the parametric equations x(t) = 4t – 2 and y(t) = /t – 3? %3D Provide…

A: To find cartesian form of equation

Q: (a) æ = sin t, y = csc t, 0 1. Thus, the curve is the portion of the hyperbola y = 1/x with y > 1.…

A: Given x=sin ty=csc t0&lt;t&lt;π2

Q: Show that the curve with parametric equations x = t cos t, y = t sin t, z =t lies on the cone z? =…

A: We have to check if x,y,z parametric equations lies on the given cone.

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t). -

A: Given is : R→(t)=t2,-cos(8t),sin(8t) In order to find the curvature use the formula . Formula for…

Q: The surface area of the surface generated by revolving the parametric curve x-2t -2sin t, y-2-2cos…

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Q: Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface…

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Q: Find the area of the surface obtained by rotating the curve of parametric equations T = 2 cos 0, y =…

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Q: Find the area of the surface generated by revolving about the x-axis the portion of the astroid x2/3…

A: Given Data The equation of an asteroid portion is x2/3+ y2/3=1.   The interval on the x-axis from…

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: determine the parametric equations of the tangent axis to the ellipse x²/9+y²/4=1 at the point T =…

A: As we know that the parametric equation of ellipse at a point acosθ,bsinθ  is given by…

Q: Consider the parametric equations x = t2 - 1 and y = t2 + 2t. (a) Find (dy)/(dx) and (d2y)/(dx2).…

A: Consider the parametric equations  x = t2 − 1 and y = t2 + 2t

Q: Find the area of the region enclosed by the parametric equation x = t³ - 8t y = 4t²

A: This is a loop formed find graph  And then find limits of t

Q: Find a parametric description for the ellipse 9x^2+4y^2+24y=0, oriented clockwise and where t=0…

A: Given equation of the ellipse 9x2+4y2+24y=0.

Q: x = 7 cos 0 y = 14 sin 0 0 <0< 2n

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Q: Find ,Y, and of the given parametric equations dy d²y dx ' dx² d³y dx3 X = cost, y = 5 sin t in…

A: The given parametric equations,x=cost, y=5 sint

Q: Consider the plane curve given by the parametric equations x = t² + 22t - 23 y = t² + 22t - 5 What…

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