- Find the area of the ellipse which is parametrically expressed as =a cos o and y=b sin ø, and verify the Green's theorem.

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

A: Moving trihedral are three unit vectors of curve  Unit tangent vector  Unit normal vector  binomial…

Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: A hole is drilled through the center of a sphere x² + y² + z² = R,², leaving a ring-shape solid. If…

A: A per your request , (b) The equation of sphere is given as , x2+y2+z2=Rs2 and Radius of drill=Rd…

Q: 1. Consider the ellipsoid x² + y² + 4z? = 12. (a) Find an equation of the tangent plane to the…

A: As per bartleby guideline for more than one question, only 1st one is to be answered. Please upload…

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

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Q: Show that the ellipse x = a cos t, y = b sin t, a 7 b 7 0, has its largest curvature on its major…

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Q: (c) The cone r² = 4(y² + z?) for (0 <x < 4

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Q: snip

A: Except for degenerate cases, the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 defines an ellipse if ____.

Q: Use the parametric equations of an ellipse, x = 5 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2π, to find the area…

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Q: Find the area of the surface formed by revolving the ellipse about the z-axis (an ellipsoid) y² + a²…

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Q: Show that the parametrization of the ellipse by the angle 0 is ab cos e Va? sin? e + b2 cos2 0 ab…

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Q: Use the parametric equations of an ellipse, x = 3 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2T, to find the area…

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Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Match the ellipsoids shown in the figure above with t 1) x2 + 4y + 4z? = 16 2) 4x2 + y +4z? = 16 3)…

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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: Find F. dr, where F(x, y) = (xy² + cos x)i+(x²y+sin y)j and C is the ellipse C x2 + 2y2 = 9,…

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Q: 35. Calculate || 9x*+4y* dx dy, where D is the interior of the ellipse (G) + (4)' =

A: Given:

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Given the equation of an ellipse in parametric form:x=acost,y=bsint,where a, b are semi-axes of the…

A: Equation of ellipse in parametric form is Differentiating with respect to t, we get Now,

Q: Find a parametrization for the following curve. a.) The ellipse centered at (2,-3) whose major axis…

A: Here we find out parametric equation for ellipse.

Q: Find the moving trihedral and the curvature at any point of R(t) = (3t2, sin 2t, cos 2t).

A: Introduction: The Frenet–Serret formulas in differential geometry describe the kinematic properties…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Find the area of the surface generated by revolving the parametric curve x = cos² t, y = sin² t (0 ≤…

A: To find: The area of the surface generated by revolving the curve about y-axis. Given: The…

Q: Find the area of the region enclosed by the parametric equation x = t³ - 7t y = 6t²

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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 mthod of trig substitution to prove the area of the ellipse " {(x^2)/(a^2)}+{(y^2)/(b^2)} =…

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Q: A hole is drilled through the center of a sphere x?+y² + z² = R,?, leaving a ring-shape solid. If…

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Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: Use the parametric equations of an ellipse, D=5 cos(@), y - 4 sin(6), 0 O 27, to find the area that…

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Q: Need some help with Greens Theorem and ellipse plz, thanks

A: It is required to calculate the value of the integral using green’s theorem:

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: 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: Find a parametrization c(θ) of the unit circle such that c(0) = (−1, 0).

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Q: Evaluate [xydxdy where D is the region D in the first quadrant of the ellipse 9x +4y = 36 in the…

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Q: Find the area of the surface generated by revolving the right-hand loop of the lemniscate r^2 = cos…

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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: Find the area of the region enclosed by the parametric equation x = t3 – 8t y = 6t2

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Q: Assume the equation for an ellipse is Ax +2Bxy + Cy D where D has the units of area. Show, by…

A: Given that Ax2+2Bxy+Cy2=D is an ellipse, where D has the units of area. To prove that the area of…

Q: A hole is drilled through the center of a sphere x2 + y? +z? = R², leaving a ring-shape solid. If…

A:

Q: The ellipse 1 can be drawn with parametric equations where z(t) is written in the form z(t) = r…

A: Given, x282+y242=1

Q: 1. Find the area of the surface generated by revolving the parametric curve x =rcos , y = r sin &…

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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: Show that the arc length of the graph of y = sin x on the interval [0, 2π] is equal to the…

A: Given, Equation of Ellipse is x2+2y2=2 Now divide the equation of ellipse by "2" we get,…

Q: Use the parametric equations of an ellipse, x = a cos(e), y = b sin(e), 0 se s 27, to find the area…

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Q: The perimeter of an ellipse is given by P = 4a V1-k-sin-8 de where, k = Using the Simpson's rule,…

A: The given equation of the ellipse is: x242+y272=1 Result: The standard form of the ellipse is:…

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: A hole is drilled through the center of a sphere x² + y² + z? = R,², leaving a ring-shape solid. If…

A: given sphere x2+y2+z2=R2s and a drill of cylinderical shape x2+y2=R2d use polar coordinate to…

Q: Use the parametric equations of an ellipse, x a cos(0), y = b sin(0), 0 seS 2n, to find the area…

A: Given that the parametric equation of an ellipse is  x= a cos(θ) , y=b sin(θ) , 0≤ θ ≤ 2π . Here we…