5. Sketch the vector-valued equations r(t)=2costi+3sintj. Then, find the curvature of the ellipse at the endpoints of the major and minor axes, by using formula K =!

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Q: Exercise 3.2.10. Using K = (In - m²)/(EG – F²), show that the Gauss curvature of the R- sphere S²(R)…

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A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

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A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

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A: We will find out the required value of curvature .

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Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t,…

A: Explanation: Given that,  Line 1: x=1+ty=1+6tz=2t Vector 1: 1,6,2 Line 2: x=1+2sy=5+15sz=-2+6s…

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

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A: In this question we will use basic of calculus i.e concept curvature of ellipse. We will simply…

Q: 7.) rCt) = (5+,3cot), 3sind), 7.1-> Find the arc length of the curve. 72-) Find the unit tangent and…

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Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: find The unit Vectors tanent and normal to The ellipse x+2y= 6 at The Point (2,1).

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A: Given  The equation of Paraboloid Z=x2+y2 The equation of Ellipsoid 2x2+y2+z2=76

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Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

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Q: 15. Show that the ellipse x = acos t, y = b sin t, a > b> 0, has its largest curvature on its maior…

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Q: What is the maximum height of a particle whose path has parametric equations x = t9, y = 4 − t2?

A: The height of the particle is given by it's y position: y = 4 - t2 At the maximum height, dy/dt = 0

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Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

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Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

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