5. Find the total length, curvature and torsion of a curve: [cos² t,sin² t, 0] 0≤t≤n?

Q: he following function: =: Find fxy. f(x, y) = 5x4y6x4y5 - 21

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Q: 2 : Let a(t) be a unit speed curve and define B(s) =| Ba(t)dt, where Ba is the binormal of the curve…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

Q: Explain why a circle tangent to y=sin(x) at x=π/2 has its center on the vertical line x=π/2. Find…

A: The objective of this question is to understand why a circle tangent to the function y = sin(x) at x…

Q: 1) Find the length of the curve? X = y 3 + -| 1 4y from y=1 to y ==

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Q: Calculate the curvature of the curve defined by r(t)=9cos(4t)i+9sin(4t)j. Give the answer with 4…

A: Given that: r(t)=9cos(4t)i+9sin(4t)j

Q: for the reparametri zations alt)= (t, Cosht, o), tER. Find two Curve %3D

A: Given curve is αt=t,cosht,0 We have to find the reparameterization for the given curve.…

Q: Use Eq. (9) to find the center of curvature to r(t) = (t 2, t 3)  at t = 1.

A: X-intercept is the point where graph of polynomial function touches/crosses x-axis, i.e y=0 . Y…

Q: Draw the hyperbola with the equation: 3x2 − 2y2 + 6x − 8y = 6.

A: Given the equation of the hyperbola : 3x2-2y2+6x-8y=6.

Q: The curvature of a point moving along the curve given as R(t)=(In sec t) i+ tj is: O t O sec t O…

A: Here, Rt=lnsecti+tj

Q: Q1. The position vector of a moving point is given as: R()=(2 Inr) (-((+1¹) j (a) Express the unit…

A: Solution:

Q: The curvature of the curve (t) = 6t, 6t+1, sin2t at t= TT 0 1 8. 01 01 18 O 2 1/2

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Q: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

A:

Q: Evaluate (x² + y² ) ds , where C is the curve represented b r (1) = (1 – sin t) i + (1 – cos t) j ,…

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Q: Let a, b > 0 be real numbers. Consider the helix a(t) = (a cost, a sint, bt), te R. (a) Find the…

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Q: 1) Find the length of the curve? X = y 3 3 + 1 4y from y = 1 to y = 3

A: we have given curve

Q: for the follawing , find the unit tangent vector: parameterized curve rit) =<2 sint) , 2 cos lt),5…

A: Given: r(t)=2sin(t),  2cos(t), 5cos(t),  0≤t≤π The unit tangent vector to curve r(t) is…

Q: Find the length of the curve y = V- from z =1 to r = e. 3

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Q: Given A¹¹'(-4, - 6) and are the coordinates of A? 3/092103/talu = Ro 180°(Ry - axis(T (5. s>(A))),…

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Q: Find the radii of curvature and torsion at a point of the curve r? + y2 = a², x² – y? = az. %3D %3D

A: Given curve is x2+y2=a2x2-y2=az

Q: The curvature of the curve 7 (t)= (2t, 2t+ 1, sin2t) at t= TT is 4. 1 18 O 1 1/8 1/2 O O O O

A: The given curve is r(t)→=2t,2t+1,sin(2t) We know that the curvature κ(t) for r(t)→ is given by the…

Q: Find the unit tangent vector T and the curvature k for the following parameterized curve:

A: the given curve:r(t)=9 cost , 9 sin t ,3tfirstly, differentiate the given functionr'(t)=-9sint , 9…