Find the unit tangent vector T and the curvature K for the following parameterized curve. r(t) = (2t+1, 5t-4,4t + 12)

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A: Find the parametric equations fot the tangent line

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A: Given curve is We know that curvature to given curve at point (-1,1,-1) , that is at t=-1 is

Q: Consider the vector function r(t) that has unit tangent vector 1 T(t)= (1,1,2t), 0≤t≤ 2. √1+5t²…

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Q: Find the Unit Tangent (T (t)) b. Unit Normal Vectors (N(t)) c. Find Curvature (k (t)) & (k (3),t=3)…

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A: We given parametric curveFormula used:Unit tangent vector :Unit normal vector:Curvature:Binormal…

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Q: Write a formula for curvature in terms r1(t) and t1(t)

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Q: Please sovle the following calc 3 problem and show all work by hand (explain answer)

A: Step 1: Given is the vector function below: r(t)=(8−2t)i+(2t−8)j+(7+t)k Step 2: The unit tangent…

Q: Calculate the mean curvature of the catenoid 2²+ y? 2= a1 a

A: The complete solutions are given below

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: A smooth curve C' is defined by some vector function R(t) with R = (π, 0, -2) and R¹(t) = (2, √5 csc…

A: Disclaimer: Since, you have requested for the answer of part 3, only part 3 has been answered.…

Q: Find the curvature k(t) of the curve (r)t=(-9sint)i+(-9sint)j+(6cost)k

A: Solution is given below:-

Q: Find the curvature K, the i

A: Given: Curve y=4+x2 and point 0,2 To find: a) Curvature K             b) Radius of curvature R…

Q: Find the radius of curvature of the curve generated by the position vector r (t) = (-40 sin(t),–9t,…

A: Given, r(t)=-40sint,-9t,40cost r'(t)=-40cost,-9,-40sint r'(t)=-40cost2+(-9)2+-40sint2=41…

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A: Consider the equation as shown below: Here, curve ft =2t2-3, 3-t, 3+2t2 Here, the object is to find…

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Q: Calculate the curvature of the cos(t²), sin(t²) >. Show all steps. parameterized curve r(t) =<

A: we need to calculate the curvature.