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kristakingmath.com
How to find maximum curvature for a vector function at a particular point — Krista King Math | Online math help
To find curvature at a particular point, we’ll 1) Find r'(t) and use it to 2) Find |r'(t)| and then use r'(t) and |r'(t)| to 3) Find T(t), and then use it to 4) Find T'(t), and then use it to 5) Find |T'(t)|, and then use |r'(t)| and |T'(t)| to 6) Fi
Jul 12, 2021
Curvature Applications
At certain place on railway track, the radius of curvature of railway track is 200 m. If the distance between the rails is 1.6 m, and the outer rail is raised by 0.08 m above the inner rail, find the speed of train for which there is no side pressure of the rails. Take g =10 m / s 2 A. 5 m / sB. 10 m / sC. 15 m / sD. 20 m / s
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SOLVED:A formula for the curvature of the graph of a function in the x y -plane a. The graph y=f(x) in the x y -plane automatically has the parametrization x=x, y=f(x), and the vector formula 𝐫(x)=x 𝐢 f(x) 𝐣 . Use this formula to show that if f is a twice-differentiable function of x, then κ(x)=(|f^''(x)|)/([1 (f^'(x))^2]^3 / 2), b. Use the formula for κin part (a) to find the curvature of y=ln(cosx),-π/ 2<x<π/ 2 . Compare your answer with the answer in Exercise 1 c. Show that the curvature i
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