math

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These questions relate to curvature problems.

a.Explain why (dÖ/ds) = (dÖ/dt) (dt/ds).
b.Explain why tanÖ = dy/dx, which equals (dy/dt) / (dx/dt).

  • math -

    I have to assume you know the chain rule.

    if x is a function of t, and f is a function of x, then

    df/dt=df/dx * dx/dt

    this is a fundamental relationship in calculus.

  • math -

    I understand that much, but I still cannot derive the curvation equation..

    a.Let x prime and x double prime be the first derivative and second derivatives of x with respect to t, and similarly for y. Show the following in true.

    dƒ³/ds = ( xŒ yŒŒ - xŒŒ yŒ ) / (vector V)^3

  • math -

    Wow that did not work...
    Prove
    (dphi/ds) = ( xprime*ydouble prime - xdoubleprime*yprime ) / (vector V)^3

  • math -

    x prime. OK that is the first derivative of x with respect to ???
    same for double prime. Your statement is just totally meaningless, it cant be proved unless it is understood.

  • math -

    I am trying to prove the formula..

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