Josephood7

 In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase. Suppose that it takes you one hour to stroll at a constant speed up one spiral of this staircase, which has a radius of 25 feet and a height of 63 feet and makes 7 revolutions.

(a) Assuming the spiral staircase is centered about the [math]-axis, find a vector parametric equation for the helical path you take from the point [math] to the point [math] that makes [math] revolutions during the time interval [math].

[math] 

(b) How far did you walk?

 feet

Which of the following integrals represents the length of the parametric curve [math] about the [math]-axis?

 A. [math]
 B. [math]
 C. [math]
 D. [math]
 E. [math]
 F. [math]

Find an arc length parametrization of [math]

[math]  , , [math]

Calculate [math] when [math]

[math]  .

For a plane curve [math], [math] Use this equation to compute the curvature at the given point. [math]

[math]