IDNLearn.com provides a collaborative environment for finding and sharing answers. Ask your questions and receive comprehensive and trustworthy answers from our experienced community of professionals.
Sagot :
The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2. the curvature of r(t) at the point (7,1,1), r(t)=<7t,t2,t3> is √14/√490.
The equation for curvature is given by κ = |r' × r''|/|r'|3 where r' = dr/dt and r'' = d2r/dt2.
We are given the point (7,1,1) which is the same as t=1.
Therefore, we can substitute t=1 into the function r(t) to obtain r(1) =<7,1,1>.
From this, we can calculate the derivatives r' and r'' of the function r(t) at the point (7,1,1).
r' = <7,2,3>
r'' = <0,2,6>
Then, we can calculate the curvature κ using the equation κ = |r' × r''|/|r'|3.
κ = |<7,2,3> × <0,2,6>|/|<7,2,3>|3
= |<0,-14,18>|/|<7,2,3>|3
= √14/√490
Learn more about equations for curvature here
https://brainly.com/question/5913342
#SPJ4
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.
