r(t)=e^(t) i +4t j , P(1,0) what does t=? at the point P also how do you find th

Question

r(t)=e^(t)i+4tj , P(1,0)

what does t=? at the point P

also how do you find that "t" value at the point P

i am really unclear about that; also i and j are vector components

Explanation / Answer

Given (1, 0) is represented by r(t)=e^(t)i+4tj. => e^t =1 & 4t =0 => t = 0 (Ans) i & j just describe x & y axis. For a function like r(t), curvature , K at a particular point is given by the formula, k = |x'.y'' - y'x''|/ (x'^2 + y'^2)^3/2 Here x = e^t => x' = e^t ; x'' = e^t As t=0, => x = 1, x' = 1, x'' =1; y=4t, => y' = 4; y'' = 0; => y=0 curvature, k = |x'.y'' - y'x''|/ (x'^2 + y'^2)^3/2 = |1.0' - 4.1|/ (1^2 + 4^2)^3/2 = 4/ (17)^3/2 or 0.000407083249

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.