(1 point) For the curve given by r(t) = (2t, 5t, 1 – 5t), Find the...

Question

Question

(1 point) For the curve given by r(t) = (2t, 5t, 1 – 5t), Find the derivative r(t) =( > Find the second derivative p(t) = (

math Advanced-Math

Answer 1

Answer #1

r(t)=⟨2t,5t,1-5t²⟩

r'(t) = ⟨2,5, -10t⟩

r"(t)= ⟨0,0, -10⟩

Curvature at 1 : k= ||r'(1)×r"(1)||/||r'(t)||³

r'(1) =⟨2,5,-10⟩

r"(1)= ⟨0,0, -10⟩

r'(1)×r"(1) = A 2. s 이 0 0 16

= -50i +20j

r'(t)×r"(t)= ⟨-50 ,20,0⟩ at t=1.

||r'(1)×r"(1)||=√((-50)²+(20)²+0) =√(2500+400) =√2900

||r'(1)||=√((2)²+(5)²+(-10)²) = √(4+25+100) =√(129)

K(1)=√(2900)/(√(129))³ = 0.036754831

Answer 2

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