Use this theorem to find the curvature.r(t) = 6ti + 3sin(t)j + 3cos(t)kkappa(t) = fracsqrt81cos^

Name: Use this theorem to find the curvature.r(t) = 6ti + 3sin(t)j + 3cos(t)kkappa(t) = fracsqrt81cos^4(t) + 162cos^2(t)sin^2(t) + 81sin^4(t) + 324cos^2(t) + 324sin^2(t)(36 + 9cos^2(t) + 9sin^2(t))^frac32
Uploaded: 2023-06-23T10:49:53-08:00
Duration: 4 min 10 s
Channel: Adi S
Description: Use this theorem to find the curvature.r(t) = 6ti + 3sin(t)j + 3cos(t)kkappa(t) = fracsqrt81cos^4(t) + 162cos^2(t)sin^2(t) + 81sin^4(t) + 324cos^2(t) + 324sin^2(t)(36 + 9cos^2(t) + 9sin^2(t))^frac32

Question

Suzanne W. · Accepted Answer

First, we need to find the first and second derivatives of the given vector function r(t) = 6ti

Question

Use this theorem to find the curvature.\ $r(t) = 6ti + 3sin(t)j + 3cos(t)k$\ $kappa(t) = frac{sqrt{81cos^4(t) + 162cos^2(t)sin^2(t) + 81sin^4(t) + 324cos^2(t) + 324sin^2(t)}}{(36 + 9cos^2(t) + 9sin^2(t))^{frac{3}{2}}}$

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