Kaplan MCAT Complete 7 X find the derivative of -3co X C https://math.asu.edu/si
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Kaplan MCAT Complete 7 X find the derivative of -3co X C https://math.asu.edu/site x C https://math.asu.edu/site x C https://math.asu.edu/site x b WeBWorK: England MAT X /webwork2/England MAT 267 Spring 2015/Section 10.8/4/?key uwMZo3rqiH Ffn3oERGZ3in EiFjJxibmb &displayMode; MathJax&showoldAnsv; https://webwork.asu.edu WeBWorK Logged in as cktreela. Log Out MATHEMATICAL ASSOCIATION OF AMERICA webwork england mat 267 spring 2015 section 1 MAIN MENU Homework Sets Section 10.8 Problem 4 Section 10.8: Problem 4 Password/Email Prev Up Grades Next (1 pt) Consider the helix r (t) (cos (-1t), sin (-1t), 1t). Compute, at t Problems A. The unit tangent vector T Problem 1 Problem 2 B. The unit normal vector N Problem 3 Problem 4 C. The unit binormal vector B Display options View equations as Note: You can earn partial credit on this problem. ages Preview Answers Submit Answers Math Jax Show saved answers You have attempted this problem 0 times. Yes You have unlimited attempts remaining. No Use Equation Editor? Email instructor Yes No Consider The Pat.Explanation / Answer
Since r(t) = <cos(1t), -sin(1t), -t>, we have r'(t) = <-sin(t), -cos(t), -1>
A) Since ||r'(t)|| = sqrt(2) , we have T(t) = r'(t)/||r'(t)|| = (<-sin(t), -cos(t), -1>)/sqrt(2)
==> T(pi/6) = <-1/(2sqrt(2)) , -sqrt(3)/(2sqrt(2)) , -1/sqrt(2)>
B) T'(t) = (1/sqrt(2))<-cos(t), sin(t), 0>.
Since ||T'(t)|| = 1/sqrt(2), we have N(t) = T'(t)/||T'(t)|| = <-cos(t), sin(t), 0>.
==> N(pi/6) = <-(sqrt(3))/2, 1/2, 0>
C) B(pi/6) = T(pi/6) x N(pi/6) = <(1/4)*sqrt(3/2), -(1/4)*sqrt(3/2), 0>
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