4

Problem 4. (4 pts) Consider the helir given by r(t) cos(nt) , 2t,4 sin(It)} Express the tangent line to r(t) centered at t = 3 in vector form and parametric fortne....

Question

Problem 4. (4 pts) Consider the helir given by r(t) cos(nt) , 2t,4 sin(It)} Express the tangent line to r(t) centered at t = 3 in vector form and parametric fortne. What is the distance from the tangent line to the point (1,3,2) ? Use calculator to give decimal approrimnation of this distance.

Problem 4. (4 pts) Consider the helir given by r(t) cos(nt) , 2t,4 sin(It)} Express the tangent line to r(t) centered at t = 3 in vector form and parametric fortne. What is the distance from the tangent line to the point (1,3,2) ? Use calculator to give decimal approrimnation of this distance.



Answers

$45-46$ . Find the unit tangent vector $\mathbf{T}(t)$ at the point with the
given value of the parameter $t$ .
$$\mathbf{r}(t)=\left\langle t^{3}+3 t, t^{2}+1,3 t+4\right\rangle, \quad t=1$$

For this program. We have a curve Heart p He opposed the three key square. So Tookie Cube and the PTO has so spirited upfront he you close to 60 square and the one half a t e to the minus one hat. So when t cost one the tender vector our prime one close to six and one half and then the unit and your back 31 goes to 1/6 divided by route off six square pass one have square in the one have to buy it. Buy this in number which is the length of this off nectar When he coasted to attention Vector ah, prime of two because 2 24 one over on two times rooftop to so the union 10 directed He too recalls to after the four develop bias lands and the one over two times wrote off to give Aleph Iceland. So just don't meet all the details here and win. T close the three. If you think you're better our prime three because to 54 1 over to a tense moment off three and then the unit and your meta 53 close to 54 develop bind stairs So one over to health, Um, and the 1/2 times with over three. Be about it by a route off 54 square process one over tells.

Vector for this, our at T equals one. So the unit tangent vector t o T. Is our prime of T, divided by the magnitude of our prime of T. So our primary duty will be four times one half T to the minus one half I was to T J. Hopes to T J. Mhm to T J plus one K. So to over the square root of T I Plus two TJ Plus K. So Our prime of one will be too 21. And the magnitude of our prime of juan will be squared of two square plus two square plus one square, Which is squared of nine, which is 1, 3, so T one is two thirds, two thirds, one third.

In this question, we have a curve are key defined by three key and the piece worth its curative with respect to pee will be three to t. So when P causes zero, um, the tinges vector up, Frankie a friend zero will be 30 old. So the union tend your record. P zero is just 10 And when he closed to minus one, the tension vector our pride minus one Because doe three minus two and the units tend your record, he minus y was through three overweight, off 30 minus two over route off 13. And that's when he closed toe one. Um, the tension vector up from one because the three to the unit tender vector t one because the three over eat off 30 to overeat off 30.


Similar Solved Questions

5 answers
The annua demand for heavy trucks in last few years has shownto follow cyclic pattern as shownbelow The demand data for the last six years shownbelow. (Total 30 marks)Demand (in Year thousands) 2014 2015 2016 2017 2018 20194 48Demand (in thousands)20112012201320142015201620172018Based onthe above data answe thefollowing questions
The annua demand for heavy trucks in last few years has shownto follow cyclic pattern as shownbelow The demand data for the last six years shownbelow. (Total 30 marks) Demand (in Year thousands) 2014 2015 2016 2017 2018 2019 4 48 Demand (in thousands) 2011 2012 2013 2014 2015 2016 2017 2018 Based on...
5 answers
Data and CalculationsDetaMass of crucible lidMass of tin, SnMass of cruciblemetal oxide product Mass of metal oxide product [(mass of crucible + lid + metal oxide product) (mass of crucible lid)] Mass ol oxygen (mass f metal oxide mass of tin)Sho . your calculations for determining the simplest formula of the compound;Simplest formula of the compound:
Data and Calculations Deta Mass of crucible lid Mass of tin, Sn Mass of crucible metal oxide product Mass of metal oxide product [(mass of crucible + lid + metal oxide product) (mass of crucible lid)] Mass ol oxygen (mass f metal oxide mass of tin) Sho . your calculations for determining the simples...
5 answers
4.054,025,424,435,425,245,055,685,205.154,894,644,394,93
4.05 4,02 5,42 4,43 5,42 5,24 5,05 5,68 5,20 5.15 4,89 4,64 4,39 4,93...
5 answers
Compute the value of the grand mean, j_ Use at least 3 digits to the right of the decimal: [2 pt(s)]Submit AnswerTries 0/3Compute the treatment sum of squares, SSA: [2 pt(s)]Submit AnswerTries 0/3Compute the error sum of squares, SSE [2 pt(s)]Submit AnswerTries 0/3Compute the total sum of squares, SST: [2 pt(s)]Submit AnswerTries 0/3
Compute the value of the grand mean, j_ Use at least 3 digits to the right of the decimal: [2 pt(s)] Submit Answer Tries 0/3 Compute the treatment sum of squares, SSA: [2 pt(s)] Submit Answer Tries 0/3 Compute the error sum of squares, SSE [2 pt(s)] Submit Answer Tries 0/3 Compute the total sum of s...
5 answers
Show how to synthesize via Michael reactionPh _ CH_CH; OCH,CH; CH(COOCH,CH,)zCH,CH,CNCH,_CH;_C CH; CH; CH 0-C-CH;
Show how to synthesize via Michael reaction Ph _ CH_CH; OCH,CH; CH(COOCH,CH,)z CH,CH,CN CH,_CH;_C CH; CH; CH 0-C-CH;...
3 answers
Intan Anovr fesl thare ar0 lovals 0l Ihe laclar and Ihie gumple siofar uach leval,9: HI ehe computcd valua ol the tost saliatlos i 4.65 which Ia true ol the P-value ot the test?05 < p < 0 025 < P < 05 01 < p < 0250 d P < 01 e P > 10Clear my choiceIn 4 single-lactor Anova procedure Ihere Ievels ol the Iactor of interest and Ihe sample size tor each levelisn = 6 bute? i> the critical value of F at the 0.05 Ievel of significance?
Intan Anovr fesl thare ar0 lovals 0l Ihe laclar and Ihie gumple sio far uach leval, 9: HI ehe computcd valua ol the tost saliatlos i 4.65 which Ia true ol the P-value ot the test? 05 < p < 0 025 < P < 05 01 < p < 025 0 d P < 01 e P > 10 Clear my choice In 4 single-lactor Anov...
5 answers
House 55.0 ft long and 48.C ft wide and has 8.0-ft-high cellings_ What Is the volume of the Interior of the house In cubic meters and cublc centimeters? m"
house 55.0 ft long and 48.C ft wide and has 8.0-ft-high cellings_ What Is the volume of the Interior of the house In cubic meters and cublc centimeters? m"...
1 answers
Use the limit definition of the partial derivative to verify the formulas $$\frac{\partial}{\partial x} x y^{2}=y^{2}, \quad \frac{\partial}{\partial y} x y^{2}=2 x y$$
Use the limit definition of the partial derivative to verify the formulas $$\frac{\partial}{\partial x} x y^{2}=y^{2}, \quad \frac{\partial}{\partial y} x y^{2}=2 x y$$...
5 answers
Discuss what factors most influence crash fatalities. How do they differ based on the mode of transportation?
Discuss what factors most influence crash fatalities. How do they differ based on the mode of transportation?...
5 answers
SownIno Fgure, black wolghngslldar dutnpnn indlinodangio 0t00 MHk
sown Ino Fgure, black wolghng slldar dutn pnn indlinod angio 0t 00 M Hk...
1 answers
In Exercises 37 - 44, find the domain, $ x $-intercept, and vertical asymptote of the logarithmic function and sketch its graph. $ f(x) = -\log_6(x + 2) $
In Exercises 37 - 44, find the domain, $ x $-intercept, and vertical asymptote of the logarithmic function and sketch its graph. $ f(x) = -\log_6(x + 2) $...
5 answers
People who inherit a mutated Rb- allele generally developretinoblastoma at a much earlier age than people withretinoblastoma who do not inherit any Rb– alleles. Why is this?(Please answer with no more than 5 sentences)
People who inherit a mutated Rb- allele generally develop retinoblastoma at a much earlier age than people with retinoblastoma who do not inherit any Rb– alleles. Why is this? (Please answer with no more than 5 sentences)...
5 answers
Pcini) Find Ine moximum Jnd momum voluot occuringIho lunclion I(n,9,=) 2v? "suclocl the constraint =? v +2 04. Marimum valuo ponls (pasitie inleger Fininilak!many" hnimum valua ponle (poallwa nlegut "Inlaulaly many)occuring
pcini) Find Ine moximum Jnd momum voluot occuring Iho lunclion I(n,9,=) 2v? "suclocl the constraint =? v +2 04. Marimum valuo ponls (pasitie inleger Fininilak!many" hnimum valua ponle (poallwa nlegut "Inlaulaly many) occuring...
5 answers
Worksheet Find the point on 3 parabola P(x)that is closest to the point (5 , Enter your answer a point; e.g (1,2)
Worksheet Find the point on 3 parabola P(x) that is closest to the point (5 , Enter your answer a point; e.g (1,2)...
5 answers
[0/2 Points]DETAILSPREVIOUS ANSWERSOSCOLPHYS2016 15.5.WA.034:MY NOTESASK YOUR TEACHERPRACTICE ANOTHER4-ton jir conditioner removes107 (50,800 Btu) from cold enyironment (a) What energy input Joules necessani this the air conditione has a EER (energy efficiency rating measured 4Re8Btul(h W)) of 12 4?What are the units which EER measured?(b) What the cost doing this the work costs 10.50 per 3.60 J0& (one kilowatt-hour)? centsSubm [ Answor
[0/2 Points] DETAILS PREVIOUS ANSWERS OSCOLPHYS2016 15.5.WA.034: MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER 4-ton jir conditioner removes 107 (50,800 Btu) from cold enyironment (a) What energy input Joules necessani this the air conditione has a EER (energy efficiency rating measured 4Re8 Btul(h W))...

-- 0.020955--