5

Find the curve's unit tangent vector: Also, find the length of the indicated portion of the curve. r(t) = 6t3; i + 23j - 318k 2<t<3The curve's unit ...

Question

Find the curve's unit tangent vector: Also, find the length of the indicated portion of the curve. r(t) = 6t3; i + 23j - 318k 2<t<3The curve's unit tangent vector is (Type an integer or a simplified fraction.Di-The length of the indicated portion of the curve is (Simplify your answer:)units

Find the curve's unit tangent vector: Also, find the length of the indicated portion of the curve. r(t) = 6t3; i + 23j - 318k 2<t<3 The curve's unit tangent vector is (Type an integer or a simplified fraction. Di- The length of the indicated portion of the curve is (Simplify your answer:) units



Answers

Find the curve's unit tangent vector. Also, find the length of the indicated portion of the curve. $$-1-3 i-1$$

So we have to pulling, characterized to function off a curb and you're us to find the any tension and it's our place. Overall, the unit vector is a factor that has a level one which can be found by dividing by its magnitude. So in killed in this case, to find a any tension, we need to find attention which is to our prime a t and divide by its magnitude. So to find our primary t, we take the similar substance we used to deal for two drew it. If we take the derivative of each company in here, so are our prime of tape. Well, we did derivative of I and iterated J So for derivative of I This is, um, product ruling here. So do video of tea is just one. So one times 90 plus the derivative signed t useco Sainty times two teeth. There will be plus t close i e d. Plus the driver, of course antes negative sighing t I invented plus saving in here product rule So it will be one times cause I ain t plus Did you read off course On his negative size will be native t Cinque Lee and then the jury off Sainty issues cause nt so it will be finest course Anke o J now thinks cancel out in here. So our sank his cancel out in here and then coastline of teas cancel out in here. So are our prime of teas, actually, as follows t co ST eel I and then minus t sign of T j. And to finance magnitude, we take dough distance formula. So the magnitude of our prime a t he's the square it off t close and he squared So it will be a t Square Coast Sinus girl tea and then plus Theo square off Need a t Sainty so it will be post he square Science Square t and then we can practice out t squaring here. So when we get is just treek identity and this is equal to one. So we have rid of T square, which is t so this is our magnitude which can also be called speed. So are you. Any tension will equal to when we use a different color. So are okay now. It's a different color. Are you Any tension will equal to DMB. Did derivative divided wise magnitude So t co sign of t divided by t just co Sainty close anti I and then same thing for t signed. He derided by teaches minus sign of tea. Jay said stance her for the first part And now for the second part, we're us to find our clinks. The arc length is the integral from A to B off this baby. Are you my who to so r s which you started clinks will be equal to from a to be so rude to to To of tea PT and we just integrate these who will be t square over to from route to to to so in here it will be four divided by two which is two minus three to squared gives us to do 80.2 in just one. So this will just be one And this is our answer for depart to

The polling characterization function of a curb and you're us to find the guinea tension in our plank begin attention is just attention factor with length of one. So it means we take the our prime of tea, which gives us detention vector and we divide whites magnitudes. Our first stop was finding our prime of tea in factors we take the derivative same way. It's just we take the derivative of each confident, so over here for our component, it's a product rule. So it will be the jury of Teach just one times co Sainty and then the dreaded or consign his negative sign So it will be negative. T science t I Plus seeing thinking here is a product rule, so it will be sign t was P course Ain t Day. I went over here is just a parlor So we bring the power down to dirties will cancel out so would have root two and three house minus one. It gives us one have Okay, so this is our our prime of tea And then to find the magnitude, we take the distance formula we take the square of each component and then we add mom. So after writing these, we just need to simplify it. So it will be Hussein squared Key minus two. T co sign T next time t plus sine square T. I'm just gonna simplify really quickly, but you can positive you and work on your own pace. Okay, So after simplifying these, we get these long function. But this can actually be simplified one for their and they get a really nice result. So this part councils out with this. So we went ending up having dysfunction during needs to be anti squaring here. So what we get is that he's part, and then this part this gives us one because it's a treaty identity. So you get one. And then over here we have because we have these over here. And when we have these over here, we can take out the T Square. This is another trick. And this is the same trick. Identity. So this is just one over here, and then we have justice being left over here. So it will be just question t whether get is the square root off. He plus one squared. We just gives us the answer of T plus one. And then now we just need to put all this together so our unique engine will equal to the Detroit. But if so close, I ain t minus t sang t I the writing bite length plus one plus the j component. So this is our answer for your first part of the question. Now, for the second part of the question we were us to find it's our clanks giving this days are it to be so are a to B. We're from 0 to 2 pi and our aren't length was our art length is equal to the integral from A to B of the speed which is over here is two plus one ET. Now we just need to integrate these so it will be t square over to plus T from zero to pi. And then our answer will be high square over to plus hi. And this is our answer for the second part of the question

We are giving the pulling back their valued function and we are us to find the unit tension vector and the art length. Usually when I'm given this format, I like real braiding Might questioning a vector farm summed is gonna do that really quick. Okay, So when we're asked to find the attention like theory, which means we need to find the first derivative. So when we take the drill, a Dave's for bettors is the same process. But just we take the derivative over each confident X, y and Z. So our new function off the dreaded you look like this follows the director. Of course, Sign is just negative sign, so it will be native to 70. The dreaded off sign is just call sign, so it will be too close. I Inti Amanda wrote five p will be just route five. So this is our Drew tive, which is also cold velocity. And to find a unit tension Director. This is our attention factor as well. But to find the inattention, we divide bites magnitude, so t will be our primal T divided by its magnitude magnetism, velocities also called speed. So to find the magnitude velocity. I'm gonna do it out in here. It will be the square it off X squared plus y square. Put c square. Um, on what we found on top, uh, this waas native to sign key word plus two car sane T square puts route by squared of a simple fight is all I did in here is just a two guard before from over here. And then I found these identity and this is just one. So this will be fruit nine, which is also called to three. So are magnitude or delight of this factor. Velocity, vector or tension Vector is three. So our unit tangent will be and then you'll just divide each competent. But to get the same format as they cave us in, the question will distribute creating I J in K format. So are getting attention. Will be native to assign t I plus two core sign T j over three. I'm past Brut five. 03 Okay, so this is our answer for the first part of the question. And then the second part of the question as to us to find the arc length from over here, You know, I saw still find the ark link from 0 to 2 pi r r clanks art length equals to the integral from A to B off the speed DT and we found that speed is it goes to three. So for us, it will be a syrah Too high three. Vicky, I'll just integrate the Isobel Big Three key from zero to pi. And this is just street high. So we found our answer to this is two pi r r clank history pie.

I have to pulling back tamales, functionary or us find the unit tension in the arc length. To do that, we need to take the derivative. I want to take the Germany of it. Get detention back there. So let's deduct first after we take the derivative. Well, when we take did riveted. We look to each competent of the competent for X. Well, we just want So it will be just I The derivative of D. J component is just negative one because there's radio teach, just want. And then you have a native signing here minus J on then the dirt off two component T K issues one. So plus Okay, so this is our degenerative or our attention. But there I'll just writing a competent form. So this will be one negative one on one. Now To find any tension, we need to find a magnitude on divide thes tension factor. Wait, It's magnitude to find the magnitude Notice we just do as follows X square. Plus why square? Because he square so it won't just be once. Girl, I'll just read eating here so well we just agree because it's one square puts nated one square puts one square, so it just gives us your dream. So this is our length off detention director. So are you Detention t will be sorry. Are you any tension? Will be our prime of tea. Invited bites, magnitude. So what we're getting here? He's 1/3. One square three on, then I minus one over three J plus one, Right. Three. Okay, so this is dancer of the first part For the second part of your us to find our planks. Art length equals to the integral from a to B off speed D t on. What we found in here was our speed, right? Three is our speed. And then we are us to value from 0 to 3. So I was really bright days. So will be easier to three off Brugge three, the key. And after we integrate this, we get Route three p from 0 to 3 on dishes equals 23 Route three. So this is our art Blank's


Similar Solved Questions

5 answers
X2 Ex 1421 lim (answer) (x) (0,0) x2 + y2No limit; use x = 0 and y Ex 142.2 lim (answer) (xy)-(0,0) x2 + y2No limit; use x = 0 andx =y_ryEx 14.23 lim (answer) (r;y)-(0,0) 2x2 + y2No limit; use x = and x = Y_xt _y Ex 14.2.4 lim (answer) (;y) ,(0,0) x2 + y2Limit is zero_sin(x2 + Ex 1425 lim (xy)-(0,0) x2 + y2(answer)Limit is 1_Ex 14.2.6 lim (answer) (xy)-(0,0) V2x2 + y2Limit is zero_~x-YEx 14.2.7 lim (answer) (x;y)--(0,0) x2 +y2Limit is -1_
X2 Ex 1421 lim (answer) (x) (0,0) x2 + y2 No limit; use x = 0 and y Ex 142.2 lim (answer) (xy)-(0,0) x2 + y2 No limit; use x = 0 andx =y_ ry Ex 14.23 lim (answer) (r;y)-(0,0) 2x2 + y2 No limit; use x = and x = Y_ xt _y Ex 14.2.4 lim (answer) (;y) ,(0,0) x2 + y2 Limit is zero_ sin(x2 + Ex 1425 lim (...
5 answers
DutExercise 14-3 Alqocons dorIha tollvnnn cenptr hpalrurttCOraet GeaotenatonsenmtftMau mu4 tincLeueherencn MhaattCnkuleeGulan" decln AlplacuiFantie IAcund mEufedlale Lhlculatiuneludal 4 D"cmar placutPrlDau0005 < Evalt0o0z AlaluaDonlAalue4oMccKUC Condeonio tt"clj
dut Exercise 14-3 Alqo cons dorIha tollvnnn cenptr hpalrurtt COraet Geaotenatonsenmtft Mau mu4 tinc Leu eherencn Mhaatt Cnkulee Gulan" decln Alplacui Fantie IAcund mEufedlale Lhlculatiune ludal 4 D"cmar placut Prl Dau 0005 < Evalt 0o0z Alalua Donl Aalue 4oMcc KUC Condeonio tt "clj...
5 answers
3 In the image below, please place the following labels in the correct box. Skin cell b. Nucleus Bacterium (a single bacteria)10 umImage courtesy of Dr: Gary E. Kaiser, Professor of Microbiology, Community College of Baltimore CountyHow did you decide which was which?
3 In the image below, please place the following labels in the correct box. Skin cell b. Nucleus Bacterium (a single bacteria) 10 um Image courtesy of Dr: Gary E. Kaiser, Professor of Microbiology, Community College of Baltimore County How did you decide which was which?...
5 answers
1 2 1] Let A = 5 5 and suppose that it is symmteric What is €, Y; 22 Ly 9 |y
1 2 1] Let A = 5 5 and suppose that it is symmteric What is €, Y; 22 Ly 9 | y...
5 answers
Compute the - gradient of the function Vfat the given point. 14) f(xY, 2) = tan 2y-47, ( 4, 0,0) _ (2,V0) 1( %42) 1#634J1 7( 17-42) Sly 40241-41)t 11 13y")i 1,(14)Slx?4(2)-
Compute the - gradient of the function Vfat the given point. 14) f(xY, 2) = tan 2y-47, ( 4, 0,0) _ (2,V0) 1( %42) 1#634J1 7( 17-42) Sly 40241-41)t 11 13y")i 1,(14) Slx?4(2)-...
5 answers
H COMPUTE BY HANDI; SHOW Tnaadi REPORT ThE {deedninumen W SAANSRd H L 1 Hh an; nanmud VAAIANCF EXPLAINED 11 1 H LELO AliGHT8/2|8
H COMPUTE BY HANDI; SHOW Tnaadi REPORT ThE {deedninumen W SAANSRd H L 1 Hh an; nanmud VAAIANCF EXPLAINED 11 1 H LELO AliGHT 8/2|8...
5 answers
Accuracy refers toA) how close a measured number is to the true valueB) how close a measured number is to the calculated valuehow close a measured number is to other measured numbersD) how close a measured number is to zeroE) how close a measured number is to infinity
Accuracy refers to A) how close a measured number is to the true value B) how close a measured number is to the calculated value how close a measured number is to other measured numbers D) how close a measured number is to zero E) how close a measured number is to infinity...
5 answers
Ofall the points of the feasible region for maximum or occurs at the pointsImum 0f objective function(a) Inside the feasible region (6) At the boundary line ofthe feasible_ region (c) Vertex point of the boundary ofthe feasible region (d) None of these
Ofall the points of the feasible region for maximum or occurs at the points Imum 0f objective function (a) Inside the feasible region (6) At the boundary line ofthe feasible_ region (c) Vertex point of the boundary ofthe feasible region (d) None of these...
1 answers
Cardioid overlapping a circle Find the area of the region that lies inside the cardioid $r=1+\cos \theta$ and outside the circle $r=1 .$
Cardioid overlapping a circle Find the area of the region that lies inside the cardioid $r=1+\cos \theta$ and outside the circle $r=1 .$...
5 answers
Problem 2 : Lcl D. Dz Iwo iudepeudent lair die rolls and let W _ D + Dz: Compute the following: The coudilional Lass lictions JDzIw (xlw) aud Jw[D, (wkz). The coudilional expeclalious E(DW 3) and E(WID
Problem 2 : Lcl D. Dz Iwo iudepeudent lair die rolls and let W _ D + Dz: Compute the following: The coudilional Lass lictions JDzIw (xlw) aud Jw[D, (wkz). The coudilional expeclalious E(DW 3) and E(WID...
5 answers
Roviow Constants Perodic Tab'0SubmitBequetLAnwtComplete and balarce each 0f Ihe Idlowing equaticns If no rezction occurs, wite NOREACTION_Per DNaOH(aq) (NH,),SO (ag) Express YouT anstter chemict equation Enter ROREACTIOH I no reaction occuns Idcnlity all- (he phases in your Jnster.AEq
Roviow Constants Perodic Tab'0 Submit BequetLAnwt Complete and balarce each 0f Ihe Idlowing equaticns If no rezction occurs, wite NOREACTION_ Per D NaOH(aq) (NH,),SO (ag) Express YouT anstter chemict equation Enter ROREACTIOH I no reaction occuns Idcnlity all- (he phases in your Jnster. AEq...
5 answers
T (minutes)60508408030207570 6510I (feet) 20 25 30510 15
t (minutes) 60 50 8 40 80 30 20 75 70 65 10 I (feet) 20 25 30 5 10 15...
5 answers
1 12 { ili { 9 8 5 } H 1 2 { I 13 9 1ia Vi 5 1 L 1 1 1 F 8 1 1 D2
1 12 { ili { 9 8 5 } H 1 2 { I 13 9 1ia Vi 5 1 L 1 1 1 F 8 1 1 D2...
4 answers
HOCH;Type of reaction_Type afreuttion_2-methyl-3-hexanoneType of reactionStudent' $ Name (In Inkl:
HOCH; Type of reaction_ Type afreuttion_ 2-methyl-3-hexanone Type of reaction Student' $ Name (In Inkl:...

-- 0.021652--