use-the-graphs-of-x-ft-and-y-gt-to-sketch-the-parametric-curve-x-ft-y-gt-indicate-with-arrows-the-di

Name: use the graphs of x ft and y gt to sketch the parametric curve x ft y gt indicate with arrows the di
Uploaded: 2018-04-20
Duration: 1 min 28 s
Channel: Numerade
Description: Use the graphs of $ x = f(t) $ and $ y = g(t) $ to sketch the parametric curve $ x = f(t) $, $ y = g(t) $. Indicate with arrows the direction in which the cuve is traced as $ t $ increases.

Question

Use the graphs of $ x = f(t) $ and $ y = g(t) $ to sketch the parametric curve $ x = f(t) $, $ y = g(t) $. Indicate with arrows the direction in which the cuve is traced as $ t $ increases.

Wen Zheng · Accepted Answer

the problem is use the grafts off half Goto After On that why you go to GT to a sketch The Parametric curve xy goto After Why go to a jetty indicated by his arrows the direction in Vegeta craft It&#x27;s Tristan asked increases. So let&#x27;s look at is a graph of axe and why so from the bath we have X is equal to he squire. Why does he go to negative T on behalf of X is equal to nectar? Why square which is it going toe? Why square then that&#x27;s catches the graph. It&#x27;s like this on DH. What? She is able to zero in half. Axel, why go to zero this point? No one tea is a good one. Actually got one. Why would connected what this direction is? The direction in which the curve is traced as tea increases

Wen Zheng · Answer

the problem is used the grafts of ex voto ft. And why could you j t to sketch the Parametric curve xy goto after she why you couldn&#x27;t gt indicated with arrows the direction in which the curve is Tristan as team pres ist first, let&#x27;s look at the grafts off. Fifty had a treaty from this. Two graphs were half won t you go to negative one actually is equal to zero y equals zero when he is Because negative one half axe is about behalf. Why is next to one? What is it called? Zero x is equal one. Why could zero he got two half, actually is about half. Why is about serial wisely? About one. What? He is equal to one, actually Sickle zero. Why cereal, then? That sketch that cross first zero zero and then a half. Next one. Who are you? Well, half next to one. Yeah, Andi one zero And then, Well, half one zero zero. The graph is the lock. This this is a direction And which is the curve? Is trist asked increases

Wen Zheng · Answer

the problem is use that grafts off our exit goto ft. And why go to GT two sketches a Parametric curve actually Goto after Why Go to G indicated ways. Arrow&#x27;s direction in Back to the curve is trist as Team Prizzi&#x27;s first to Nestle Cat is a graph from the graph. We have access is equal to negative, absolutely off key. Why? Why? Why is about he scored so behalf? Why it&#x27;s the Court x month. One square Your axe is between serial on what Now Let&#x27;s catch the graph from zero to one zero one When he is they called too Next one we have acceded to zero Why could want this point and I won t go to zero acsi goto one Why put zero year to this point? So first particle goes from this point to this point and then twenty it is equal to one actually go to zero like one when she worries from zero to one, the party goes from this point back to this point

Jeffrey Russell · Answer

we&#x27;re going to use the graphs of X is a function of T. And why, as a function of teeth to graft the Parametric Curve, exit e and Y t. So first, we&#x27;re gonna identify a few values of T where we can get the values of X and y so at people negative 10 and one. We can see what the corresponding value of that&#x27;s and I should be. So, on the graph of exit a function of T we can see that won t is negative one x zero 20 a zero That&#x27;s a negative one and lastly, wouldn&#x27;t see is one x zero on the graph of y is a function of t We can see when t is negative one. Why is negative one when t zero why is zero and wins? He is one wise one. So now we can use these values of t the graph values of x and Y on here. When C is equal to zero or negative one, I mean X is equal to zero and why is equal to negative one zero negative one when C is equal to zero X is equal to negative one and why is equal to zero. So here we have the point. Negative 10 and when t is equal to one, X is equal to zero and why is equal to one? So here&#x27;s the point 01 Now we need toe discern the general shape of the graph. We can see the graph of X is a function of T is somewhat like the graph of T squared and on the graph of y is a function of T. It looks like T cube or some higher power, so we can use that information to get the shape of the Parametric graph over here. When T is between zero and one X squared will be increasing faster. The T Square will be increasing faster than T Cube, so X is increasing faster than why. So we can use that to drawn between Teeples. Your own one curve like this when T is greater than one X squared does not increase as fast as y squared. So why will be increasing faster than X at this point, when we consider negative values of T, we see that X does the same thing. It does nt it&#x27;s positive, and wine does the same thing that he does once positive acceptance negated. So we&#x27;re just going to near this graph along the X axis because the X values are moving in the same way and the Y values were moving in the same way. But negative. So between zero and one, we haven&#x27;t like this. And then it was like this. And since negative values of tear down here in positive values of tear up here, the graph is moving in this direction and there we go. We&#x27;ve drawn the Parametric graph of extra functionality and white.

Jeffrey Russell · Answer

we&#x27;re going to use the graphs of the functions X as a function of T and wise, a bunch empty to graft the Parametric graph of X and y. So first, we&#x27;re going to find a view values of T, where we can get values of exit like pretty usually from the graphs. And we can do that. It&#x27;s he is equal to negative 10 and one on both graphs. So when T is equal to negative, one X is equal to zero. When T is equal to zero, X is equal zero and when he is equal to one, X equals zero on the graph of wise amongst in empty, when T is equal to negative one y 00 when t is equal to zero, why is equal to one? And when T is equal to one? Why is equal to zero? So we&#x27;ll use these points. A graph points on the Parametric graph. When&#x27;s he is equal to negative one action while you&#x27;re both equal to zero when C is equal, zero X is equal to zero and why is equal to one? And when t is equal to one, X is equal to zero and Y is equal to zero. So that&#x27;s actually only two distant points. Me, I&#x27;m gonna have some kind of loop around here. So now we&#x27;re gonna look at the shape of these two graphs to get the shape of the Parametric graph. So when t is less than negative, one X is having a sharp decrease from being positive to being zero. So we&#x27;re gonna have something that&#x27;s pretty quickly moving this direction on this graph and on the graph of y is a function T. We&#x27;re having a sharp but not quite a sharp possess increase to zero. So we&#x27;re going to have something that looks like this with ex decreasing more quickly than why decreasing less quickly. Excuse me? That should be more like this. Okay, Now, when t is between negative one and zero, ex briefly becomes negative, but circles back pretty quickly and why pretty steadily increases from 0 to 1. So it&#x27;s going to look something like this when tea is from 0 to 1. T excuse me. Ex briefly becomes positive again. Then much the same way became negative. So we&#x27;re gonna have something similar there. And why steadily decrease is back to being zero again. Similarly, the other side, this is pretty symmetric and lastly asked. He increases from one onwards to Infinity X has a pretty sharp and decrease downwards. So it&#x27;s going to decrease pretty quickly and why has a less sharp but still sharp decrease? So it&#x27;s going to look like this somewhat and asked, He is increasing. We&#x27;re moving this direction along the graph and there we go. This is the graph of X and y as parametric equations.

Jeffrey Russell · Answer

we&#x27;re going to use the graphs of X is a function of T. And why is a function of teeth to graft the Parametric equations X a function of T and why a function of T. So first, we&#x27;re going to identify a few values of T where we can also get a value of X and y. Since we can always find a value of X here, where we can find a value of why we&#x27;re going to use the ones where you can easily find a value of why that&#x27;s a T equals zero T equals 1/2 and two equals one. So starting with the graph of excess function of T 20 is equal to zero. X is equal to zero. 20 is equal to 1/2 X is equal zero, and when T is equal to one, X is equal zero on the graph of Liza Function T, when T is equal to zero, Y is equal to zero. 20 is equal to 1/2. Why is one and when t is equal to one? Y is equal to zero Now we can use these points to plot a few points on the graph of ex and why, as Parametric equations, when he is equal to zero, X and Y are equal to zero. When T is equal to 1/2 X is equal to zero. Online is equal to one. And when t is equal to one, next on wire rope people zero again. So we actually have two distinct points, meaning we&#x27;re gonna have some kind of loop going on here. So 14 from 0 to 1/2 Why steadily increases The one X, on the other hand, goes up the one back down to zero back down to negative one, and then it returns to zero again. So X has kind of Ah, 10 negative 10 So it&#x27;s going to look something like one zero negative 10 now from Tito, 1/2 to 1. Why is decreasing back down to zero? And X is doing the same thing from 120 to negative 10 So it&#x27;s going to mere itself here one zero. It&#x27;s a negative 10 and the arrows are a little complicated here, but this is the direction we&#x27;re moving in. That&#x27;s team boots from 01 lots of arrows here and there we go. We have drawn the Parametric graph of X and Y

Wen Zheng · Answer

So if we want to sketch this graph in the Cartesian plane, let&#x27;s first go ahead and maybe just graph a couple of these points. That might be easy for us to find Well, over here. Um, so they give us 11 so we can estimate negative one is probably around here. Negative one is here, so let&#x27;s just make a little chart. So when t is equal to negative one, it looks like First X is equal to one. And why is going to be equal to one also? Okay, um, when tea is able to zero, it looks like ax zero. It also looks like Why is zero And then when t is equal to one X is one again, and then it looks like why is equal to, uh, negative one? So let&#x27;s come over here now and just graph those points that we have X Y, uh, I&#x27;ll just put all those are just gonna be one for the tick marks. So at negative one, we have X is equal to one. Why is it good to one? So that would be right here, and this is T is equal to negative one. Now, when t 00 both X and wire zero. Alright. T is zero. And then when t is he going to one Access one again and then y is negative one. So this is t is he took one. Now we can kind of see So X is going to grow a lot quicker than why it&#x27;s so when we&#x27;re going through this or actually I should say access first, going to be decreasing to the left and why is always going to be decreasing So we should know that why should always be going down and then X was going to decrease up until we hit zero and they will start increasing again. So that means we can just go ahead and connect these points and it will kind of look like this quadratic here now for us to figure out what the direction is, we&#x27;re just going to follow the points. So it goes from negative 1 to 0 and then 0 to 1. So this here is going to be a sketch of what this would look like in the XY plane

Problem

Use the graphs of $ x = f(t) $ and $ y = g(t) $ t…

Problem 25 Easy Difficulty

Use the graphs of $ x = f(t) $ and $ y = g(t) $ to sketch the parametric curve $ x = f(t) $, $ y = g(t) $. Indicate with arrows the direction in which the cuve is traced as $ t $ increases.

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