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~/4 pointsMy NotesFind the polnt of Intersectlon of the curves 71(t) = (t, 2t + 7,+2) &nd Fz(r) = (72 + 1, 4r + 9, 1 T), and then flnd the angle between the cur...

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~/4 pointsMy NotesFind the polnt of Intersectlon of the curves 71(t) = (t, 2t + 7,+2) &nd Fz(r) = (72 + 1, 4r + 9, 1 T), and then flnd the angle between the curves at thls point:(x,%, 2)Submit Answer5/5 points Previous AnswersMy NotesCintTots

~/4 points My Notes Find the polnt of Intersectlon of the curves 71(t) = (t, 2t + 7,+2) &nd Fz(r) = (72 + 1, 4r + 9, 1 T), and then flnd the angle between the curves at thls point: (x,%, 2) Submit Answer 5/5 points Previous Answers My Notes Cint Tots



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Use graphing technology to sketch the curve traced out by the given vector-valued function. $$\mathbf{r}(t)=\langle 8 \cos t+2 \cos 7 t, 8 \sin t+2 \sin 7 t\rangle$$

And the exercises we want to refer to the busier curve defined by the equations and we want to show that with the given control points it has a specific parameter Ization. And we're going to be looking at this inn problems 73 through 76 with different points available. So in doing that, we end up saying that the parameter Ization For problems 73 is going to be CFT is equal to one plus 60. Yeah, Last three t squared um minus three P cubed. That would be the X coordinate and there are white coordinate would be um for plus 2040 minus 15 T squared minus 90 cubed. Um So that is going to be our answer and then we see that for other problems we can use our computer algebra system and that's going to be looking at busier curves again, which is a form of parametric curve.

And this question we will find We will learn how to find out the land of any Parametric equation which is given to us. So we are given that mhm X is equal to eight Costea plus eight d 70 and by is equal to 8. 70 in his head, the cost d and he is wearing from 0 to 50 No, we have to find Landau given carte no. First to find out the land of the living. Using the integration, we first have to know the formula of finding this length. So the black black l the the length, of course, Yeah. It can be calculated using the formula representation of X with respect to the police car. There's differentiation of by with respect to t holy square lady. And the limo itself from Cuban total to 81 is equal to zero. And D two is equal to Piper too. No. First we have to calculate differentiation of X with respect to take as X is equal to did cost. Yeah, Yeah. 82 The scientists Yeah, No. So we will differentiate it and they will get differentiation. Of course, he is nothing but minus 70 Yeah. And uh huh. As it is a complex function. So we will differentiate one by one, I think cost less well and to scientists on simply find it we will simply like Oh, we will simply get it 50 cost to this minus 70 at this world scientific Get canceled. Now we will find the vibrate people You as far as equal to 8. 70 minus pretty cost too. We will differentiate it. It will be eight costing minus date will be outside as it is a complex function. So we will differentiate you and we will first differentiate t differentiation of T s one and two Costea. Then we will differentiate Costea. Label them as it is in cost differentiation. Of course, to minus side D Uh huh. One simplifying it. Yeah, these miners Then this miners will become four plus on simplifying it they said costly and they said Constable, council and we are left with only 80 scientific. Now we have got all we have got both differentiation that the differentiation of active this majority is the differentiation of I with respect to t now we will put it in the integration. That is hell is equality. The limits are from you. Don't get it. Bye bye. Cool. And the plantation of expertise spectrum. He was laid the cost to Okay. All the square and the transition of I with respect to he was eight. He scientific police square. Oh, duty. It's really become 64. The square causes quality. Listen, we welcome 64 k square Sinus quality As you consider 60 40 square is common So we will take it outside. Oh, mhm. Okay, yeah. Mhm. And we are causes quality here and they have Sinus quality. Mhm. Now, as we know that from the diplomatic identity that courses square the place Chinese square the is equal to one. So we will apply it here. 1960 40 square will come outside of the route and it will become will become a B. And this causes particular Chinese quality will become fun. Someone Bill is equal to one only. So did he. And on integrating it, we will see debt. Please clarify too. And the limits are from zero to buy A way to. Sorry to will be for a little bit for intelligent. Mhm. Yeah. Uh huh. 02 by two. So once are living it. We will see that l is equal to four. These for from zero to buy a right to this will be that relevant for yeah, I squired by four final zero That will be helped by square units. So they said the land of the Given Parametric question pardon?

For the following problem, we're going to be taking the derivative of our with respect to theta. So it's going to be our prime equals a negative sign theater. But we're ultimately looking at this when theta is equal to pi over two. So it fits pi over two of them were getting um negative one. So we'll have negative one. Okay. Hi over to I mean And then we'll have um positive one pirate ship and these are going to be in polar coordinates. So they're not going to look like they normally do in rectangular coordinates. Um And we see that the slopes of the curves Is going to be negative one and the slope is here to me one that's going to give us mhm. Our answer. And we can also see us with other problems. For example, if we're given other cardioid shapes or different rows, shapes, we just take the derivative D R D. Theta. So the derivative are with respect to theta. Then we evaluate it at the value of fada So high over two or report whatever it is. And that will give us the slope. And we can also identify the specific point


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