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Trania danaxinum banding nomcut [01ucam choun belowh++4404+j_0 < 760QUESTION?Dxtcrmine the magritude of the resultant forcc = of tha forcce Ft.FzFy; Jnd FsF1-ak;...

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Trania danaxinum banding nomcut [01ucam choun belowh++4404+j_0 < 760QUESTION?Dxtcrmine the magritude of the resultant forcc = of tha forcce Ft.FzFy; Jnd FsF1-ak;f2" J0k;Fj-R2LF4-6[04127 Onnse olctns o daa

Trania danaxinum banding nomcut [01 ucam choun below h++4 40 4+j_ 0 < 760 QUESTION? Dxtcrmine the magritude of the resultant forcc = of tha forcce Ft.FzFy; Jnd Fs F1-ak;f2" J0k;Fj-R2LF4-6[ 04127 Onnse olctns o daa



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In $\mathbb{R}^{2},$ let $S=\left\{\left[\begin{array}{l}{0} \\ {y}\end{array}\right] : 0 \leq y<1\right\} \cup\left\{\left[\begin{array}{l}{2} \\ {0}\end{array}\right]\right\} .$ Describe (or sketch) the convex hull of $S .$

For this for this problem? We want to find the area of the part of the surface. X equals X squared plus Y. That lies between the planes, Y equals zero equals two. Z equals zero and Z equals two. So to start off we can make the parameter ization then X equals. You are actually excuse me, I'll be careful here. Why equals you? Z equals V and X equals R of UV. Which will then equal the squared plus you. So the significance of that is that with this? Or actually need to be careful X is a function of you envy. Which then means that we can define our vector or you have our vector equation for our plane or are surface. To be careful here uh defined as the squared plus new I hat. Yeah. Plus you J hat plus v. K hat. So next thing that we want to do is take our partial derivatives with respect to U and V. But so partial with respect to you is going to be, Oh, actually there's a shortcut that we can take here. You can see a proof for how this will turn out. But we can essentially skip using results from the textbook, you can skip to the point of saying that the surface area is going to equal the double integral over our domain, which I'll discuss in a second of the square root of one. Plus the partial with respect to U squared. Um or rather the partial derivative of X with respect to U. Squared and then plus the partial of X with respect of the squared. So in this case that will be, you know, the partial with respect to you will just be one. So we'll have to plus two V squared or two V all squared. So it'll be two plus four V squared. Yeah. And then we are integrating over our domain. So next thing, as I said, we need to discuss the domain but we can see we have this very clear definition that it lies between the planes, Y equals zero equals two, is equal zero, Z equals two. Which means that that's actually telling us the intervals over which to integrate U and V you is going to be between zero and two and V is going to be between zero and two. So what we need to do here a second. So what we can do is first, let's divide out that four on the inside of our square root, we'll have 1/4 times two times four. So that's going to be eight plus just the squared. So when we expand those brackets out, we'd get back what we started with. Then we have that as the same thing as the square root of 1/4 times the square root of those brackets, which is going to be the same thing as one half times the square brackets. So we can bring this the one half out front and then it's multiplying integral with a double integral of the square root of eight plus v square. Now, the reason why I did that because there is a formula in the textbook for integrating something in the form of a squared plus U squared where in our case A is going to be, I suppose yeah, square root of a. It's just going to be the square of um to route to so to to and you squared is just going to be our V squared. So when we integrate over, let's integrate over V first. Um when we integrate over V, we will end up having the over two times the square root of eight plus V squared plus 8/2. Lawn of V plus the square root of eight plus V squared evaluated from 0 to 2. And that 8/2 we can reduce is just four, two. And we are still integrating over D'you next. But notice we don't have any use inside here. So that's going to do the same thing as just multiplying by two. So really we're going to end up with the over two times the square root of eight plus B squared plus for lawn of the plus the square root of eight plus B squared evaluated from zero up to two as our into grand or our indefinite integral, I should say. And that will come out to one second here. So that will evaluate out to two times the square root of three minus log four plus log four. Or I should say the natural algorithm long before plus four times lawn of one plus route through.

Hello, You are today. I'm going to thought problem number 11. He had to function and feels given math, ex allies it And for X square like you, my nazar on ink course a square. Could we have to find a girl off Girl of Darb? Andy? Yes. The the points given our 001 onda 011 on the one Only one you want on a 101 and singles to be. And when he goes to zero And that because to one so later the eggs it goes through didn t And the way equal to zero on desire equal to zero zero last article Duty left the not it goes to our okay, bring fine. Maybe he's so It was a little off the river f dark diar will be equal stew feel, uh, X lies that the X bless for exist square like you, my Zack, Be right, bless eight cause eggs that square be said it is from There are two while, right? Um right you syrup. For this government become zero the ways the loss of this term will become zero There. Here, this, uh, be be the desert. Is there authorities will also be zero inter duty. So this integral you get us. You know, next we are that makes you go Really? From one serial over here You're seeing you 90 clockwise that whenever the front group Why are you lying? Why X equals one? Why? Because he there Because one on that the young Because it'll the right Because they on desire. Because zero the 11 year old Well, easier invigorate You see too, Jeff Dark the are will be cause to seeing Do exercise that be yes plus north sea Be express for a piece choir like you, Mina said Do you like bless a cause except square diesel miserably getting us in the girl's 0 to 1 The this seriously the exit is there also a syrup Here we will get us four Indo and squares is one square and one Q b stick you my enough. Why indo do they on Dhere? These they're this They're all so this will be a serial. Okay, In battle level, we can bring us, you know. Zero Fire for big U minus one minus for taking minus again For what you get this for. Take your place Wine in. Don't be with June Big Good day as see it all. Okay, right. No, we had certain men. See Pretty, I think if from 111 do zero ver y here, X peak was why I may not be. Why? Because one they're because one on the X equals minus duty. Andre de vie equals zero. These are equal zero. This is the role is then recorded daily, counselor. Easy in Bagaric. Little simply if dark, The yard will be because to in the X lies that be if plus full exit square like you. Mina said, Do you like, bless eight? Cause if they're square days it literally getting us in the 0 to 1 one minus the Indo minus Mark plus zero plus B y and be that are there. That's right. It could be between getting us. Bigas, you don't go. Do you mind this alarm? What do you think? Also minus one by two. Okay. Oh, we're trying for C for Regis The men drunk zero violent cool 00 Over here anything is taking anti clockwise direction. OK, that I had to say X is equal to C zero y equals one dynasty they're because one and the X equals zero de y equals minus duty. Andi that because little leave, it seems from the rollers that I go to Payless goingto. So if you pray and I got a C for Bardiya, not the, uh will be equals two in the X Allies that the yes plus four X squared like you miners that the right plus eight growth X's square is there. This is equal scoop zero less, minus one Indo minus one plus ill indoor dignity resist equals two intervals. Zero So far. Why did the president goes to one? So, you know, we had a great stocks here and there, dark and the yes, we did. It comes to Seaver. Half dark DEA. Plus they do half dark DEA plus C three after the year plus, see, for after the, uh, did you have been getting us 00 minus half Bless. Learn. We got us run by that. Is that the question? Thank you.

Right today, we're going to solve a problem. About 30 years. We had to maximize people, which is because to pick you was toe Cure plus toe PR. Subject to P plus Q plus articles. What be at peak coma? You coma are coma. LeBlanc was to take you plus to cure was toe beer minus lambda in do P plus Q plus R minus one equals zero. Be with respect to P equals Q plus The work by an Islam bike. +10 be with respect to Q equals two p plus Tau work by Nesler Bike A. Zero Be with respect to our equals. To be plus to Cuba by an Islam like a zero be with respect to lamb Nyquist P plus Q plus R minus one equals zero If we signify p equals Q equals R P plus Q plus R minus one equals zero. It has a solution off one by three. Come on, one by three. Come on by three. Thank you


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