5

The sphere >? +y? + 2 = 5 above the plane - = 1 if the density at any point is equal to the distauce from the point to thc zy- plane. [4v5r]...

Question

The sphere >? +y? + 2 = 5 above the plane - = 1 if the density at any point is equal to the distauce from the point to thc zy- plane. [4v5r]

the sphere >? +y? + 2 = 5 above the plane - = 1 if the density at any point is equal to the distauce from the point to thc zy- plane. [4v5r]



Answers

Sphere and plane Find the volume of the smaller region cut
from the solid sphere $\rho \leq 2$ by the plane $z=1 .$

Oh, yes, we have. But these Aubert hemisphere worry the zone eggs. Who? I see access. You have. Ah, that, monsieur, I was really You. So do the others, too. On the way. Make your cut. Siegel's one for a plane. Well, please. That it was gonna give us. Ah, this is the plane. Um, c equals once we want to computer greasy volume of these vision in there. So it's you will be the reasoning inside of ah, this year. So it's here, So mmm. Roll. Listen to on both, uh, well, this plane Sequels one. Um, So how do we do that? So? Well, first time you have here this sea access and these two and one now here. Yeah, exactly. Said, I love you. Why you call zero. So now this is fear. Something like that. So there are love. Not which this happens. He's at, uh Well, um, you can't theory that they where these joint, huh? That should be like that half turned airplane ready by three. It was like, uh oh, this is so hold these angle. There is B equals by thirds. So that leaves is ah, this point, uh, also that, uh, scene should be zero on you. Bye, thirds. Um, you do the old tradition around Syria because it's a mature, respectful. So that was from Cyril off to buy when they know our radius role. So as you can see here, hero of the sea axis rose from one I talked to. But, uh, as you give one stretching there the range or roll. This is so rule. Uh, so they playing? See, those one is getting by or this is grow Call sign. Well, see, it was one you have to be or both. Well, that plane Ah, uh, she so rule has to be bigger than one American. Sign off key, Ana. So, uh, well, so you can check that on. Uh, well, you can check by. He's looking at zero one. Huh? Huh? Uh oh, yeah. We're always between zero on two. I've been at these points. Bye thirds. We're gonna have by thirds on the roads. You go nowhere. It is because one of the local sign off by thirds is equal to 1/1 half mexican too. So you would be saying with these equations that role has anything to want to Jesus. There is no space. So about that. Is it bound for rule on that? This is, uh, she can trophy. So these, uh, computing these volumes we can use very cool. Cordy. It's so that her room was routine. Sequined. Well, fie on two these zero natural squares. And he then, um, fee goes between zero and 2/3 cereal by thirds feet, and feta goes all the way around Syria to buy so that our leaving to be first row squared row. But he's, uh that is equal to broke. You thirds. Some of these will be able to well, that volunteer meeting to second. Do you see a totally with people? D'oh! 1/3. Oh, um two. Okay. Cube rule. Y nos See you again. Oh, you're cute. Monday. And, um yeah, that's it. So he if you feel 19 No, but, uh, you know, multiply by, uh, sign sign from the 18 0 dy hurts. Now it is your room to buy. Um, so we're really Dribble, dribble, sign. First internal There. That was a constant is gonna be equal to minors co sign. So that awaited Bye. Thirds and zero B minus co signed by thirds, minus sue. So, uh, all these number that he's done half miners want to these minus one, huh? We don't mind us a toe physical, too. I know one tough. Was it? Um, so that is, uh, these introduce of that. That would be one there Inter forms here by from dean bodies to the third. That's one house. Well, we have Lisi to lift. Um, Also these do feta. And then miners and drop bombs were took by on the trail from zero. No, Brian, this is here. Uh, if my thirds over sign off. Definitely big, um, seek and you will do one of our local science. That would be you are a vital sign. Q. And so here we can do a new substitution because, uh, because ever co sign off legal, do you, you legal toe mind sign. We'll see. Uh, so So a decent girl would be you for you squared? No, you're cute. Um, this is really the minus sign. Well, so the troubled minus Sino fee. This you quick the same off the cube. We'll be able to these with you, because to cool sign. So what, you're really doing these, uh, that is equal to Myers. Hey. Oh, our way. Um um You squared. So we have a negative Power is a minus one over to you. It's quote. Yeah, you differentiate. So she would be that evaluated, Nitin? Well, little sign. So it would be minus one over two. Assign a fee. Uh, squid. So that, uh, that body meeting by thirds you Bye. 3rd 0 will give us Myers Way. Doesn't have whatever because I know my third sees one, huh? Word. Well, then, minus, um wasn't a Jew is one on one, So these would be just two squared minus one. So these numbers these, uh three so minus you are to minors. Three house. Oh, so that controlled these minus three halves? The central here. These homes, We've been Mina's. He's minus three house. So that, uh, well, putting, putting everything together. Oh, what? So our little angel is one third intel from zero to buy? Oh, uh, so these term would be two squared. You know who's in the white of the squared? We're, uh ah. Well, these term waas was that my mystery house? My monthly halves. So? So they should be our volume from then. Uh Well, you drill off the hair from your device just to buy me to fly. Hurts involved. These numbers burned its study itself for runs the house with four people. Do you have more interesting house of V five bucks? So this is B times five homes, General. So is volume is five. Bye Herds. Oh, so really, all these reason highs by thirds, but

S with this grace. It's natural. You promised rises. Cartesian coordinates. X Y now, In which case, our Jacoby in the first few columns. Partial grip. It is with respect. That's a lie. But these two, respectively, being 1001 uh, for the cake column. We saw her said hundreds of excellent giving the equation of the surface or which were integrated s so that you'll zed is too last x by three last y by two eso partially differentiating that said now, respect to X. You have minus 1/3. And with respect to why we have minus 1/2 No, to compete. The norm of the cross product we could see were the request product. As I component 1/3 j component. 1/2 you take opponent one s so that all of that better than the square root one plus one night. But this 1/4 wish inside the square root is 36. US nine is 45 plus for 49 uh, divided by 36. Taking food, huh? Um, he have seven through 2 49 61 40 cents. Six word 36. No one had to go. Since we're computing A s. Well, we just have the density function, which we can insert exclusive. Then, of course, given the courtesies we can see of a rectangular region the ex like playing. You can see exes between zero and one. And why is between the two over this rectangular region can integrate. And then we can recall that the density functionary given is ah for X y six then so we can better generic density in here. No, you know, the Sequels for Excite Plus Six said we console for the six Said in, uh, using the equation the surface over which are integrating when she old sick, sad, equal to 12 minutes to excellence. 31 infamous point. You could be straightforward. So you're calling me at 76 for me? One of the Jacoby the four x Y term we can spread to the product of two acts into I where it was with respect, Axl. I respectively integrated too x squared. And why squared? Then evaluate between bounds. So we have one square that zero squared. Just one well replied, by truth, where love zero squared is, uh, four. So we have four correspond into the for X y term now for the 12 term. We can integrate with this by tax, and it's like, Why, uh, take the product, which is one minus zero turns to money. Zero So too time shop. So we had on 24. Well, course, this could just be seen that we have 12 times the integral over our region, which is a region of area of the region which is the product of its sidelines being attained. You over to see times alone. That's two times hold its 24 again no minus X squared and minus two acts degrades too minus X squared. So we have minus one squared plus zero squared, minus one multiplied by the introspect. Why? Just minus one times two minus zero. So when it's too Oh then finally the by this three. Why? With brains to minus three homes while squared this we have to square glad, serious words before rented. Three has tons for is just minus six. Then that minus six get smothered by by the intervals. Bike accident. You're one which is just one. That's just I minus six. So we can see we have 24 28 26 Ah, six is 20 through your seven tons, two times 10 divided by three times two s. So we just have 70 but about 73rd. And this, uh, since three Divide 69 for instance, that 70 it's foryou, 73rd of Hollywood satisfaction and equal to the answer This question, which is the mass of the planet's surface specified with the given density function. And, of course, um, assuming that Princeton's ex wines that are measured in centimeters then our area is in use it. Centimeters squared in this mass will be given in units of millet bands in that conclusive solution.

So you want to find the must? These this shit is in the barbell, Lloyd. But around, uh, that is even by si is equal to 1/2 off x squared. Plus, why square on, uh, utilize of off the travel. But he's in the X Y plane, Uh, with coordinates. Cyril, Cyril with burgess 20 on a well 24 people in town 24 So off these reason. Well, when we have big density capacity on these service, he's, uh, like these many grounds centimeter square, and you want to finally thought almost eso Well, um, Brie dimensional space. This is, like full wins for a home you have here X y on the sea and never triangle in the X y plane. So this point B c to zero is you. Me put it in three dimensions, Barron. A serial, because the diaries of the plane C zero and then the other point is 24 zero. So it is thes strangle. But there. Yeah, sure. She is, uh, the region in the cylindrical home that gets project there. So it's gonna be something like these, but but, uh, but he's involved off these triangle, so this surfaces the service. Uh, so do find it with almost Well, me too. We call the surface is we need to do it over us, the density. And then we have a differential. Very other. Here's differential of area. Well, if you're gonna try to the surface in there, so x and y the differential Varia is gonna be equal to Meyer. Soup, eggs, cross border are So why the norm off the spectre? The y dx uh, So what is he's He's, uh is the normal the victor? Our exclusive is what I as a white that can obtain by but in the well on these roads First, the civil role We write our subject. So directive off X, with respect works, we'll expose works. Why does Why running See Rose to one, huh? Four x squared plus y squared. So they had the ball. Thanks of this sprinter. That's one. Why? With respect books zero There they will see will be two x that of Actos O X. And then here are so why? But will be, uh no people next Respectful. Why? There are people who I will respect. Why one under it seemed respect light with Why? So that these better is I, James, uh, my no sex live it when a section direction go by being for Jim would have Yeah, these times up my eyes up. And that's a minor G. That was food. Where is why times you and then Kate them cinched one key one of these. Victor? No, these When you have normal BC, we're there. It's gonna be photo square root of the components squared on it together. So x square. That's why it's where that's one. Why the X on to what you get travel? Yeah, In the X Y plane we have That is the points 00 to see you on the point or 24 24 24 under voice thes triangle. Should I, uh, won't these line? He's, uh, benign. Why School two x so we can see that exposed from Syria up to. And then why goes from how? Seal up the Twix. So we have that exposed from cheer up to none of y from cheer up to two x roomed. Uh, well, with the gentle great these so that EMS nine x. That's why, from being you know why, Who's Why? From syrup, twigs. And, um, next from two to do so, uh, the stats have been doing all the trouble in respect of why we can make a new substitution. If you call you being ableto Why squared then? Do you was gonna be ableto Why the white? So we almost have that we have. Do you have you have to do? Why give wide so that these would be changeable off the nine x, uh, square hotels X square. Oh, plus one. Plus you. Yeah, you have. No. So we have, uh, not internal. I'm being. Well, uh, the center would be, um, intervals. That would be just done today. Exit Square. That's one. Plus you on this Is we that to the 1/2 you need to do while that power plus one. So three for three. House from being Well, that was nine. Extending that times two darks. We have another one house. She would be that involved. Way you can sure known, uh, two x two x, uh, which leave us so not to eggs. You would get nine x times x us to X plus one, 23 halfs. Um, these castles or three and then that zero would be No, my news nine x No for you, Uh, you means you're nine x times. Excess square looks warm. Mm. Shirts. So you need to do these in general or that 33 on, um, you can see her until the total Mars will be that, but their own this year until the X. Also, there's something very nice here and in that Is that these part? Um X squared plus two x plus one people do X plus one squared explosively squared so that we of that the three house that would be just these first part with me nine x times X plus one gray third power. Yeah. Room not divided by three. So you have that between sheer are two x minus these zero. The trouble is you on two of nine eggs. I m six is four plus one, 23 house like me. Do X so well for abusing to go. Oh, we can We can make an honor substitution. We go. W being will do, uh, Expects plus one. Oh, this would be we'll get out with you. Cool the X so that D c drill becomes well I'm x is equal to w miners warning These becomes nine w minus one times doubling power. You're buying three and angel these She's going to You drove nine double you The four hour miners will nine hurts mine us all these actually design councils. That and then we would have just three. So you can So you know that. And then it would be, um So from you times, Indra off w fourth minus. Uh, that would mean this third w So that indigo, this would be none. Three musically w to the future. Power back by five No, minus no value to the fourth power. Bye bye. Four better noble Iwas Explosive one. So we will be three. No mix. Last one flower. What a life. Five minus No X plus one. He wasn't by four, Doctor, The fourth power. And then well, X is between two once you through zero. Well, it's she, um So that is this first thing to go on in port, Not one. We need to make another substitution on, then a green internet X squared. Plus Want to be equal toe. All right, hold school. Oh, you Teoh! You have not do you Legal toe. Two x, the X But you almost have there. These all these to cancel to you three. She would have a drawl. Oh, we're, uh, three a droll Oh, you today three hubs the u police. Because the you have sees xcx and then all the trouble. These? Yes, we go to our through times two divided by five. No, you could it five close more. But you see, people do X plus X squared plus one. So these were the about six. So six. Well, the five uh oh, x squib a swarms three. Oh, live house. Andi In these ex Mr Gable, we didn t you, uh, CIA until to this year. So these waas initially read our dumplings My mind was that total area with me He's, uh, which where we compute that they were being so three over. No, treat them small show x plus one of the two plus one that is three free three huge power by five minus four power like for I'm that minus. Well, that material would be just 1/5 from Visa Teoh. It will be whatever for From Dana, it is that minus No. 6/5 multiplying True square is four sold, four plus one. That is life. Well, because wise life her life today live house from the inner a tear would be just one I wanted if I bomb cigarettes. One, um So perhaps you can simplify these a little bit. So we have a these will 5 5/2 physical, too square riddles. This number is his Quit off five times my today, four house people for hawks is withdrew to, so these would be scruple five times. Those quirk that's fights word on, then all these were here can be simply fight before over to any these four times life minus five or trenny she wants to lioness wanted would play minus one. Will the train, then mining. And then, for these number, you have that a common border free to the fourth Power should be three to the fourth point out. Thompson are three on Dean that times 3/5, minus 1/4. Um, what are these? Three was also moved the plane there, so this would be minus three times that Myers me. Is that And then here, uh, all these number, she will Teoh four games three or 20 minus five. Well, there too. So I said this would be more bodies. 12 12 minus five. Don't miss. Why? He's, uh, 7 7/20 number 20. And then that multiplied by three. Those three, 24 minus Well, he becomes a plus. 3/20. I'm being that number there is minus seeks over five. Rhonda is number, please. So 25 or 55? Square it off. Five minus one. Because these numbers no, No worries. Um, that number is, uh, square. The five times five squared. She's standing five to be like that. No. Perhaps you can simplify for 23 times, three over a plane. And then you have about three. Fourth. I'm seven plus Oh, one u minus. All right, six, five times five squared off. Five minus one. That's me. The total must great

The question. We have used the well integrity, my people, you, the volume and the forced in Wondered by the morning that plane the plane Why puts 249 The plain X by three Blessed by now get awards dissolution. The volume is a right prism off with site three and fight with John. Intercept off expired three. This sent by 5 to 1 the whole You can be evaluated by using the integrity 40 p by my nest five x divided by three yet divine evaluation way. So people finally 41 question.


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