5

SET UP BUT DO NOT EVALUATE: integrals as specified find the volume enclosed by the cone = = Vr" +>" and the plane Draw the projection for each case:a) ...

Question

SET UP BUT DO NOT EVALUATE: integrals as specified find the volume enclosed by the cone = = Vr" +>" and the plane Draw the projection for each case:a) Triple integral - cylindrical coordinates_b) Triple integral spherical coordinates:Double integral rectangular coordinates order dydxTriple integral- rectangular coordinates; orderdxdzdxNow actually compute the volume using any method:

SET UP BUT DO NOT EVALUATE: integrals as specified find the volume enclosed by the cone = = Vr" +>" and the plane Draw the projection for each case: a) Triple integral - cylindrical coordinates_ b) Triple integral spherical coordinates: Double integral rectangular coordinates order dydx Triple integral- rectangular coordinates; orderdxdzdx Now actually compute the volume using any method:



Answers

(a) find the spherical coordinate limits for the integral that calculates the volume of the given solid and then (b) evaluate the integral. The solid bounded below by the $x y$ -plane, on the sides by the sphere $\rho=2,$ and above by the cone $\phi=\pi / 3$ (FIGURE CANNOT COPY)

I have promised 77. So are the triple integral for the volume is going to be the following Plugging in her function. That's a good 22 pipe bombs H r squared over two nice h r squared over three. Give me this. One third each r squared pie. Uh huh.

Marie have these reasons that he's being was bounded by Yeah, X see waxes. So it is bounded below by the cone. This colder Sample these five boards. So these defines a cone. She was one of the scone. We're here. It's below that Cone Indian. No, it is also supposed to be inside of this year. The radio's on three. So it is, uh, this vision inside. So, uh, I'm boned, you know, Lady Cone, huh? Equals through my faults. You sigh well, missing. They're off this year. Ovary already. These three. So you have these boys in D? No. Well, I mean, it's very cool. Cornelis circle? No. So that bones for she, uh, he must be between. So, between zero, we're four days for, uh, Rose between you're on three cereal three. And then, um there goes all the way around. So whole turn from zero to Dubai. It's your goodbye level element in Sprinkle coordinates. His row squared sine wolfie to the volume during this because the volume by the So now we wanted to do things boil you in. It's, you know, people, Gordon. Until we have their restrictions that are well, you have here the X, the seaplane. So, uh, maybe he's, uh, over. These is going on inside That, uh, this few of ages three. Um, also, the restriction is nothing c square plus R squared. Well, must be smaller. Done, huh? She Yeah. I'm being, uh, so o r please. Our It's, uh, was vying from here to there. There, there, there, there. So this is their projection. You should be the positional farm. So this is the line. See, people's toe are But is that gives you Yeah. Why? Works. So are her Really use will be between, uh, zero on and, uh, see. But we have this condition that well bound stops being good at this point. That point has something not that is That would be all these long years. Three. So that is seen not wishing the three times sign. Well, you are my fourth. She's, uh, three. Everybody squared off two. It's quite of Dewey's one of Earl's court of Please sign off my fourth fine forth. So you should do, uh, Well, this bond is good for for C. It is. You on, uh, that that number Duffy, Where is good to know, But you should be you are is gonna go from zero up to see So they're gonna be relenting, Cylindrical. These are our undying, uh also the sea. Uh uh. Zeros from zero off. Do. There's no number. You ever squared off too, when they indeed theater, uh, goes old, we're on. So it's like 13 these rooms, the oracle. But then you have to do after plans. Either. Another needle, uh, which you have the bone for. See you eating three squares of film from that number. So there the bond. Versi. He's even by that. So that you simplify that together. C o the bone for our do you have when she's three minus c squared fleeing When is he squared? He's goingto are square e r. We'll go between zero and squaring the three minus c squared. So the bone for our should be It is zero on the ground. No, she squared Radios think so. Three square minus. Is he squared on dinner? Ovaries? This is the bone. For our there is a lot of mercy on being thorough has can go hold the way around so is easier to. So the volume should be able to those two intervals I did in Cylindrical. So Ivy's easier to complete it in. These gets one. So wherefore dog off things go from zero two guy four squared sidle he the p and then rose from zero off the three free on there. Hey, I goes all the way around. Yeah. So do it, huh? Do a thief eat first. So they drove. Sign what will be minor school sign. So you want it bad in 54 on zero or this is gonna be miners like Ford's minus close. I know. Do you mean? Well, was in my forties. Whatever score of two is one. So mine is That would be hotel. Well, these, uh, these one can hear it in us. Uh, do ours too. So you have minus one minus one minus one one minus squared off. Or is going to do so. These numbers, it's quarter to ah, minus one over. Squeals off. Do No, That is this First for the people, too, too Screwed up to my as one. We were escorted through, huh? Things interval with Inspector Federer into old respect too. Row from 03 Scored the road there. So will they go? Angel bro squared. You don't kill your old Q. You're like three. So that the awful waiting for people to two to his one device placed too times. Uh, three Q If I would like three. My nose. Uh, well, your cube got away free. It is you, Rhonda, All times these interval. Bye. Oh, the fear. Uh, So before moving on, let's make some simplification. See these as those Weren't power so useable conserving that would be the square. Right? So we have that volume's you see, Phil two for the two might is one over square with two. There's three squared. That's three square. Sometimes Inderal from zero to buying. Ferre is central visible to do. Bye. So that the vehicle to hole seeing Yeah, that would be excludes a tool in his one. Yes, that's nine. Because mind them still, there will be 18 bye over square. So that is so where is avoiding on these of these? Well, that region

So have the region region He in the first opened the first opened under. He's bounded by this fear. Um, the inside this fear Ah, he It's fear of radios Ruggles three on Uh, yeah. Bake on Described by coun Do you buy? She equals fight over four Eso is gonna be the helper region so we have the angle here by a floor that uses a cone. It's good to see because 5/4 you have the school Very nice being We cut because either considered a region inside of the screw reduce three. So something like that, we're he's, uh, zero physical toe tree on the school is given by fi sequel to, um, by over four. Well, she would like to sit up in this very gold gold in it. What is the volume? So as we see here, our uncle he is between zero from that angle there. That is fiber for feel. Leveraging Syria by over four. Uh, well will go from zero up to three World's goes from zero pill three and then you won't do consider just the region. One day first talked him, you would do You'd have to cut like that sort of the only obtained this portion. Well, being for that portion, we would be through a street. Thiago Vieira. So what we have you here, X Some. Why? That actually is there. You see, Data is going from that. Like that. Actually sexy obtained by said it goes you on the Y Axis is obtained by saying that later Siegel do by house. So there will be between zero ne buy a house. And so the volume would be well fair. Goes from zero up to I have so that that would be Vera. Mom, feed goes from zero. Okay, by were four. You I mean and rose from sear up to three. You roll. I'm Dana. Was this region the first off them on the volume element? Is there a square sign off? So this is the volume in this variable. Do you want it to consider the volume in cylindrical cylindrical? What we have for federal, We have, uh, the san Restriction, because this it up in this very believes the same fit us you since cylindrical coordinates. So this will be the range more fair in that case. And then you have the restriction between are. And, uh, so you have, uh we don't need to concede there these portion. And so, uh, well, here you would need to have here. Are you have here, Um, we have here, See, on the that. He says there's are so as we can. Not this Ah, for a Z between sear on this point, it's called that see, Not, um very These are is gonna go from zero. A deadline that is even by c is equal to Are these the beaches? The angle g equals two by over four. But that angle is not is gone is not in cylindrical coordinates. So we have to express it like that. Are you able to see? So that is, uh, for C between zero. I'm see, not the restriction for our is that our goes from zero, uh, from zero up to to see and then between. Ah, well, that point there should be three. Because I have a radius off our sphere. I'm being for C line between See, not I'm free is gonna be given by these. Oh, ladies, curve. So that our we'll go from zero of the boundary of that curve. The curve is this curve here is, uh, c square you described through C square blocks are square. Ableto three squared is nine. So that our our goes since it is positive you go up to nine square root off mine minus c squared mine c squared. Um, so that would be making God range on Dana. All the only thing that we need to All right, find out is what what he's ever seen. Not what is that. See? Not not. And so we can find that by saying that, uh, well, on that point So she's thesis angles by over for these distances, three so seem not should be able to three. That is that these US times sign off by over Well, off by over four for that. Well, that angle, by or for on the sign off by over four. He's, uh, one over. Square it off to. So we're be the BBC. Not no. So a decent Drago are fair. Go from sear up to by house that he's the data well mean are or a scene what was gonna go need to separate it into two pieces. So from, uh, from Syria, Tool three squared off to the city for you see? And then we should have another interval. Ah, from three squared off to. So we should have another deal from by saying that. Um, see those, uh, from three. Very square it off to of the three. These so that these 200 girls cover the whole range. We'll see. You could see blue go from zero up to three on then in these fish first, integral Well, r release are was from Syria to see So that would be the are on the volume element is just are she would be that. And then over the central there goes from ah, sirrah off the square root of nine miners see squared So that is for BR being before doing well in the SAR. So these should be volume Onda, uh was you guys he It is easier to build this integral. So let's do that Interval. So, for it is William. You know Indra from Cyril up to by house wolf the, uh, Feagles from zero to buy over four. No, the sea rovers from zero off the three year Oh. Then they be helpful. We'll square sign, throw square sign or feel so Uh, well, we can compute the interval. Respectful, uh, data. We feel our first because nothing here depends on fear. So getting teary that separately the center got would be go to just fair. I evaluated meeting by house zero. That's gonna give us by house. So you have my house terms. All these are very intervals from zero by four from 0 to 3. Rose squared. Sign off. We grow Onda. Um, all the drilling for no squared the role. Is it really possible to row Cube third's? I said that between three on Syria with people, too. Three Q third's my no cereal. So these councils want powers. He would have three squared. There's gonna be equal to nine. So he's internal goals away when we get on nine. Teoh vehicle, The Central Legal Tau nine by, Huh? Mind my house. I'm being being a girl from zero off to buy over four off. Ah, sign. Oh, Do you feel I'm being trouble? Sign of fee. Hey, Intel of sign off we Is it really possible to minors? Cross key? So you do literally not meeting zero by over for that That is equal to minors. Course five before minus cause of zero on the clothes off by over four people to one over a squared off to because that's here is one that one can also be written as a school off to or a skirt off to so that you will confine us one minus x squared off to no holder. Square it off. Do it Seems we have a minus that makes you to be able to score a total minus one. Oh, very. Square it off. Um, sort of these will be photo the volume of people too. Do you have that? So nine by halves there's around there being terms that you know very well that times screwed off pool miners one over a squared off to So they should be the volume When, uh, well, perhaps we could simplify by multiply allies. Quote of to I'm tough on them bottom. And so if you do that, you get the physical to ah, you know, to the it's on mine by And so tu minus squared off to over, um, growth of two times that. So two squared people before so nine by as to square it off to Well, we're for So you get Ah, So the volume musical toe these Where do you prefer that which are the same

I have problem number 80 said the best way to do this is using Cartesian coordinates and then use a change of variable, so we're gonna set it up. Since the volume of the lips oId is eight times of all your the och tens with multiplied by eight. Integrate from 0 to 1 Integrate from zero to one minus x squared over a squared Have the integrate from zero one mice X squared over a squared minus y squared over b squared of one d z d y the x and then using X is you go to a U Why is it gonna be V and Z? Is he going to C W We got the new integral of eight times integral from 0 to 1. You grow from zero square toe, one minus you squared. Zero squared. One months, you squared minus v squared ABC D W D v d u. And since we can pull out, ABC is Constance. That means it's just a B C times the volume of a sphere of radius one, which is 4/3 pie. ABC


Similar Solved Questions

5 answers
Find the point on the plane 4r + 3y + 2 = 1 that is closest to (1,-1,1)_ (Recall: the distance between two points (T1, Y1, 21) and (12, Y2, 22) in space is V(c1 T2)2 + (y1 = 92)2 + (21 22)2 .) [4 marks]
Find the point on the plane 4r + 3y + 2 = 1 that is closest to (1,-1,1)_ (Recall: the distance between two points (T1, Y1, 21) and (12, Y2, 22) in space is V(c1 T2)2 + (y1 = 92)2 + (21 22)2 .) [4 marks]...
5 answers
Find the area ofthe region bounded by y to the right of the y-axisand y = 2 _ 2r" and3/ 15 6 / 17 44/15 40{17 None of the aboveSet but not sof-e the integral for the a70 length of the cuve y =2 + 1 for <r < 2.Vi-erdrV1_4"dr2TV1+42dr2TV1+lr?dr None of the pove
Find the area ofthe region bounded by y to the right of the y-axis and y = 2 _ 2r" and 3/ 15 6 / 17 44/15 40{17 None of the above Set but not sof-e the integral for the a70 length of the cuve y =2 + 1 for <r < 2. Vi-erdr V1_4"dr 2TV1+42dr 2TV1+lr?dr None of the pove...
5 answers
10)= (? + 10)= . (3, 3 36' + (2x) + H62 + 10)7(+' + (x2 + 10) )
10)= (? + 10)= . (3, 3 36' + (2x) + H62 + 10)7(+' + (x2 + 10) )...
5 answers
01010.0 pointsThe matrices I2 #[6 9 Jz = J[4 %] are perpendicular and have unit length with respect to the Standard Inner Product on R2*2 True or False?1. True2.0 False, they don t have unit length_3. False, they aren t perpendicular.
010 10.0 points The matrices I2 #[6 9 Jz = J[4 %] are perpendicular and have unit length with respect to the Standard Inner Product on R2*2 True or False? 1. True 2.0 False, they don t have unit length_ 3. False, they aren t perpendicular....
5 answers
I0. Determine which of the following is true; cot" 1420 Csc" 1420 + cos" HS" + tan" HS' = | tan (-1939) tan /930 None of these10.I. Delermine which of the following is true. (an 50" tan 550 Uilm) 1050 tan 50" tan 550I.sin 2279 sin [070 cos |209 cos [070 esc |209 cos 850 cos 120" cos 350 sin 420" sin 350None of these
I0. Determine which of the following is true; cot" 1420 Csc" 1420 + cos" HS" + tan" HS' = | tan (-1939) tan /930 None of these 10. I. Delermine which of the following is true. (an 50" tan 550 Uilm) 1050 tan 50" tan 550 I. sin 2279 sin [070 cos |209 cos [070 es...
4 answers
Yoedue dark 5 thrown_ sec room W Uheroch eDecteamie' an ettlee object edengtn at of ftlsec 7 wall throw ow agais the at r ft/sec wall sand
yoedue dark 5 thrown_ sec room W Uheroch eDecteamie' an ettlee object edengtn at of ftlsec 7 wall throw ow agais the at r ft/sec wall sand...
5 answers
(8 points) The position of _ car Is given according to the following equation, where SI units have been suppressed;[J*+ 4Y'where is the veloclty vector and and v are the unit vectors in x and y respectively:: (Canvas makes it hard to place arrows and carets above the vectors )Write an equation In symbols to determine the velocity of the car;Determine the velocity of the car att 2.0 $.
(8 points) The position of _ car Is given according to the following equation, where SI units have been suppressed; [J*+ 4Y' where is the veloclty vector and and v are the unit vectors in x and y respectively:: (Canvas makes it hard to place arrows and carets above the vectors ) Write an equati...
1 answers
Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises $1-46$. $$\int_{2 / \sqrt{3}}^{2} \frac{\cos \left(\sec ^{-1} x\right) d x}{x \sqrt{x^{2}-1}}$$
Use the Substitution Formula in Theorem 7 to evaluate the integrals in Exercises $1-46$. $$\int_{2 / \sqrt{3}}^{2} \frac{\cos \left(\sec ^{-1} x\right) d x}{x \sqrt{x^{2}-1}}$$...
1 answers
$$\text { The range of a projectile: } R=\frac{v^{2} \sin \theta \cos \theta}{16}$$ The range of a projected object (total horizontal distance traveled) is given by the formula shown, where $v$ is the initial velocity and $\theta$ is the angle at which it is projected. If an arrow leaves the bow traveling $175 \mathrm{ft} / \mathrm{sec}$ at an angle of $45^{\circ},$ what horizontal distance will it travel?
$$\text { The range of a projectile: } R=\frac{v^{2} \sin \theta \cos \theta}{16}$$ The range of a projected object (total horizontal distance traveled) is given by the formula shown, where $v$ is the initial velocity and $\theta$ is the angle at which it is projected. If an arrow leaves the bow tra...
5 answers
Question 17 (1 point) A sample of 271 one-year-old baby boys in the United States had a mean weight of 22.4 pounds Assume the population standard deviation is 6.0 pounds What is the upper bound of the 90% confidence interval for the mean lifetime of the components?Round vour answer to twotlecimal places (for example 24.28). Write only _ number as your answer:
Question 17 (1 point) A sample of 271 one-year-old baby boys in the United States had a mean weight of 22.4 pounds Assume the population standard deviation is 6.0 pounds What is the upper bound of the 90% confidence interval for the mean lifetime of the components? Round vour answer to twotlecimal p...
5 answers
2 ptsQuestion 20For the situation described below, what attribute of the object must be measured? Buy ' the right amount of wallpaper for room"perimeter or circumfercncevoluinearea or sunace en
2 pts Question 20 For the situation described below, what attribute of the object must be measured? Buy ' the right amount of wallpaper for room" perimeter or circumfercnce voluine area or sunace en...
5 answers
In sequence alignments such as those generated by BLAST search, the significance of the alignment can be presented as an E-value which specifies how likely it is for match this good to be found in a database of given size by chance You have scanned large sequence database with sequence query; hoping to find significant match: Which one would you look at: (A) match with an E-value of [, or (B) one with an E-value of 0.001? Write down A or B as your answer.
In sequence alignments such as those generated by BLAST search, the significance of the alignment can be presented as an E-value which specifies how likely it is for match this good to be found in a database of given size by chance You have scanned large sequence database with sequence query; hoping...
5 answers
How to prove a no is divisible by 9
How to prove a no is divisible by 9...
4 answers
The following
the following...
5 answers
In a survey; 510 adults were asked if they drive a pickup truck and if they drive a Ford_ The results showed that 1 in 6 adults surveyed drives a pickup truck, and 3 in 10 adults drive a Ford. Of the adults surveyed that drive a Ford, 2 in 9 drive a pickup truck Find the probability that a randomly selected adult drives a Ford and drives a pickup truck
In a survey; 510 adults were asked if they drive a pickup truck and if they drive a Ford_ The results showed that 1 in 6 adults surveyed drives a pickup truck, and 3 in 10 adults drive a Ford. Of the adults surveyed that drive a Ford, 2 in 9 drive a pickup truck Find the probability that a randomly...
5 answers
Question 18 (3 points) Listen 104 Write the numerical value: Simplify completely: 317101-3)1
Question 18 (3 points) Listen 104 Write the numerical value: Simplify completely: 317101-3)1...
4 answers
Jilyr'+}- &Jnvs-7 &32f + 1
Jilyr'+}- & Jnvs-7 & 32f + 1...

-- 0.063663--