5

Find the flux of the vector field Fkacross the surface $ in the outward direction: Let $ be the upper hemisphere of x? +Y +22 =4OA5* 0 B. 5" 0c. 8 0 D. 8...

Question

Find the flux of the vector field Fkacross the surface $ in the outward direction: Let $ be the upper hemisphere of x? +Y +22 =4OA5* 0 B. 5" 0c. 8 0 D. 8

Find the flux of the vector field F kacross the surface $ in the outward direction: Let $ be the upper hemisphere of x? +Y +22 =4 OA 5* 0 B. 5" 0c. 8 0 D. 8



Answers

Find the flux of the vector field $\mathbf{F}$ across $\sigma$ $\mathbf{F}(x, y, z)=x \mathbf{k} ;$ the surface $\sigma$ is the portion of the paraboloid $z=x^{2}+y^{2}$ below the plane $z=y,$ oriented by downward unit normals.

This question are the circular region enclosed boy X squared plus y squared equals four. So the reintegration off regions sigma off f got and yes, equals double integration off this region off to Y square minus one DD, which is equal. Double invigoration, off toe order square, Sinus square seat a minus one and our limit zero to Zito to buy and are the hors d zita. So these will be equally for boy.

So in this situation when rectangle is there in X Y plane and vector Field is in that direction here. So if we take a differential area Victor D, then we can write it as d X de Wei and its direction is in zitka. So if we want to find the flux because of with this differential area differential flux, we can light it as mhm the since the direction off Victor filled and area is in the same direction. So the angle between them is zero degree and the value of course, zero is one so directly we can right here defies equal to Edie. So now if you substitute the value here, it will become defy easy equal toe Alfa over excess choir. Plus why Squire and the value off dia is DX and dy way. Now we need to integrate on both sides. So on integrating on both sides, it will become integration. Defy Now we need to integrate double integrated. You could be, except the way so it will become a lot worse. X squared plus y you Squire, they're dx dy way now if this attitude limit off excess since the rectangle is wearing in next direction from A to B. So the limit for X DX will become a Toby. And for the way that is the limit of y will vary from C today. So but this is the final answer for a part. Okay. No, let us. Okay, So this is a dancer. Now let us go for be part. So if we go for be part So in be part, since the rectangle is in why is it plain rectangle in ways it plain? Then the direction off d will become equal to We can write d y d dead and the direction will become ex cap. And so here the angle between E and D is a 90 degree and value off course 90 0. So the flux is also a weirdo zero. Okay. Thank you.

This question we have and equal negatives that X oy minus that YG plus key. So the integration off region R or F got and GS will be equal. End of integration Off this creation off to a square plus two y squared plus two I minus X squared minus y squared. Yes. If we substitute in this integration, we will get to are the hors d sita for, uh, tradition, dammit! Zero 102 Boy, we'll get a final solution equal to bond.

If the suffix is arranging downwards then we have the flats giving for this formula. So from formula chain it's going to be equal to this where our F. It's equal to that. So giving F. This is F. Yankee vein. Then for said greater than or equal to saru. We can write it in this form. So then it implies that our floods our flights that W. T. Girl. If the S using this formula we have P. P. Which is why. Why? And the pasha derivative of this with respect to eggs is going to give us my next eggs divided by square root of four minutes, X squared minus Y squared plus Q. Kill aids. My next ex he from here. So my nets yes. Then the derivative with respect to Y. Gives us my let's Y divided by square roots of four minus X. Squared minus Y. Squared minus R. R. Is to Zeke. So we have to said the mm. So if you simplify this this will give you the W in Segre of minus two Z. The mm. Why? Because this and that's good. So we this becomes positive and this is negative. So you only have this left. So from here we can substitute. So we have T. You can substitute for Zeke. And if you substitute you have the double in Siga here. D You have -2. said it's square roots of four minus X squared minus y squared T. A. Don't forget D. Is the projection of the surface on the X. Y plane. So D. Is inside the cycle. So this is the cycle, it's inside D. It's inside this X squared plus y squared equal to four. And if we use polar coordinates, let's apply polar coordinates here. So easy Hola coordinates coordinates we have we can write this uniform the -2 square roots off X. For my next x squared mhm. Four minus x squared minus y squared The a. To be equal to the integral from 0 to 2 by 0-2 you have -2 are square roots of four minus out squared. The are the T tell. So if you use the substitution method for thieves, let's say we apply a substitution method here and we make used to be equal to four minus out square. Then what it means is that we have -2 uh the uh the vehicle to be you. So if you do this then Their limits as well. We'll have to change from 0 to 2 to the Integra for my name. Service squared 4 -2 square. And this would give us 42 sustain from here It implies that we have the integral from 0-2 pi. Then from serve 4 to zoo. Yeah 4 to 0 four for two zoo square with so few do you the theater and this is equal to zero Suit Suit Pie. This will give us minus the tita. You have 0-4 because you are reversing the order square roots of you the you. So if you integrate, if we eat degrees we have this will give us minus tita the interval from 0 to 25 Then this would give us two divided by three U. To the power three on to the interval from zero to four. So evaluate and you have minus 32 divided by three. Hi so then this implies that our flats it's going to be -32 by divided by three which is a finer answer.


Similar Solved Questions

5 answers
Moving to another question will save this response:Question 5In a histogram, the widths of the rectangles represent the class frequencies class marks class boundaries class intervalsMoving to another question will save this response;TnehereF
Moving to another question will save this response: Question 5 In a histogram, the widths of the rectangles represent the class frequencies class marks class boundaries class intervals Moving to another question will save this response; Tnehere F...
5 answers
Stcp 5 ot 5; Make the cecision far thehypothesisAntwerPuinlKeyuad Kenoand shetciteKuelNuhrpoues_~Failta Re Ect Null Hypo ntsis
Stcp 5 ot 5; Make the cecision far thehypothesis Antwer Puinl Keyuad Kenoand shetcite KuelNuhrpoues_ ~Failta Re Ect Null Hypo ntsis...
5 answers
7 8i 1 SP (z ' 7 0 2)dS For10 < 'L>z*fk,%2) =
7 8i 1 SP (z ' 7 0 2)dS For 1 0 < 'L>z* fk,%2) =...
5 answers
7) An excellent way to protect a carbonyl group is to convert it into this functional group which is stable to acidic conditions:an alkane an alkene hemiaminal an imine an enamine 9) thioacetal g) an ester h) geminal diol hemiacetal 3 an acetal
7) An excellent way to protect a carbonyl group is to convert it into this functional group which is stable to acidic conditions: an alkane an alkene hemiaminal an imine an enamine 9) thioacetal g) an ester h) geminal diol hemiacetal 3 an acetal...
5 answers
Question 210 ptsAperson stands at the deepend of a swimming pool and looks at his dive mask which isat the bottom of the pool at a depth of 3.89 m The index of refraction for water is 1.33At what depthdoes the person see his dive mask (apparent depth in meters)?Your answer should be a number with three decimal places;do not include the unitActual ocouApparcnt depthFlshE8 0 _Image
Question 2 10 pts Aperson stands at the deepend of a swimming pool and looks at his dive mask which isat the bottom of the pool at a depth of 3.89 m The index of refraction for water is 1.33At what depthdoes the person see his dive mask (apparent depth in meters)? Your answer should be a number with...
5 answers
L = 2.958 10" ma' AIIll 760 [0fe 00206 Ln Inoi-tke1 10= Latet #e433 [I [ JM 760 mnHg 4,304/mol"6626 4n2170 * [0" ALI Vjgsbir 1 Cl 4.191 6.02 10:110132504 K m0512 K mLug K 4FXIfthe below reaction 4,s percent yleld 0/997,9906,what 46gof NO,(e), umning 40 e"t45s hi N_ 'ASs In Hrams 0l oxygen 4s needed t produce N IA4) 0,(rl NO_(c) I,o (unhalancet]
L = 2.958 10" ma' AIIll 760 [0fe 00206 Ln Inoi-tke1 10= Latet #e 433 [I [ JM 760 mnHg 4,304/mol" 6626 4n 2170 * [0" ALI Vjgsbir 1 Cl 4.191 6.02 10:1 10132504 K m 0512 K m Lug K 4FX Ifthe below reaction 4,s percent yleld 0/997,9906,what 46gof NO,(e), umning 40 e"t45s hi N_ &#...
5 answers
What types of forces exist between the individual particles in an ionic solid? Are these forces relatively strong or relatively weak?
What types of forces exist between the individual particles in an ionic solid? Are these forces relatively strong or relatively weak?...
5 answers
1 +4 1, dx Jvtr+zr J) 2 58 dx X-8
1 +4 1, dx Jvtr+zr J) 2 58 dx X-8...
5 answers
Question 16 of 20If sinewhich of the following bre possible for the same value of 0?cosdand tanecoseand tanesece75 and tane 3sece = - 2 and tane = 75SUBMIT
Question 16 of 20 If sine which of the following bre possible for the same value of 0? cosd and tane cose and tane sece 75 and tane 3 sece = - 2 and tane = 75 SUBMIT...
5 answers
Draw the expected phenotypic variance of a trait encoded by 5genes with 25% environmental variance vs. a trait encoded by 5genes with 2% environmental variance.
Draw the expected phenotypic variance of a trait encoded by 5 genes with 25% environmental variance vs. a trait encoded by 5 genes with 2% environmental variance....
5 answers
Determine whether the below statement is true or false:parametrization of the line segment from the point P(2, 1, 3) to the point Q(1,3 ~2) is r()=(2-0)7+(1+20)]+(3-St)k for t€[O,Select one: TrueFalse
Determine whether the below statement is true or false: parametrization of the line segment from the point P(2, 1, 3) to the point Q(1,3 ~2) is r()=(2-0)7+(1+20)]+(3-St)k for t€[O, Select one: True False...
2 answers
...
5 answers
Question 1The current in : 5-mH inductor has the waveform shown in Fig. 1. Compute lhe inductor vollage for each of the time segments shov i(t) (mA) 20((Ms)Figure 1Show work O ms < t < 1ms ->vt)=1ms < t <2ms ->v(t)=2ms < t < 3ms ->v(t)=3 ms < t <4ms -->v(t)=4ms < t < 5ms -->v(t)=
Question 1 The current in : 5-mH inductor has the waveform shown in Fig. 1. Compute lhe inductor vollage for each of the time segments shov i(t) (mA) 20 ((Ms) Figure 1 Show work O ms < t < 1ms ->vt)= 1ms < t <2ms ->v(t)= 2ms < t < 3ms ->v(t)= 3 ms < t <4ms -->v(t)...
5 answers
Graph jold 1 50 3 U 0 Fd me pnce-drmanu 1 CuuLaD L V dally d2man0 dectelslt 1 Jhu E4UIDMMMAUA netes ol2 L209 Dusne 1 1 1 1 DusneisU I 50.{B Cer Buenaldle LasuunNong olur Joovo
Graph jold 1 50 3 U 0 Fd me pnce-drmanu 1 CuuLaD L V dally d2man0 dectelslt 1 Jhu E4UIDMMMAUA netes ol2 L209 Dusne 1 1 1 1 Dusneis U I 50.{B Cer Buenaldle Lasuun Nong olur Joovo...

-- 0.023428--