5

Y + 2 =4IOm tic polt (U,2,u) Lu poiit Tu, potential function for F(g,y,2) = 17+ (2y + e8z)j + (Bye8z)k Find...

Question

Y + 2 =4IOm tic polt (U,2,u) Lu poiit Tu, potential function for F(g,y,2) = 17+ (2y + e8z)j + (Bye8z)k Find

y + 2 =4IOm tic polt (U,2,u) Lu poiit Tu, potential function for F(g,y,2) = 17+ (2y + e8z)j + (Bye8z)k Find



Answers

Find a potential function for $\mathbf{F}$. $$\mathbf{F}=\frac{2 x}{y} \mathbf{i}+\left(\frac{1-x^{2}}{y^{2}}\right) \mathbf{j}, \quad\{(x, y): y>0\}$$

Hello. There's a problem. Number 27 asks us to find the little potential function. Uh, well, we could go ahead and find it, but at least you should know that this, uh, few f is actually conservative, so let's just make a quick check. What are we going to have? This is your P since you em and the end zero. All right, so here, partial p would respect it too. Why, like this Nero make it look like Parsa p, which respect to why is zero And that is the same with parcel and would respect the doozy as we get partial. M which respect to Z is there? That's the same wood Parsa p would respect it too. X, This hopes that's huh? This is an office. He's there. And then we checking the last guy partial and with respect to next this negative to x over. Why square and that a spar? So am I, which respected to why? Therefore your big is conservative. You could Now let's find our little potential function. Noticed that this domain is simply connected. Therefore you will have you. You will have the heat a little after function. All right, and the strength of partial F with respect to excellent going to be EMS. And it's two x over. Why that mean you f is going to look like I What does that look like? X where you see your ex? Where over? Why? Plus some function G that only have lines here. And then we take partial would respect why you will get X where l what is? Uh because we do it would respect it too. Why person, What is the riveter? But one over? Why gonna be X where and when? Why? Ah, sorry. Sometime people make could you It's X with him one over. Why? Square negative. Okay. And plus g prime line. Then we're looking for Ah, and compare it with the M term. The M term ease one minus x. Where? Why square? So that would give you g prime. But why is actually one of a wife square and your she is going to look Why negative one over Why? Plus some, uh, because we don't see a Z component a p zero. So it's just constant here. All right, so I'll laugh in conclusion. Going to be X. Where over? Why minus one over. Why Glass akin to see that would be a little potential function. I see you in the next video.

Here we are given occasion occasion it y two divided web Why police squad left three. Why plus six divided by by it could do for now the simplified if and fall for why we get If I do well, why holy square, The common three That is why bless Good Bad Rabbi is equal to four Now let us as you y plus two divided by y that is a call to X. We get exit squad lefty X Mina four is equal to zero now Fact arrived If we get X plus four x minus one that is equal to zero X plus four is equal to zero R X minus one is equal to zero We get X. It called to mind a for our X equal to one now He called the value off X we get why could divided by wise that is equal to minus four You are why that's good about a rabbi that is equal to one now Solvable dictations. Here we see that practically we thought this this one we get why it's glad playschool is equal to why by square minus y slash two is equal to zero. We get that in the resolution for dedication. So but if Cardiff Now we saw edification. Vice squad, Pashto political to minus four, right, right square Before way. Pashto is equal to zero now. Use that quadratic formula. Kartik for Life X equal to minus B plus minus. Be square Mina four. Easy hold divided by two A. Here a is equal to one B is equal to four and say the call to to use the value of ABC and find the value off why we get why is equal to Pinafore. That's fine of is square Root off B squared that it's 16 pinafore is one and see that it's too who were divided by to. Now, if you get Mina four best minus, so it's quarter to To add it back to final answer it Via is equal to plus minus the square root off to That's the final answer

This question asked us to solve the initial value problem explicitly. What we're no we're gonna do is given d y over DT. We're gonna put the d Y in the left hand side, Then write out our function and then put the DX on the right hand side. Take the integral of both sides we get. Why is this part over here is the same thing as Ark Tan You can write. This is 10 to the minus one of tea. This is simply too to the t and then plus C cause we're integrating. Now we know we're substituting the initial conditions. Why is three won t is zero. Therefore, plug in three is why and t zero in order to solve for what see is a prevalent too we get three is one plus zero plus c Therefore see Haas to be equivalent to plug into are integral and plus two

We have y prime equals minus y squared plus 10, y minus 21. And want to get solutions of that differential equation for and why? Why attempt equals zero equals 1 and four. Now let's see here is yeah, three is 0 And I think seven is also a zero. Does that make sense? seven is -49 plus 70 brian. This trying to get So three and 7. So this has roots at three and 7. And it's very much like um the previous case, but now just just shifted. If we start out here, why is positive but the derivative and negative. So we're gonna go to smaller values of why and then smaller and smaller and then get basically smaller until we go off to negative infinity. Now, if we go to over into this region here, we say at four we have a positive derivatives that we're going to go to larger values of why and even larger values. And then we're gonna deliver is gonna start to slow down Uh and we're going to approach this point here at seven. And likewise, if we started over here, we would approach into this point here. So when we started one, we basically rapidly go off to minus infinity, I guess that would be here and we started four. You can see that for a while, I think the inflection point where this is the maximum that when y is five, so we have positive coverage er here because the slope is increasing and then the slope is decreasing Until it approaches zero. Um And as White Horse to seven, so we have something like this and again, quite a bit like the previous problem. But again, if we started up here, we would get something like we had over here.


Similar Solved Questions

5 answers
It can be shown that +3 e-ax? dx:xe ax dx(note integration limits!) Use the approach above to find Za
It can be shown that +3 e-ax? dx: xe ax dx (note integration limits!) Use the approach above to find Za...
5 answers
Vy = exy =X <x =2
Vy = ex y = X < x =2...
5 answers
Consider the hydraulic lift shown in the figure. The small piston has an area Ap of 0.0330 m?, and the large piston has an area Az of 4.00 m?. What force Fz will the large piston provide if the small piston is pushed down with a force Fi of 18.0 N?Fz
Consider the hydraulic lift shown in the figure. The small piston has an area Ap of 0.0330 m?, and the large piston has an area Az of 4.00 m?. What force Fz will the large piston provide if the small piston is pushed down with a force Fi of 18.0 N? Fz...
5 answers
Find all the values of x such that the given series would converge_ 11n(.")(n + 1) (n + 8) n =1The series is convergent from x left end included (enter Y or N):to xright end included (enter Y or N):
Find all the values of x such that the given series would converge_ 11n(.")(n + 1) (n + 8) n =1 The series is convergent from x left end included (enter Y or N): to x right end included (enter Y or N):...
5 answers
Evaluate this complex expression and enter your answer in rectangular form:(62-309/6+32602 2+j
Evaluate this complex expression and enter your answer in rectangular form: (62-309/6+32602 2+j...
5 answers
Example: A ball is kicked from the ground with an initial velocity of 8 m/s at an upward angle of 300 with horizontal: The maximum height in m is (b The maximum range in m is The time of flight in $ is
Example: A ball is kicked from the ground with an initial velocity of 8 m/s at an upward angle of 300 with horizontal: The maximum height in m is (b The maximum range in m is The time of flight in $ is...
5 answers
A car drives on circular track with radius of 0.5 km. The of [he car is 850 kg: tangential speed of the car is 50.0 m/s. The mass What ' is the magnitude of the car' centripetal aeceleration? 0.05 m/s? 413,5 ms? 5.0 mls? 0.1 mls? What is the: magnitude of the centripetal force On the car? 85 N 4250 N 43 N 3.7 kN
A car drives on circular track with radius of 0.5 km. The of [he car is 850 kg: tangential speed of the car is 50.0 m/s. The mass What ' is the magnitude of the car' centripetal aeceleration? 0.05 m/s? 413,5 ms? 5.0 mls? 0.1 mls? What is the: magnitude of the centripetal force On the car? ...
5 answers
Problem 6 (10 pts): Solve the following differential equation by applying the Laplace Transform and its inverse2y + 8y + 2y = e-Zty(0) = 1, 9(0) = 1
Problem 6 (10 pts): Solve the following differential equation by applying the Laplace Transform and its inverse 2y + 8y + 2y = e-Zt y(0) = 1, 9(0) = 1...
5 answers
Given the vector function F(I,9,2) =< F=+y+2 Fz =-+2y: F3 = IVz > _ Calculate F and V < F.b) Given any vector function F(r.y-2) =< Fi(r,U-2) Fz(I,9,2) . Fs(z,V. 2) nd any scalar function o(T-Y- 2).Explain in detail why the following hold:i) V. (V x F) = 0 ii) V x (Vo) =< 0,0,0 >. |Hint: Use 3 J |
Given the vector function F(I,9,2) =< F=+y+2 Fz =-+2y: F3 = IVz > _ Calculate F and V < F. b) Given any vector function F(r.y-2) =< Fi(r,U-2) Fz(I,9,2) . Fs(z,V. 2) nd any scalar function o(T-Y- 2). Explain in detail why the following hold: i) V. (V x F) = 0 ii) V x (Vo) =< 0,0,0 >...
5 answers
A jogger ran 3 miles, decreased her speed by 1 mile per hour, and then ran another 4 miles. if her total jogging time was 2 1/2 hours, find her speed for each part of her run.The speed for the first part of her run was.... mph.The speed for the second part of her run was.... mph.
A jogger ran 3 miles, decreased her speed by 1 mile per hour, and then ran another 4 miles. if her total jogging time was 2 1/2 hours, find her speed for each part of her run.The speed for the first part of her run was.... mph.The speed for the second part of her run was.... mph....
5 answers
QuestionFor the following ODE y "-4y" +y +6y = 0 the general solution isOAy = Cpe2x C2e3x Cze-X (C1,C2 and C3 are constants) Oey = Cte-4x CzeX Cze6x (C1, C2 and C3 are constants) Ocy= Cpe-4x +C2 x eX (C1 and C2 are constants) Opy = C1e2x Cz x e3x (C1and C2 are constants)
Question For the following ODE y "-4y" +y +6y = 0 the general solution is OAy = Cpe2x C2e3x Cze-X (C1,C2 and C3 are constants) Oey = Cte-4x CzeX Cze6x (C1, C2 and C3 are constants) Ocy= Cpe-4x +C2 x eX (C1 and C2 are constants) Opy = C1e2x Cz x e3x (C1and C2 are constants)...
5 answers
Question 13Not yet answeredMarked out of 2.00Flag questionA solenoid 10.0 cm long has 500 turns and carries a current of 2 A. the magnetic field strength inside this coil isSelect one:a. 12.5mTb. Nonec. 1.25mTd. O.6mT6 mT
Question 13 Not yet answered Marked out of 2.00 Flag question A solenoid 10.0 cm long has 500 turns and carries a current of 2 A. the magnetic field strength inside this coil is Select one: a. 12.5mT b. None c. 1.25mT d. O.6mT 6 mT...
5 answers
0 d_NH0 eZI0NHCl
0 d_ NH 0 e ZI 0 NH Cl...
5 answers
Driver travels northbound on highway at speed of 24.0 m/s_ police car; traveling southbound at speed of 37.0 m/s_ approaches with its siren proc ducing sound at frequency of 2450 Hz What frequency does the driver observe as the police car approaches?What frequency does the driver detect after the police car passes him?(c) Repeat parts (a) and (b} for the case when the police car is traveling northbound_ while police car overtakes after police car passes
driver travels northbound on highway at speed of 24.0 m/s_ police car; traveling southbound at speed of 37.0 m/s_ approaches with its siren proc ducing sound at frequency of 2450 Hz What frequency does the driver observe as the police car approaches? What frequency does the driver detect after the p...

-- 0.018910--