5

Points)Find and classily the equilibriu points of the systemdx dt dycy +I _ 2y(r2 _ 1)(y - 3)...

Question

Points)Find and classily the equilibriu points of the systemdx dt dycy +I _ 2y(r2 _ 1)(y - 3)

points) Find and classily the equilibriu points of the system dx dt dy cy +I _ 2y (r2 _ 1)(y - 3)



Answers

Evaluate dy/dx at the given points. $$x y^{2}+3 x^{2}-y^{2}+15=0 ; \quad(-1,3)$$

Okay and this problem we're gonna be using implicit differentiation to find dy dx and we're going to evaluate it at the point to negative one. So my first step here is we're just gonna do implicit differentiation. So for this first thing we have dy the derivative of D Y is just gonna be too but then we have to put the dy dx And then we have five Since five is a constant number. The derivative of five is just gonna be zero. Then the derivative of negative X squared is negative two X. Then we move on to negative y cubed. So the derivative of negative y cubed is negative three, Y is squared dy dx. And then the derivative of zero is 0. So we want to get do Y dx completely by itself. So I'm gonna get rid of this negative two X. By adding it to both sides. Mhm. And then I'm going to factor out a dy dx. So I'm left with two three Y squared equals two X. So my last step to solve for Dubai dx would just be to divide by two minus three Y squared. Mhm. So those would cancel out and grd X equals two X over two minus three Y squared. So now we need to evaluate dy dx at the point to negative one. Mhm. Which means we just substituted to for an X. And the negative one for why? So this is really gonna equal to times two Divided by 2 -3 Times -1 Squared. So we just need to simplify this And we get dy DX at 2 -1 that's going to equal for over two minus negative one squared is just one. So two minus three Which is just negative one. Which means dy dx at this point would just be equal to negative four.

Into this lesson in this lesson performance implicit differentiation question at the point five and one. So let's start with the differentiation. Mhm. Mhm. Mhm. Yeah. Mhm. So here we have three on 2 then we we reduce the power by one so we have half. Then we differentiate what we have in a bracket. So this becomes y minus X, divide Yepes minus two. I you I. D. X. Then go to the left hand side is the constant. So we have 10. Why do ideas at this point we can put in the values because a lot of expansion. All right yeah so we put in 54 X. Than one. For why? Yeah mm. What? Oh mm. Yeah wow. Yeah Okay so at this point you have three on two that is 4 -1. Uh 5 -1 sort of those four Square root of four than one. So here we have five oh mhm. Five minus two. And that gives us -7 do I? The X. This is equal to 10 d. y. e. Okay so at this point we have this to goes there so we have three out one minus seven Y. Dx. Yeah. Mhm. And that is a call to 10 do i. x. So you multiply up three when it's 21 Y. Dx. Does she called to? Okay. 10 wide yaks. Then we have three. That is she called to? Yeah. 10. The last 21 do I. D. X. So this becomes three is according to 31 do i. d. x. And this is equal to dy dx? That is equal to 3/31. Okay so the ideas at five one is given to us this way. All right. Thanks for the time. This is the end of the lesson.

In this problem we will cover computing partial derivatives. So we want to find first the partial derivative with respect to X. And to do that. We will hold the variable Y fix. So we're going to treat all white terms like Constance while finding the derivative of this function with respect to X. So we want to find the derivative perspective X of X cubed plus three X squared. And we're going to ignore the why Constance. We know because we know that taking the derivative of Constance is going to yield us zero and that's what we'll get. And so our answer is going to be three X squared plus six X. And so to find where this partial derivative is going to be equal to zero. We just set three X Squared plus six x equal to zero. We see that we can factor the left hand side. So we have three x Times X-plus two. Okay, equals zero. So we know that X has the equal either zero or -2. If we want the whole expression to be zero and these two values of X are what's going two Yield the partial derivative of zero. So now we move on to the partial derivative with respect to why and to do that instead of holding why fixed? We're going to hold ex fix this time. So we're going to treat the X terms like constance. So we're not taking their derivatives is going to yield us zero. So we're going to ignore them. And we're only going to look for the derivative respect to why? Of why huge minus three. What? That looks so wrong. Three Y and that is going two yield us three Y squared -3. And to find out where this partial derivative is equal to zero. We're just going to set three Y squared minus three equal to zero. And we see here. But mm maybe we can factor the left hand side to make things easier so we can take out a free and we are left with why squared minus one And all of that equals zero. And we see that the y values that would yield zero Are going to be y equals one And why equals -1. So we have our X values and are y values. And now to put them together to create four points. So our first point is going to be 01. Our 2nd point is going to be 0 -1. 3rd point is going to be negative to one and our last point is going to be negative too negative one. And what these are Are the points that are going to yield us zero for both. The partial derivative with respect to X and the partial derivative with respect to Y.

Alright in this problem are going to be using implicit differentiation to find dy dx and they were going to be evaluating that at the point 12 Let's go ahead and start with first just doing the implicit differentiation. So if we take this equation right here for this first part, the three X cubed y squared. We're going to have to use the product rule. So it's gonna be the first, so three X to the third times the derivative of the second derivative of the second would be to y do I. D. X. And it's gonna be plus the derivative of the first, which would be nine X squared times the second. Which is just going to stay y squared. Then we go on to this negative two, Y to the third, which is just gonna become negative six. Why squared dy dx? And then then that's going to equal the derivative of negative four since that's a constant number is just zero. So now our goal is to get dy dx completely by itself. So let's go ahead and get anything without a dy dx to the other side. So I'm actually gonna combine this first part as well. So I get six X cube Y do I D X minus six Y squared. Do you I. D. X. It's going to equal negative nine X squared Y squared. So just some algebra there and then I'm going to factor out a dy dx. So I'd get six X cubed y minus six Y squared equals negative nine X squared white screen. So to get dy dx by itself we're going to just divide by six X cubed y minus six Y squared. Yeah. Yeah so that's what do I. D. X. Is gonna equal but now we need to substitute in our values that were given to us. So this 0.12 to figure out what do I. D. X. Is gonna equal at that point? So do I. D. X. Evaluated at one two is gonna equal negative nine, replace the X. With the one. So one squared replace the Y with it too. So two squared all over Then it would be six X. Is one. So one cubed times two minus six times two squared. Mhm mm. So then dy dx evaluated at 12 is going to equal negative 12 squared is four. So negative nine times four is going to be negative 36 divided by six times one cubed times two is just gonna be 12 minus six times two squared. That's four. So that would be 24. So do you rdx evaluated at that point it's gonna be negative 36 over negative 12. Which just simplifies to positive three.


Similar Solved Questions

5 answers
Lety= fG)=(v'-4r-s):. (IS pts) Find intervals - (15 pts) Find on which f is increasing: intervals on which f is concave downward.'
Lety= fG)=(v'-4r-s):. (IS pts) Find intervals - (15 pts) Find on which f is increasing: intervals on which f is concave downward. '...
5 answers
Sunsetof Nia} 0 suepice5.1) Let $ =#nesct of all Eppef trianguler iatrices;52Lt $ele sce of all skew-symEtFic matricusn Matr skew-sycitlria 4 onkiDateimine eaetEicf
sunset of Nia} 0 suepice 5.1) Let $ = #nesct of all Eppef trianguler iatrices; 52Lt $ ele sce of all skew-symEtFic matricus n Matr skew-sycitlria 4 onki Dateimine eaetEicf...
5 answers
EsuonB. 1.00 molC.2.00 mol0 D.4.00 molQUESTION How would you describe the following equation?2 Al (s) - Fe2O3 (s) = 2 Fe (s) - Al203 (s) AH= -850 kJOA Endothermic 0 B ExothermicC. Impossible t0 delermineCDNo heat is transierred in this reactionQUESTIONHow many grams of waterproduced from the reaction of 4033 g 0f H2oHa (2) 01 (3)
esuon B. 1.00 mol C.2.00 mol 0 D.4.00 mol QUESTION How would you describe the following equation? 2 Al (s) - Fe2O3 (s) = 2 Fe (s) - Al203 (s) AH= -850 kJ OA Endothermic 0 B Exothermic C. Impossible t0 delermine CDNo heat is transierred in this reaction QUESTION How many grams of water produced from ...
5 answers
2. Car A is travelling west at SOmi/h and car B is travelling north at 60mi/h. Both are headed for the intersection of the two roads_ At what rate are the car $ approaching each other when car A is 0.3 mi and car B is 0.4mi from the intersection?
2. Car A is travelling west at SOmi/h and car B is travelling north at 60mi/h. Both are headed for the intersection of the two roads_ At what rate are the car $ approaching each other when car A is 0.3 mi and car B is 0.4mi from the intersection?...
5 answers
Draw out the full mechanism (proper arrow pushing) for the dehydration of 1-butanol: #2SO4 /HsPOt Draw out- the full mechanism (proper arrow pushing) for the debromination of 1-bromobutane: Vo 046
Draw out the full mechanism (proper arrow pushing) for the dehydration of 1-butanol: #2SO4 /HsPOt Draw out- the full mechanism (proper arrow pushing) for the debromination of 1-bromobutane: Vo 046...
5 answers
In this exercise we will use the Laplace transfomm solve the following initial value problem:8y" 25y 25,y(0) = 0,9 (0) = 2 (1) First, using Y for the Laplace transform of y(t) ie Y = Clylt)) , find the equation obtained by taking the Laplace transform of the initial value problem(2) Next solve tor Y(3) Finally apply the inverse Laplace transiomm t0 find y(t)
In this exercise we will use the Laplace transfomm solve the following initial value problem: 8y" 25y 25, y(0) = 0,9 (0) = 2 (1) First, using Y for the Laplace transform of y(t) ie Y = Clylt)) , find the equation obtained by taking the Laplace transform of the initial value problem (2) Next sol...
5 answers
DNA quenco IhitFEFEFTTHETCNEEEEHHEEHHTKRARG FUVALSERALAARGGLXHISILE SToPMutation RI: Let'whathencentpointJoquence thun tranelate /into I0 Amiino OcidiEEEEEHEEEEN
DNA quenco Ihit FEFEFTTHETCNEEEEHHEEHH TKR ARG FU VAL SER ALA ARG GLX HIS ILE SToP Mutation RI: Let' whathencent point Joquence thun tranelate /into I0 Amiino Ocidi EEEEEHEEEEN...
5 answers
(-331(0,31(0,2)4 (-2,01(2,01(-i.0i (,0)Enter the local minimum value for each graph: If there is not an local minimum, type in NA_Graph a:Graph b:Graph c:Graph d:
(-331 (0,31 (0,2) 4 (-2,01 (2,01 (-i.0i (,0) Enter the local minimum value for each graph: If there is not an local minimum, type in NA_ Graph a: Graph b: Graph c: Graph d:...
5 answers
A$.00 L tank at 1.42 "€ Is filled With I0.0 g of boron trifluoride gas and 9,67 g of chlorine pentafluoride gus You can assume both gases behave Iseal gases under these conditions. Celculare the molz froction pareia pressuce each gas_ and the total pressute the tonk: Be sure Your answers have the corect mumbar 08 slanlitcant digits ,mo @ Trcuon:poton tnwandrpartic| pTessutcmola Iractian;cuaxina pentaruoridceertinl E RessuinTctal preseuto LankD0
A$.00 L tank at 1.42 "€ Is filled With I0.0 g of boron trifluoride gas and 9,67 g of chlorine pentafluoride gus You can assume both gases behave Iseal gases under these conditions. Celculare the molz froction pareia pressuce each gas_ and the total pressute the tonk: Be sure Your answers ...
5 answers
Mz = Iookcq mze? Cconlo Fusc) Foc ce)0 -% & ((0.3020 o2STbedyLcllyiig A Va( m / = 24ks
mz = Iookcq mze? Cconlo Fusc) Foc ce) 0 -% & (( 0.302 0 o2ST bedy Lclly iig A Va( m / = 24ks...
1 answers
Identify the coordinates of any local and absolute extreme points and inflection points. Graph the function. \begin{equation} y=x \sqrt{8-x^{2}} \end{equation}
Identify the coordinates of any local and absolute extreme points and inflection points. Graph the function. \begin{equation} y=x \sqrt{8-x^{2}} \end{equation}...
1 answers
A woman walks due west on the deck of a ship at 3 $\mathrm{mi} / \mathrm{h}$ . The ship is moving north at a speed of 22 $\mathrm{mi} / \mathrm{h}$ . Find the speed and direction of the woman relative to the surface of the water.
A woman walks due west on the deck of a ship at 3 $\mathrm{mi} / \mathrm{h}$ . The ship is moving north at a speed of 22 $\mathrm{mi} / \mathrm{h}$ . Find the speed and direction of the woman relative to the surface of the water....
5 answers
A gaseous compound has a densityof 1.64 g/L at 24.8 °Cand 1.50 atm. What is the molar mass ofthe compound?
A gaseous compound has a density of 1.64 g/L at 24.8 °C and 1.50 atm. What is the molar mass of the compound?...
5 answers
The temperature ofa 337mL sample of gas increases from 219C.to 38PC What is the final volume of the sample of gas in mL; if the pressure and moles in the container is kept constant? This question requires math support;
The temperature ofa 337mL sample of gas increases from 219C.to 38PC What is the final volume of the sample of gas in mL; if the pressure and moles in the container is kept constant? This question requires math support;...
5 answers
A 900 kg elevator moves upward at a constant velocity for 8 m. How much work does the tension in the elevator cable do n the elevator?70560 Nm70560 Nm7200 NmUnable to answer without knowing the velocity: OoNm
A 900 kg elevator moves upward at a constant velocity for 8 m. How much work does the tension in the elevator cable do n the elevator? 70560 Nm 70560 Nm 7200 Nm Unable to answer without knowing the velocity: OoNm...
5 answers
Translate the following Vverba statement intc Use for your vanablealgebraic expression:Eleven less than the quotient of number cubed and eight:
Translate the following Vverba statement intc Use for your vanable algebraic expression: Eleven less than the quotient of number cubed and eight:...
5 answers
Gucstcn 26 No:yet anwered10.0 N ball is traveling at 2.0 m/s It strikes - 10.0 N ball; which is at rest The two balls stick together: Their common fina speed (iIn ns) is;Marked cu: 0fa.1,2 b, 1.33 0.,67Fr09 [ quesuon
Gucstcn 26 No:yet anwered 10.0 N ball is traveling at 2.0 m/s It strikes - 10.0 N ball; which is at rest The two balls stick together: Their common fina speed (iIn ns) is; Marked cu: 0f a.1,2 b, 1.33 0.,67 Fr09 [ quesuon...

-- 0.021031--