5

Use partial fractiong to find the indefinite integ{Rememberuse Joso lute valuesPproprate Use tor the Congtantor integration;...

Question

Use partial fractiong to find the indefinite integ{Rememberuse Joso lute valuesPproprate Use tor the Congtantor integration;

Use partial fractiong to find the indefinite integ {Remember use Joso lute values Pproprate Use tor the Congtantor integration;



Answers

Use partial fractions to find the indefinite integral. $$ \int \frac{3}{x^{2}+x-2} d x $$

Mhm. So whenever you want to perform a partial fraction decomposition, you got to watch the top and the bottom of the rational function. So, what is the highest power of the top? The highest part of X at the top. Right? That is three. And in the highest power of X at the bottom is to So that is an example of an improper fraction, right? Whenever the highest power of the top is equal to or exceeds the highest power of the X. At the bottom, that is an improper fraction right? For us to have a proper fraction, the highest power of the X at the denominator should be greater strictly greater than the highest power of X at the numerator. Anything other than that, that is an improper fraction. Whenever you have an improper fraction, you want to do a mixed, you know, you want to find a mixed form. Okay, So uh what we're gonna do is take the proper um the denominator right here and divided, take the numerator and divided by the denominator. Right? So we're just gonna do something like this. Now whenever this device that what you have, you have an X. Right at the top, right? This divided by X squared is going to be X. Now I'm going to multiply the entire expression here by this X. Whenever I do that, what is happening I have X cube plus X squared minus two X. Now I'm going to take this and subtracted from the top. What do I have? Well they're subtracted by that is zero. There's nothing here. I mean you can you can in your mind's eye you can view here as zero X squared minus zero X. Right there. Just zero. It's a bunch of zero. So whatever you subtract X. Where from zero X. Where you have negative X. Where and then whatever you do this you have a positive two X. Right? Because these are just zero. So you're just trying to negate these terms. I put it had a negative. So now This divided by that is going to be the -1, right? You're dividing This guy by, this guy says -1. Now I'm going to multiply everything here again by -1. When I do that, what is happening, I have negative X squared minus X plus two. Okay? So when I do this then I'm going to subtract again. So this goes away. Uh then I have you know You have two x minus X. So what is happening? That is gonna be three X. And then you have negative two because there's a zero here plus zero. So zero minus two is negative two. Right? So that is uh what we have after the subtraction. So now we can't do any division again because this one's power is this one's power? The excess power is one and this one is to right? So I don't wanna do anything else. So this is gonna be my remainder term, this is my remainer. Okay? And this is my quotient, Okay? And this is my divisor. So what I'm gonna have in mixed fraction form is going to be the quotient plus the remainder over the divisor, which is a denominator, right? That is X squared Plus X -2. This is what I have after performing this operation. Now, what I want to do is, you know, integrate both sides. No, so I have a proper fraction, right? This is a mixed fraction. This is like the quotient and this is not a proper fraction. So, partial fractions can only work on proper fraction. So I'm gonna work on this one uh decompose it into a partial fraction for Okay and I'm going to do that just to decide right? I'm just considering this one. Okay, just leave this one out for now. Which is considering that's what so this is gonna be now the denominator. Uh It's fact trouble. Right? You can factor it. So whenever you do, what do you have? Well you have, The numerator is going to stay the same and the denominator is X -1 -1 uh expose to. Okay, so whenever you have this one you can attempt to perform a partial fraction of this one. This is a proper fraction now, so I'm going to call it uh a over X -1. Right? Like we've been doing throughout and then be over X plus two. Okay, now what is the L. C. D. This is the L. C. D. Of these two terms. So whenever I multiply by the LCD so I multiplied by the L. C. D. This and divide by the same thing. Right? I create and I destroy. So this is going to cancel and then you have one. Okay whenever I do this then I'm going to have AX plus two Plus B. X -1. Then over this denominator which is gonna be X minus one explains tube. Okay so this is equal to this. Okay. And since they're equal and the denominators has seen as this denominator then I'm going to set the enumerators equal to each other. Right? If you have A. Or B equals C. Over B. Since the bees are the same then A can be set equal to see they're the same. A. N. C. Or the same. Because here would be equal to see it would be and this is being this will be the denominators are the same. So you can say that enumerators are also the same right? It's just a principal in math. So since this is equal to that and they have been the same denominator here then I can say that enumerators are the same. So I'm just gonna set the numerator equal to equal to each other. Right? So that's what I have. Now I want to do some illumination. I'm gonna let put Eggs to be positive one When I do that. And this is going to be 3 -2 which is one. This is gonna go to zero because 1 -1 is zero. Yeah this is gonna be three B. 3 8 Mega part. So 38 So you can see that A divided dividing both sides by three. You can see that A. Is going to be one third. So that is what you're gonna have After you do your You put x equal one. Now I want to eliminate those one. So I'm just gonna put X equal negative too. When I do that this one is automatically eliminated. So what I have left is put a negative two. Here is gonna be negative six minus two is negative eight. Put a -2. Here is gonna be -3. B. So when I write divide both sides by negative three, you can see that B. Is going to be 8/3. Okay. Yeah, so that is the uh A. And B. So I'm just gonna replace and be right here. Okay. So the A. Is one third 1/3 and replacing I'm replacing this A. And this be So it's gonna be 1/3. Uh huh. X minus one. And then the B. Is eight thirds. So eight thirds exports to. So this is what I have after I do the perform the partial fractions. Okay, So I performed the partial fraction on this uh proper fraction right here and I get this. Okay. And do not forget there's this guy here, so I'm just gonna put it here. So plus X -1. So this is the entire expression here, right? That is the same as this expression. Yeah. So now I want to take the integral because you're supposed to perform partial fraction and take the integral. So I take I take the integral here and I'm going to do it on a term by term basis. Right? What is the integral of this first term? That is going to be a third? No, I'm gonna be pressed for space. Let me do it here. And I was going to be a third. Natural Log, -1. Okay. And what is going to be at the integral for this one? It's gonna be plus eight over. Okay. Do you mean natural X plus two? What is the integral of this 1? That is plus X squared over two. And what is the integral of negative one? Well, that is just negative X then plus the arbitrary constant C. Okay, so the answer of there is the solution to the problem is one third. Natural log x minus one plus 8/3. Natural log x plus two plus X squared over two minus x. Policy. Right? So what I did at the beginning was that the function was an improper fraction. So I had to convert it into mixed fraction by dividing the numerator by the denominator. But I did that I had a mixed fraction, a combination of some number or some expression and a proper fraction. So this is a proper fraction. An impartial uh, partial fraction decomposition can happen on a proper fraction. So I performed the partial fraction decomposition on this proper fraction, and then this came out. This came out right, this one came out and then I just added this expression to it, which is this guy. And then I performed the integral right, performed the integration, and then that's it. So this is the final issue.

So we have a rational function. Uh And we want to take the integral of that. But we can do a partial fractions too. You can use that one to split the uh the rational function then perform the integral. So uh you know, yeah, that function can be written as two over X. All right. I just factor an X. So I'm just gonna have X. Plus three. Okay. Okay. And this is just gonna be the same thing as what we did in a previous one. Right? I can just make this one a over eggs and plus uh be over expo three. And so if you watch the last tutorial, I explained how we can do this one. Right? So this is just gonna be too eight times that then plus be times E. X. Right? So this is what we get right. If you don't understand this one, watch the last tournament before this one, you're gonna understand explain that. And now we want to get rid of some variables. We're gonna put X to the zero whatever report except zero. This one goes to zero and so you have just two equals three. A right guess this one is zero and this one is three and three times A is three. A. And therefore I divide both sides by three. And I can see that A is going to be to over three. No, I would have put X equals negative three. Right? You want to get rid of this? A. So this is just gonna be through to of course, now this is zero. This is gonna be negative three. Be so negative three B. And when we divide both sides by negative three, then we have B two B negative to over three. So the partial fraction decomposition right here is going to change you. I'm going to write it in a different color. This is going to be to over three over X. Rite Aid is to over three and to be is negative through negative. Yeah, nearly 2/3. So negative 2/3 over X. So I'm just gonna drop the denominators right to the bottom. So this is just gonna be to over three eggs then minus 2/3. I think this is going to be explored three. So expose three. Right? The denominator for B is exposed three. So then this one is just three X plus three like that. So I just dropped the denominators of this, one's right to the bottom right here and that is allowed. Right, okay. So this is now the so this one has been slated into partial fractions like this one. Right? So now I want to take the integral, so take the integral and then you take the integral. Right? So you're taking the integral of this uh quantities right here. So what is that going to be? And I'm gonna whack this one clean to have some space. So now we continue with the integral. So this is just gonna be the what is the integral of this one? Well, I can just bring out the constant and I have one for X then minus. I bring out the concert again. Then I have one over expose three. Right? I can just I just distributed the integral to these two terms. That's what I have here. And then I just brought out the constants because I don't want them inside the integral. So what is gonna happen then this one here is gonna be to over three natural log of face and this is also negative to over three natural log of expose three. Right? So that is the plus the arbitrary caused it. Alright, arbitrary. Custom C. So this right Here is the solution to the uh, you know, integration right? You have uh see cross two or three natural log of x minus two of the three natural log of expose three. Right? Yeah.

Okay, so this this one is a little different from the previous ones who have been doing right? This is what we call a mixed fraction, right? How is it? A mixed fraction. Look at what is the highest power of the denominator? The highest power denominator is too the highest power of X. Are the denominators to and the highest power of X. The the numerator is also too. So you can see that both the highest power of the denominator and the highest part of the numerator are the same. That is a mixed fraction in order to be a proper fraction. Whenever you perform an irrational a partial fraction. In order for you to have a proper fraction. The highest power of X. At the denominator must be strictly created in the highest power of the numerator. Whenever the highest power of the denominator is the same or less than the highest power of the numerator, you have an improper fraction. Okay, so this one is an example of an improper fraction improper fraction. So supposed to uh you know, transform this improper fraction into a mixed fraction before we can do anything. Okay, A mixed fraction is a combination of a whole number and a proper fraction. The partial fractions are always going to be performed on proper fractions. So whenever you have an improper fraction converted to a mixed fraction first and then work on the proper fractions separately. Okay, So how do I do a mixed fraction? I'm going to perform a long division. So this is going to be X squared minus X square plus x minus six K. I'm going to divide the numerator provided denominator. That's what I'm doing. So this is two X squared minus x uh minus 20. Okay, so this divided by dad. What is happening? Well, when you divide that, you're gonna have to then we multiply to buy whatever is here, this is gonna be two X square. This multiplied by that is plus two X. This multiplied by that is negative 12. Right? I just divided this one with this and I had this too and I multiply this to buy the entire things here. That's what I did. Now I'm gonna subtract. Right? So to minus two X squared minus to extradite zero. Now negative X minus two X. That is negative three X. Negative 20 minus negative 12. That is positive 32. Right? This is negative 20 and this is minus and this is negative to us uh minus negative 12. That is positive 32. Okay so that is what is happening. So that's what I have now. This one cannot divide this one again because uh this one this one's power is one and this one's powers too. So you can you can divide So now I've converted this one into a mixed fraction than a proper fraction over x. Were plus x minus six. Okay. Uh huh. This one devised this one and that is this one. And then this to here is the remainder after the division. Right? So the rational function in the intervals under the integral signed in to grant cannot be written as this form. Right? So this is a mixed fraction. It is a combination of a and whole number, a whole number and then a proper fraction. This is a proper fraction because uh you know, the highest power at the denominator is two and the highest power of X. Numerator is one. So that is strictly the highest part of the denominator is strictly greater than the highest power of the numerator. So that is a proper fraction. So it was a proper fraction, that we cannot perform a partial fraction on that. Okay, so let's forget about this to here for a sec and let's perform a part partial fraction here. So this thing right here can be written as actually let me just let me just make it negative three X plus. In fact you can put it in a different color today, it makes a little more sense. So negative and performing a partial fraction decomposition on the a proper fraction that was left right. The remainder. Actually, this is a question actually and this is the remainder. Right. Do you mean your turn so quotient remainder divisor? Okay, these are the technical names. Okay, so this one can be written as you know. Oh yes, Now I want to factor this denominator, so what is that? Well that is x minus, do you? Yeah, and then X plus three. Okay, so now I'm gonna yeah take it write it as a over X minus two. You then plus B. Over X. Plus three. Okay that's what I have. So now I'm going to perform the uh Mhm. I'm going to multiply this quantity by the L. C. D. Divided by itself. Right? So this by the LCD time over the LCD whatever you do that this is just gonna be a over X. Plus three. Close be over X minus two. Right? Just multiply this one by this over itself. This over itself. And for it you're going to have you're gonna have this one had enumerated right? And then the denominator is just gonna be this one. But since the denominators are the same I'm just gonna I just forgot about it. Nominators and I said the numerator equal to each other. Okay. Okay so now I'm gonna uh eliminate some things hurt eggs to be to for example. And this one is eliminated. So what I'm gonna write put extra fee to hear and this is gonna be negative six negative six plus 32 is positive 26. When I put two here this one is eliminated when I put two here, this is five. Right? So this is five A. Okay. So uh uh I think I made a little mistake here negative 20 minus negative 12 is negative 20 plus 12. And that is negative eight. So I'm just gonna make the correction before it affects my final answer. So this is not supposed to be 32 supposed to be negative eight. So this one right here is now I'm gonna beat negative eight. Okay? And then that is uh that is going to affect uh this thing right user now if you want to consider this one then it's going to be negative three. Force 93 plus eight. So this is about eight. How is it? Plus eight? Well this mine is here, it's affecting these two. So what you're doing is you're foiling, it's going to recoil. Uh This this negative becomes positive because he multiplying by negative. Okay, that is why it becomes a plus eight. So this is a plus eight right here. So this one is also going to be plus eight. So here you're gonna have a plus eight. Okay. Okay. So no, I was put in eggs to be two. So two times negative three is negative six then plus eight is positive two. Okay, let me do something here. Uh because I have a feeling that this is gonna be a problem. You know this negative three ace minus eight. That is correct. Okay, how about I factor out a negative and this becomes three X plus eight like this. Okay so when I do that then this one is going to be three X was eight and then this negative is just going to be here. This is correct. I'm just putting it in this form and that is what I have. So now because I don't want to deal with the negatives, it has the potential to ruin everything to make things uh you know go or why to go wrong? Okay so now we're considering justice fraction this negative is going to be there. We're just gonna do with do with that later. Okay so now I'm gonna take away this negative because we're just dealing with this fraction the negative has been put here aside so that it does not interfere with our operation. Okay? So then here is positive, here is positive good. So now we're good to go right, it is always advisable to avoid negatives. So you can just put them here, you have negative negative. So you factor it out when you factor it out, you have negative out then you have three plus positive eight. So those three plus positive eight over that is what we're dealing with. The negative is out here. I don't want to interfere because it can give me trouble. Okay? So I have this one. So now I think everything is perfect. So whenever you put eggs to be too, then this becomes 14, right becomes 14 to this right? Here is 14 and this is five, right? Two plus three is five. So you can see that A is going to be 14/5. Now, what about the well, put X to the negative three when I do that. What is happening when I put thanks to the negative three right here, this is gonna be negative nine negative nine plus eight is positive. Would And I put in 83 here, this one is eliminated for the negative three. Here that is negative five. It's a negative five B. Okay. And this one is negative one because negative three times three is negative nine plus eight is negative one. I'm gonna write it by both sides by negative five. You can see that be right here is 1 45. Okay, so is 14/5 Bs 1/5. So now I can do the replacements. Okay, so this guy right here cannot be written ass. I'm going to write it down below this is two minus two minus what minus three X plus eight. Let me put it in parentheses three X plus eight. I don't have to but I'm just for simplicity and clarity over X squared plus X months six that can be written as two minus what is happening to minus. You know, this is a right and the A is 14/5 to minus. Let me bring a parenthesis 14 over five times X x minus two. And then plus he's one of the five. So 1/5 exports three. Okay, this is how you know, troublesome the negative is you have to be careful now this negative is affecting everything. Okay, so you're just gonna foil. Okay, so the rash partial fraction decomposition is this guy right here that you're saying Now I want to really take the integral of both sides, which is supposed to be what we're doing right? What is the integral of to respect to X? That's just two X. Now, what is the integral of negative? 14 or five times X minus two. Right, do not forget this negative. Well, I can bring out the negative 14/5. Now, what is the integral of X minus one? Over x minus two? That is the natural log of x minus. Do you? Now? This negative is affecting this one as well. So I can just bring out the negative 1/5. What is the integral of one over X plus three? That is natural log X plus three then? Plus the arbitrary constants. C mm. So yeah, this is the find a solution to the problem. The rational function was an improper fraction. So we converted it to the mixed formed by dividing the two, you know, expressions, then we got this mixed form and then the mixed form is a whole number and a proper fraction. And then we performed the partial fraction decomposition on the proper fraction. So that is the proper fraction. And this is the partial fraction decomposition that we did. And then we had this idea and after the partial fraction under proper fraction, and then we performed the integral on the, you know, the partial fraction. And so this too, is that the integral to respect to access to X. And then the integral. I just foiled right. Just distribute this negative to these two terms. And they performed the integral whenever you do that you have in this one. Okay, so this is the solution to the problem.

This problem. If we look at the denominator, we have X cubed plus two x squared plus x right. This could be vacuuming to x Times expert plus two X plus one, which equals backs times X plus one squared. Right. So in this case, since we have Oh, are you all the factors of this, uh, political meal by the factor form this polynomial we can actually make our partial fracture. Andy conversation be a over X plus be over excess wood plus c over. Express one squared. Right. This all equals this. You here, right? I'm Howard. For us to be a last service, we need to set a common denominator and do that remote by a by X plus one square. Um, believe by X times X plus one and see by ex. Right, So this gives us for a excreted plus two x plus a plus B x squared plus bx plus e x trait. Once we have this of this, all this equals of new married or are original integral, right. Um, And since we are given those, we can make the systems of equation right by sitting all the ex squares all used to each other, for example, on this case would be a plus. B equals splint, Right? Because they have the X script likes I can't sell off. Um, two way plus b plus C because negative six and a equals to worry, because we know that it was two. That means that b equals negative one. Um, meaning that C equals no live nine. Right? So once we have all these values right here, we can deposit them back into a partial fractions. Right. So this would make from two over X minus one over X plus one minus nine over X plus one quantity squared, right. Um, and all these or to be integrated The 1st 2 could be simply integrated as two times Ellen of Ellen X minus Ellen of X plus one. However, this loss integral here is a little different because we can make this into the form negative nine times the integral of explosive. Want the night to x two. Then I go to the X. This is a little awkward to integrate. That we're going to use up here would have exploits one goes you. Therefore do you equals DX, right? Once we get that we can get off this center call comes used the NATO to do you write and interview this It comes negative one over you. However, plug it back in. Are you when you're at this as a negative one over X plus one. Right. So once we have this, we have to begin most by the negative nine back by and get this equals nine over explosive one. So, once we have all these value, this value, we complete this back in two. Original party, uh, integrated triplet right there to get the final answer off to own of X minus Ellen of that's plus one plus nine over X close one. Proceed.


Similar Solved Questions

5 answers
NameLet A= [436 ] List all elgenvalues and for each eigenvalue find corresponding eigenvector:[Apts] Then write diagonalization factoring for = (i.e write matrices and such that 4 = PDP- IExg points for finding inverse of P]
Name Let A= [436 ] List all elgenvalues and for each eigenvalue find corresponding eigenvector: [Apts] Then write diagonalization factoring for = (i.e write matrices and such that 4 = PDP- IExg points for finding inverse of P]...
5 answers
Which teaction sequence is preferred for this conversion? 0 HO CH;CHZCOH CH;CH-CHz'(A)CH;MeBrHOSOChHO(B) Oz,followed bx DMS(E) None(C)BH3. THF
Which teaction sequence is preferred for this conversion? 0 HO CH;CHZCOH CH;CH-CHz' (A) CH;MeBr HO SOCh HO (B) Oz,followed bx DMS (E) None (C) BH3. THF...
5 answers
AnindustricLengineeris_ checking _ q shipment et12o_computersby choosing_asampleof fourcomputers_Assumethat 9 of thecomputers do_not conform to customer requirements Howmany_different samples are possiblezIt ofAnswer;
AnindustricLengineeris_ checking _ q shipment et12o_computersby choosing_asampleof fourcomputers_Assumethat 9 of thecomputers do_not conform to customer requirements Howmany_different samples are possiblez It of Answer;...
5 answers
Cyclopropane moves with speed of 2 m/s through tube of diameter cm and enters tube with diameter of 0.02 cm. The speed as it enters the second tubenone of the choices_b. 50 mls.2 mlsd. 100 mls_
Cyclopropane moves with speed of 2 m/s through tube of diameter cm and enters tube with diameter of 0.02 cm. The speed as it enters the second tube none of the choices_ b. 50 mls. 2 mls d. 100 mls_...
5 answers
Using the data in the table calculate the rate constant of this reaction.Trial [A] (M) 0.400(M) 0.360Rate (Mls)0.02130.4000.972 0.3600.155A+B=C+D0.6000.0320UnitsM-15-1M-sM-28-1
Using the data in the table calculate the rate constant of this reaction. Trial [A] (M) 0.400 (M) 0.360 Rate (Mls) 0.0213 0.400 0.972 0.360 0.155 A+B=C+D 0.600 0.0320 Units M-15-1 M-s M-28-1...
5 answers
R = 3 Ohu experieuces magnetic force of 0.50 N 7: ^ wie of leugth L = L0 m and resistance Find the magnitude of the magnetic field due to uniforn magnetic feld perpendicular to it: if the potential difference across the wire is 30 V.
R = 3 Ohu experieuces magnetic force of 0.50 N 7: ^ wie of leugth L = L0 m and resistance Find the magnitude of the magnetic field due to uniforn magnetic feld perpendicular to it: if the potential difference across the wire is 30 V....
5 answers
89 &nd standard devlation 0 = 5. Find tho indicated probability Assume the random variable x Is normally distribuled with mean | P(72 <* 85)P(72 <x < 85) = (Round to four decimal places a5 needed )
89 &nd standard devlation 0 = 5. Find tho indicated probability Assume the random variable x Is normally distribuled with mean | P(72 <* 85) P(72 <x < 85) = (Round to four decimal places a5 needed )...
5 answers
Tbe Lewis rcprescatation abote dpicts Texctlon betuecn bydrezrn (blcc) and : mzin-group clcment from grou M(red)In thts rcprcscntaton ech atom needsclecbonls) - complete its ccTet and gains these clectons by; foringbond(s) with atoms ofHTbete &eunshated ckexuon pau($) =bonding ckccuon pauts)product mokeculeThe bonds in tbe product uc
Tbe Lewis rcprescatation abote dpicts Texctlon betuecn bydrezrn (blcc) and : mzin-group clcment from grou M(red) In thts rcprcscntaton ech atom needs clecbonls) - complete its ccTet and gains these clectons by; foring bond(s) with atoms ofH Tbete &e unshated ckexuon pau($) = bonding ckccuon paut...
5 answers
The normal to the curve, $x^{2}+2 x y-3 y^{2}=0$, at $(1,1):$ $[2015 mid$(A) meets the curve again in the second quadrant.(B) meets the curve again in the third quadrant.(C) meets the curve again in the fourth quadrant.(D) does not meet the curve again.
The normal to the curve, $x^{2}+2 x y-3 y^{2}=0$, at $(1,1):$ $[2015 mid$ (A) meets the curve again in the second quadrant. (B) meets the curve again in the third quadrant. (C) meets the curve again in the fourth quadrant. (D) does not meet the curve again....
4 answers
Section 1Use the following data to determine the molar heat of vaporization of rholineT(PC)94.5-67.2~47.3P (mmHg) 33.6369.11469Answer= kJ/mol Your answer should have three significant figures.
Section 1 Use the following data to determine the molar heat of vaporization of rholine T(PC) 94.5 -67.2 ~47.3 P (mmHg) 33.6 369.1 1469 Answer= kJ/mol Your answer should have three significant figures....
1 answers
Find the Fourier series of the following function on the given interval: 0,-T < x < 0 f(x) = {sinx ,0 < x < T" Also show that "i+13 5
Find the Fourier series of the following function on the given interval: 0,-T < x < 0 f(x) = {sinx ,0 < x < T" Also show that "i+13 5...
5 answers
Find the maximum and/or minimum value(s) of the objective function on the feasible set $S$.$$Z=2 x+3 y$$
Find the maximum and/or minimum value(s) of the objective function on the feasible set $S$. $$ Z=2 x+3 y $$...
5 answers
Calculate the equilibrium pressure of COFzlg):2 COFzlg) cOzlg) CFalg). At equilibrium; [CFa] = 0.32 atm; [COz] = 0.44 atm, and Kp = 7.88 x 10-413.37 atm0,0105 atm178,7 atm1.11 X10 4
Calculate the equilibrium pressure of COFzlg): 2 COFzlg) cOzlg) CFalg). At equilibrium; [CFa] = 0.32 atm; [COz] = 0.44 atm, and Kp = 7.88 x 10-4 13.37 atm 0,0105 atm 178,7 atm 1.11 X10 4...
1 answers
For a pulsar that rotates 30 times per second, at what radius in the pulsar's equatorial plane would a co-rotating satellite (rotating about the pulsar 30 times per second) have to be positioned to be moving at the speed of light? Compare this to the pulsar radius of $1 \mathrm{km}.$
For a pulsar that rotates 30 times per second, at what radius in the pulsar's equatorial plane would a co-rotating satellite (rotating about the pulsar 30 times per second) have to be positioned to be moving at the speed of light? Compare this to the pulsar radius of $1 \mathrm{km}.$...
5 answers
(a) With a neat sketch; explain the working of Floating gas holder type biogas plant: List any two disadvantages of this type of biogas plant: [1+3+1=5M] (b) Differentiate between bioethanol and biodiesel: (Any two points) [2M]
(a) With a neat sketch; explain the working of Floating gas holder type biogas plant: List any two disadvantages of this type of biogas plant: [1+3+1=5M] (b) Differentiate between bioethanol and biodiesel: (Any two points) [2M]...
5 answers
2. If the random variable X is distributed through the Normal distribution with mean-80 and variance-800, using a random sample of size n=50, the standard deviation of the sample mean= (3 Points)16410080
2. If the random variable X is distributed through the Normal distribution with mean-80 and variance-800, using a random sample of size n=50, the standard deviation of the sample mean= (3 Points) 16 4 100 80...
5 answers
Question 6What will be the main product of the following sequence of reactions?1) BH] 2) HzOz a4 NaOHHO_Ho_Question 7
Question 6 What will be the main product of the following sequence of reactions? 1) BH] 2) HzOz a4 NaOH HO_ Ho_ Question 7...
5 answers
Question 2In the (gure shown belaw select thie dlmens onal tolerance by clicking on it using the mouse: 500 t .005 004Suseated Cooralnatoa
Question 2 In the (gure shown belaw select thie dlmens onal tolerance by clicking on it using the mouse: 500 t .005 004 Suseated Cooralnatoa...

-- 0.068152--