5

A particle is moving along the curve $y=x$ ln $x$. Find all values of $x$ at which the rate of change of $y$ with respect to time is three times that of $x .$ [Assu...

Question

A particle is moving along the curve $y=x$ ln $x$. Find all values of $x$ at which the rate of change of $y$ with respect to time is three times that of $x .$ [Assume that $d x / d t$ is never zero.]

A particle is moving along the curve $y=x$ ln $x$. Find all values of $x$ at which the rate of change of $y$ with respect to time is three times that of $x .$ [Assume that $d x / d t$ is never zero.]



Answers

A particle is moving along the curve $y=x$ ln $x$. Find all values of $x$ at which the rate of change of $y$ with respect to time is three times that of $x .$ [Assume that $d x / d t$ is never zero.]

The problem is find distance traveled about particle was position X y as t worries in given time Interval Empire Ways allowed of the curve Rex is you go to consign his squire. Why is he go to Basanti? He is between zero and full pie First a look at its a graph here When ki worries from zero to high the particle If this a particle won t zero why is you called to consign? Zero is once I wasn't particle is here won t worries from zero to pie Particle goes from his ond Yeah, this point and the one t worries from Pi to Opie Patco goes from thiss point back to this pond. Similarly, when he virus from full pie to a three pie What particle goes from here to here? And from three part two Well old high powerful goes for here back here So the lower half of the curve is just Auntie girl from zero to high Tough yaks Yeah Squire us You Why you squire here on things x the relation between acts and why is axe Iko too? Why square you can also use the formula into girl from once he goes from zero to pie. So why goes from wanted Nick to want? So it is the same ways integral from neck to want one yourself. One plus Why, Squire? Why? This is the same thing. Andi, it's Ah, peace tense. Traveled about particle. The distance, as we explained it is you go to four times into girl from there to pie. You're tough yaks. No. Where plus why he It's quiet. Yeah. Now look at it. This function uh, this's Iko too. Or times in. Throw from there. Oto pie. No turf to assign. We're signed. Square us. Sign He's square. This is the code off. Four times Motive at the integral from their toe pie. Tough. This is for sorry. This is for a sign He square swan times. Fine, Andi, If way that is you, it's equal to sign here. Francis is for into girl from making one one. You're tough all times Your square plus one. You Andi, it's integral. Is this one? It's not easy to calculate. Yeah, I just give you the final results. This is ICO too. Or times Well, half Alan thiss iss through you class. You're tough old times, you squire plus one. I have a sort of the wild, you know. Plus a half hammes to you hams. You're tough. Oh, you square block, Andi from negative one. And what? That's if we want to account Integral. Integrated. This definitely integral. You need to use a trick substitution. So let two years ago, too. And in the data. So it's not easy to calculate. Yeah, just give the user the results. And the compare with the love of the curve, the laugh of the curve. It is one force the distance traveled by a particle.

So for small time change within approximately the last years of Constant, So can have V. We can just approximately the be off to one equals Xia Host chooses for actually was too white horse once on three and for the small time Change, which is approximately velocity, is constant. So location is three point or so of his original location processor point zero One time, Sir Velocity, which is four three So which is two point zero four and one point zero three.

So you know that the acceleration and turn to and Cho Santee you know that it starts from rest, so and 00 we now go to your zero The position of time. Zero three. Yeah. So first rule I have to 18. That's the rule. Cosette. Teo signed Too close inconstancy. This is No. This was a colossal time to we know that the velocity A time cereal which happens to me cereal A sequel signs, you know, close. See, which was just see? So that tells us two It's just fine. Two. Now, your team, which is a position of time, Tio is the rule. Yeah, Team two, which is the integral sign? No, which is negative. Kosaka two close some constant of integration was calling d What? Another three is equal to zero physical too Negative co signed here. Clos de Dozens. No, this is negative. One plus two that tells us that Big Siegel for yeah, in the tunes you have to Yeah, lto plus four. Oh, that makes sense.

So we're given a particle's position and on the X axis is going to be X equal. Teoh three coast on TV, clothes for sine of t So packs is in my feet or that and t is in seconds Eso we want to find its position AT T hold a zero so TV at zero high over two and pie and we also want to find its velocity at the same times. So just make a little chart. It will be easier to have read. So let's look at the so this is really like except t. So my velocity is gonna be ex prime of TV which is gonna be so we take the route of a three co signer t will have negative three sign of t. We take the derivative Ah, for sine of t people have four empty my velocity. There is my position. So let's make our charts. We have tea x v So t is going to be zero for over two and part. Okay, so we'll start with position. So three co signers heroes 34 sign a 00 So it'll be three and then a pi over two eso coastline zero signs. One so before and then at high. So coastlines negative one sign zeroes. That's negative. Three. All right, so now for V. So it zero, uh, signs here of both sides once. That's for at high over to, uh, sign is one and co sign zero. So we get negative three and a pie. We have signed zero co signs native ones will have naked for.


Similar Solved Questions

5 answers
The Moon has radius of [.74*[0"m. It is orbiting the Earth at distance of 3.84*10*m, taking 27.3 days for complete revolution. The free-fall acceleration on Moon is [.62 m/s? . From the information given, find the mass of the Moon and the mass of Earth.
The Moon has radius of [.74*[0"m. It is orbiting the Earth at distance of 3.84*10*m, taking 27.3 days for complete revolution. The free-fall acceleration on Moon is [.62 m/s? . From the information given, find the mass of the Moon and the mass of Earth....
5 answers
An air-filled capacitor consists of two parallel plates; each with an area of 7.6 cm?, separated by distance of 50 Mm: (a) If a 22.0 potential difference is applied to these plates, calculate the electric field between 0.1466 the plates: kv/m (b) What Is the surface charge density? nc/m? What the capacitance? 4.48 (d) Find the charge on each plate 98.6
An air-filled capacitor consists of two parallel plates; each with an area of 7.6 cm?, separated by distance of 50 Mm: (a) If a 22.0 potential difference is applied to these plates, calculate the electric field between 0.1466 the plates: kv/m (b) What Is the surface charge density? nc/m? What the ca...
5 answers
Whcrca4and 02 Are functions defincd 57 T:c"[a,b] 7 Rdcfined by b T(f) = [ fu)dr:6. T:M,(R) + M,(R) defined byT(A) = AB BA,where B is # fixed n * n matrix
whcrca4and 02 Are functions defincd 57 T:c"[a,b] 7 Rdcfined by b T(f) = [ fu)dr: 6. T:M,(R) + M,(R) defined by T(A) = AB BA, where B is # fixed n * n matrix...
5 answers
Which of tha following is & propagation step in the chlorinatlon 0f eihanoHocchiHclHoccthaH"Oaa L 2Ci"H,C Ch, a 1o Mscos; HaHsCcn; Hscors;"CCCichl
Which of tha following is & propagation step in the chlorinatlon 0f eihano Hocchi Hcl Hocctha H" Oaa L 2Ci" H,C Ch, a 1o Mscos; Ha HsCcn; Hscors; "CCCichl...
5 answers
Skcet Melall he} tp crer 4 Coni esll m diamefer Ke} Hc Akal @n qes 6 m Surcfcu hnd On ~vnetton aluq A & #2 [email protected] hugkt h: fbx+) J6 f (w) 2372 20 +4; Jio& 444L ; Fvq b (e 20) ath (49) k (2) 13+564 $ () =1 2 VT 2746 2510 _ ( 6 Y = 22_4 g2-5 2-6} 8 ~21 eo skfha FvaHm Yz2 8 . fY - 7f # Kkl n +c nulha hezkh 024 dxon 3 fun4imn .
Skcet Melall he} tp crer 4 Coni esll m diamefer Ke} Hc Akal @n qes 6 m Surcfcu hnd On ~vnetton aluq A & #2 [email protected] hugkt h: fbx+) J6 f (w) 2372 20 +4; Jio& 444L ; Fvq b (e 20) ath (49) k (2) 13+564 $ () =1 2 VT 2746 2510 _ ( 6 Y = 22_4 g2-5 2-6} 8 ~21 eo skfha FvaHm Yz2 8 . fY - 7f # Kkl n +c nu...
5 answers
What is the half-reaction occurring in the copper half-cell?
What is the half-reaction occurring in the copper half-cell?...
1 answers
Respond with true or false to each of the following assertions. Be prepared to justify your answer. If $\lim _{n \rightarrow \infty}\left(a_{n}-a_{n+1}\right)=0,$ then $\lim _{n \rightarrow \infty} a_{n}$ exists and is finite.
Respond with true or false to each of the following assertions. Be prepared to justify your answer. If $\lim _{n \rightarrow \infty}\left(a_{n}-a_{n+1}\right)=0,$ then $\lim _{n \rightarrow \infty} a_{n}$ exists and is finite....
5 answers
A continuous random variable is defined with the following p.d.z f: +2) -3 < I < 3 f(r) = {56" otherwisea ) Find the value such that f f(r)d. = 1 Find the cumulative distribution function, F(c) Find the probability X lies between zero and 2 (d) Find the mean and standard deviation of X.
A continuous random variable is defined with the following p.d.z f: +2) -3 < I < 3 f(r) = {56" otherwise a ) Find the value such that f f(r)d. = 1 Find the cumulative distribution function, F(c) Find the probability X lies between zero and 2 (d) Find the mean and standard deviation of X....
5 answers
Ings Reviewt View Help941 Esaa# PurcrapnAaBbCcl AaBbCcl AaBbC AaBbCcL Aab AaBb AM INo Spac; Heading HeadingsulesConsider the reaction that occurs when 0.060 Grjms (NHa] POs (s) is added to 18.5 mL of 0.030 M (OHJz Calculate how much Ba_(PO4h will form and indicate how many moles of the excess neadantremains (Note that the phosphate compound has . different formula from the campound used in the lab-|n
ings Reviewt View Help 941 Esaa# Purcrapn AaBbCcl AaBbCcl AaBbC AaBbCcL Aab AaBb AM INo Spac; Heading Heading sules Consider the reaction that occurs when 0.060 Grjms (NHa] POs (s) is added to 18.5 mL of 0.030 M (OHJz Calculate how much Ba_(PO4h will form and indicate how many moles of the excess n...
4 answers
3. (2Opts) The lifetime in hours of a certain kind of radio tube is a random variable having probability density function given by 100 f(r) T > 100. I2(c) What is the prohability that at least 2 of 5 such tubes in radio set will have to be replaced within the first 150 hours?
3. (2Opts) The lifetime in hours of a certain kind of radio tube is a random variable having probability density function given by 100 f(r) T > 100. I2 (c) What is the prohability that at least 2 of 5 such tubes in radio set will have to be replaced within the first 150 hours?...
5 answers
QuestionWhat is the mass of sulfur in 3.0 moles of carbon disulfide?0 96.080 64.180 32.1 8Question 8What is the molar mass of barium hydroxide?171.3 g/mole154.3 g/mole137.3 g/mole308.6 g/mole192 8
Question What is the mass of sulfur in 3.0 moles of carbon disulfide? 0 96.08 0 64.18 0 32.1 8 Question 8 What is the molar mass of barium hydroxide? 171.3 g/mole 154.3 g/mole 137.3 g/mole 308.6 g/mole 192 8...
5 answers
[email protected] pttoaleo diteohirg 15 0 € ol CHaNHZ (MM = 31,05 0 morIIn 1.670 0l 0.432 CHANHJCI elto na colul on Wnnl [ Fenn tnaini pH 04 INva buhen (J ptai (p1 I 49 mL 0t 0550MhcI (MM - 30.44 9 mol-'| Ie ndded la Ihis trizturre, Whal Kll Ina Dod PHbo?67.529 mol ecubon (rrtlttvokunie changa upon EYd In
[email protected] pttoaleo diteohirg 15 0 € ol CHaNHZ (MM = 31,05 0 morIIn 1.670 0l 0.432 CHANHJCI elto na colul on Wnnl [ Fenn tnaini pH 04 INva buhen (J ptai (p1 I 49 mL 0t 0550MhcI (MM - 30.44 9 mol-'| Ie ndded la Ihis trizturre, Whal Kll Ina Dod PHbo? 67.529 mol ecubon (rrtltt vokunie changa upon...

-- 0.019997--