solve-the-problems-in-related-rates-a-variable-resistor-r-and-an-8-omega-resistor-in-parallel-have-2

Question

Solve the problems in related rates.
A variable resistor $R$ and an $8-\Omega$ resistor in parallel have a combined resistance $R_{T}$ given by $R_{T}=\frac{8 R}{8+R}$. If $R$ is changing at $0.30 \Omega /$ min, find the rate at which $R_{T}$ is changing when $R=6.0 \Omega$.

Amrita Bhasin · Accepted Answer

we&#x27;re gonna be using the formula for resistance differentiation, which is D over dt. Princes are one are two of our one times are too. So plugging in what we know, we&#x27;ve got 0.5 minus 1.1 times 1000 1000 minus 78 times 25 minus d&#x27;oh one squared, which gives a 0.0 81 oems per minute. Is the unit homes permanent?

Amrita Bhasin · Answer

Okay. Recall the fact that we have our run R two d r one over d, t and D are two over DT in this problem. Therefore, we know we can write out an equation. One over R is one of 11 over 80 plus one over r two. This simplifies to nine over 400 if we hop eight common denominators simplified which gives us our is 400 over nine because of one over ours. Not over 400 men are over. One of just our is 400 over nine. Therefore, we know we can multiply 400 over nine squared comes one over 80 squared times 0.3 plus one over 100 squared times 0.2 and then we know we can simplify to get 0.132 on the November. This is in terms of the units for resistance

Caelan Thomas · Answer

So if we take the derivative of one over R equals one over R one plus one over r two, we get negative one over r squared 10 TRD t equals negative one over r one squared times tr one t minus one over r two squared Tim&#x27;s Tr two t and now we want to plug in are known values. But first we need to figure out what the value of our is. So we&#x27;ll plug in are known values for R one and R two, and we get that one over. R is equal to 1/80 plus one over 100 and that&#x27;s going to give us one over. R is equal to 100 plus 80 divided by 100 times 80 and so we get one over R is equal to 180 over 8000. For that, R is equal to 8000 over 180 which simplifies to 400 overnight. And now, if we plug in the values of our along with r one R. Q. Dont t In the r. Two d t, we get negative one over 400 over nine squared times. TRT t equals negative one over a squared times 0.3 minus one over 100 squared times with a 0.2. And that gives us DRG t equals negative. 400 squared over nine squared times negative 0.3 over 80 squared minus 0.2 over 100 square. And if we put this into a calculator, we get 10. Tr Tichy is equal to a doubt 0.132 homes per second.

Alvar Garcia-Fernandez · Answer

we&#x27;re in where I&#x27;m problem to 56 of cockles. 3 to 4. Second five. And we have the resistance in a circuit as three individual resistance is for center X, Y and Z is given by or r of X Y z is X y z over. Uh, why ex? This is why ex things from white Z Z plus it makes what Supposedly at a given time X is 100 homes. Why is 200 homes and these three, huh? Also, uh, the was that the resistance ex isn&#x27;t is changing that rate of the ex CTU. Our ex prime is too old for a minute. And why prime is one homes for a minute? Why resist changing rate of one home formidable? That Why prime with your tea, it&#x27;s time through this really change changing resistance, respected time. And then the ziti is not changing the secret of zero. So we&#x27;re given these conditions. Okay. All right. So find the rate of change is a total resistance in this circuit with total resistance are so I want the Arditti is the first partial off our with the spec tax because our function of X Y and z times the derivative of X suspects Memorex print, which we know is so this special plus first partial of our respects You Why time swept? What&#x27;s the Chris partial of our suspect? Z clumsy. All right, so it&#x27;s playing this first part here. Let&#x27;s calculate this much because the special laws for Texas will be a doozy. All right, go. So what is the Chris partial of our respective ex lips? Times Express First partial R is we could do, uh, coastal so low. But this is a why this is an X Y Z racer. We should say X y zebra. That&#x27;s a year&#x27;s X y you see? Okay, uh, so, plus x y all right. So low D high and with different in depressions. But the exit through the top Respected Texas. Just crazy, my ass. Uh, well, behind this high the loan that we&#x27;re doing, the derivative, the bottom there&#x27;s a partial respect axe. So that&#x27;s just gonna be experts. Weigh as equals all over Lo square all over times, expert. Okay, great. Now, if you plug in all these lumbers All right. So I worked this out already. I got, um Why Time Z is 60,000 and x times these 30,000 and extends Why is 20,000 and white Ramsey&#x27;s again 60,000? When a Sexton&#x27;s white can see is 6,000,000 times X plus y, it&#x27;s 500 over. Uh, this quite the same quantity squared. I worked it out. Times two is 72 over 121 homes for a minute. But that&#x27;s only this first component for special moments with X times X prime. I just did the next compartment. Just do it. Nothing. I meant to get any pitch. Okay, let&#x27;s get in the cage. All right, So what I want to do now is figure out if a special our inspector White white pride. So the first pressure of our inspector, Why? Seriously, why did see or my prime his what we do the same thing when I was differentiating with prospective wife. So it&#x27;s gonna be low Course you may low, which was y z plus X Z plus x y and D Hi would be the true. That&#x27;s half, Inspector. Why was egg zeke was his X y Z minus the top, which is X y Z. Is it true about him during the bottom, Inspector. Why, it&#x27;s gonna be Zico. Sex? Yeah, all over Love Square since quantity y z plus xy plus that&#x27;s why square time&#x27;s wiped right. Okay, so again, we worked this out. And why z waas close it down under 10,000 x z? No, sir. This whole thing adds up 110,000 x times e was 30,000. Extends reckons he was 6,000,000 experts. Izzy is 400. Why? Prime is one and this is 110,000 square to work all this out you get nine over 100 homes for a minute. All right, so the first part first marshal, our respect to X times our ex prime was 72 1 21 The second part was nine. Everyone, everyone, let&#x27;s forget this. Last, uh, the first special of respect Z as you pray here, the first partial of our respective z times to ziti tears your crime Well, that&#x27;s going to zero. Cozy prime with zeroes won&#x27;t have to worry about. So what do we got? We guess nine over 1 2170 to 72 plus nine over 1 21 is swell. 81 120 firsts books almost for a minute or this incident. Time resistant trains. That resistance changes 181 homes every 121 months. Okay. All right, so that&#x27;s stupid to six. Uh, four second five. Enjoy. Thanks. Watching himself which homer By buying rate.

Doruk Isik · Answer

in this problem. We&#x27;re circuit and were given that the will to that second circuit is 12 wolf. Any party ever has to find their Israel change. Insurance is expected, uh, resistance. So does a order. One resistance changes brain a 0.1 to 8 or 88. Um, so, firmness, we know that changing current using the also the slow or rape or inform my spoke. 08 So during final minus burn. So And we find this to be Nathan 01 you&#x27;re 18 but And for me given Interval, we know that our teams from a 0.1 changing businesses point fun that people ovals In this in question, we find the average rate of change of current suspect thio business be negatives 0.0 when a fine right back for months. Or this is native ones on 9 to 5. The first bird Oh, the part. You were asked to find the change of terms respectfully uses those 80 um so we carry function for current S V over r there. Forget Liza Pilsen. So then my problem where there talk during the late to be o r sprint Now all we need to do this, but numbers in you find the I they are to be there. 12 you wanted but a spray. And this is nature. One negative. 0.187 If I ever. For every proxy, where has to find the right of changing resistance of spectra current members So the are over the eye eyes walking by again We&#x27;re gonna have all the same procedure our zebra Rubio, hon Don&#x27;t forget the end that he&#x27;s accustomed. So are most people are going to be late to be spreading that. Let&#x27;s just, uh, get numbers in well, this week on the orderly to be next 12 squared and that is ICO to about negative 51 33 home for four.

Problem

Solve the problems in related rates. The radius $…

Problem 14 Easy Difficulty

Solve the problems in related rates.
A variable resistor $R$ and an $8-\Omega$ resistor in parallel have a combined resistance $R_{T}$ given by $R_{T}=\frac{8 R}{8+R}$. If $R$ is changing at $0.30 \Omega /$ min, find the rate at which $R_{T}$ is changing when $R=6.0 \Omega$.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Samuel H.

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus