solve-the-given-problems-the-reliability-r0-leq-r-leq-1-of-a-certain-computer-system-is-given-by-re-

Question

Solve the given problems.
The reliability $R(0 \leq R \leq 1)$ of a certain computer system is given by $R=e^{-0.0002 t},$ where $t$ is the time of operation (in h). Find $d R / d t$ for $t=1000 \mathrm{h}$.

Edward Downes · Accepted Answer

Okay, this girl question has some application led to it, but essentially were given an equation which is R equals either the negative zero point three zeros to T. And we&#x27;re asked to find the odd ET when T equals 1000. So take the derivative and substitute in 1000. Is basically are two jobs here. Quite a simple problem. Once we strip the application layer off of this, so taking the derivative of this function, we get the core fishing with T down in front and then we&#x27;re gonna substitute this value that were given in and I can eat at the negative 0.2 times 1000. Okay, we can go to our calculator here for this to get an estimate. If we want, make sure we get enough zeros in there and then either the parent negative three zeros times amazon. And here is our it&#x27;s a negative 1.64 times 10 to the minus four. Or you could say this is three zeros 164 And then the units here are put out. Pretty simple problem. Once we get the application layer out of the way

Gregory Higby · Answer

Okay, So the way I would do this problem and you might notice that you at this 0.1 I was in teas. Yeah, T cubed, um, dot, dot dot And they&#x27;re saying we&#x27;re equal zero s. Oh, What I would think about doing is multiplying both sides by 100. And the reason why I&#x27;m choosing 100 is because one hundreds times 100 will give you one. And think about if you multiply a growth rate of zero by 100 you&#x27;ll get zero. So what that does has changes this treaty cubed, um, minus 80 squared, um nine plus eleventy and then plus 20 is equal to zero. So the only possible rational roots are factors of this, you know, +12 C, four, 5, 10 and 20. But we only care about numbers between zero and sudden so you can start crossing off. Don&#x27;t across off one. But you can cross up 10 and 20 or are your possible answers. And, uh, as I&#x27;ve looked through the answers one that works, it&#x27;s four Nega vain. And you could just use synthetic and see if you get a remainder of zero. That&#x27;s how you know you&#x27;re right. So bring the one down and multiply, adding straight down and multiply, adding straight down and multiply. Yeah, so T equals four is one of the answers. Now, from here, you could use synthetic, um, or analysis. Use synthetic or you could factor. Um, the other answer I know that works is T equals five eso Bring the one down and multiply. Adding down and multiply. S o. T equals five. So these are your two inch There&#x27;s four and five. Now for a full explanation. There&#x27;s one more route that does work negative one because of you bringing one down and multiply and adding straight down you get a remainder of zero. Except that&#x27;s not within the range. Um, we want answers bigger than zero, but smaller than seven. So I believe it&#x27;s in seconds. Nope. It&#x27;s an hours, four hours and five hours. There you go.

Jillian Rae Villa · Answer

the question asked to find amount of days it would take or 1000 to grow to one million at 14% annual interest rate, which is compound and continuously. We could start off by knowing that the equation for continuously compounded interest which is a equals p time t to the power of rt a being our future value or one million p being our principal amount or deposited amount or are $1000 are being our interest rate in decimal form and t is the amount of years. The goal is to isolate T In order to do that, we can first divide a by P to take rt of the exponent e we can take the natural log of both sides. Taking the natural log of e to some exponents equals that exponents. So now we have Ellen of a overpay equals r Times T that we could divide both sides by our and get Ellen of a overpay divided by R equals t. Now that we have an equation for tea, we can plug in A and P. But first we would wanted convert 1000 and 1,000,002 scientific notation because it&#x27;s a lot easier, so $1000 equals 1.0 10 times 10 to the third dollars in a one million equals 1.0 times, 10 to 6. So going back to our equation, Ln off a which is there one million or 1.0 times 10 to the six and divided by p, which is R 1000 or 1.0 times 10 to the third and divide it by our, which is 40%. But it has been Dustin perform, so will be 0.14 to simplify 1.0 times tend to the six divided by 1.0 times tend to the third is just 1.0 times 10 to the third and we divided by 0.14 So in the end we get for the 9.34 But this is the amount in years and we want the amount in days. So what we do is multiply this by 365 and finally we get 18,000 in nine days

Ali Soave · Answer

we want to know. How many years will the value be 20,000? The value is V, so we could replace that with 20,000 and then the rest of our equation can be used to solve for y. Next, we can subtract 32,800 from both sides. Those cancel out 32,800 we get negative. 12,800 is equal to negative 8 1050 Why divide both sides by negative 8 1050 so that these cancel out negative 8 1050 why is equal to 6 29 years?

Christy Galilei · Answer

so a new machine zero years is $120,000. And then in 10 years time, it will be worth $4000. We want to find a formula, which is a linear Michael&#x27;s MX plus B type of formula. So the 01 20 the 1 20 would be your Why intercept? Why? Intercept always has an X value of zero. So next we need to slope, since we&#x27;re gonna use a soap formula changing. Why? Over change in X denominator. Negative 10 1,116,000. Divide that get negative. 11,600. That would be the slope. And then we want to use that formula to find the value of machine. After eight years, we&#x27;re gonna put in an eight for X, and that will be 27,200.

Taylor Shimono · Answer

now will I multiply both sides of my equation by DT And I did this because now we have a separation of variables and that&#x27;s going to allow us to integrate each side of our equation independently. Um, so we&#x27;re gonna go ahead and do that. We integrate the left side of our equation on the integral of one d y is just going to be why? And this will be equal to 14 you to the four t power plus C. Um, And again, all I did was integrate the left side. And so, from our initial value problem, we know that if t is equal to zero, why is going to be equal to 10? So, to get our equation, we&#x27;re just going to plug these values in and soul. So when we do that, um, or equation becomes 10 is equal to 1/4 e to the zero power plus seat. And so since we know that each of the zero power is one, we can essentially just subtract 1/4 from each side of the equation and we get C is equal. Thio 39 over four. And so to finish solving our initial value problem. All we have to do is plug this sea back into our equation. And when we do that, we will find that our equation, um that solves our differential equation is why is equal to 1/4 sometimes in parentheses, e to the 14th plus 39. And the reason I wrote this in parentheses was just so that I didn&#x27;t have to write my Fraction 39 over four. I just went ahead and wrote 39 as a whole number there. And this is just because I think it makes it a little bit easier to look at the problem. And for the last part of our problem, we want to find the time at which why is going to either increase to 100 or dropped 10. And so first, we&#x27;re gonna have to decide whether it&#x27;s going to be increasing or decreasing. And so since we know that you two, the fourty power is going to always give us a larger number, um, as we increase our time, that tells us that we need why to be increasing to 100. So we&#x27;re just going to plug in 100 for why and solve for teeth. Um, so when we do that, we&#x27;re going to start by multiplying both sides of our equation by four. So we get 400 is equal to each of the 14th last 39. Um, next, we&#x27;ll go ahead and subtract 39 from both sides of the equation. We get 3 61 is equal to e to the 14 power. And so next to sulfur t, we&#x27;re going to take the natural log of both sides and we get the natural log of 361 is equal to 14. So we find that the time where why will increase to 100 is going to be given to us by the natural log of 361 over.

Problem

Solve the given problems. A thermometer is taken …

Problem 49 Easy Difficulty

Solve the given problems.
The reliability $R(0 \leq R \leq 1)$ of a certain computer system is given by $R=e^{-0.0002 t},$ where $t$ is the time of operation (in h). Find $d R / d t$ for $t=1000 \mathrm{h}$.

Answer

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

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus