anonymous
  • anonymous
Water is poured into a bucket according to the rate F of t equals the quotient of 7 plus t and the quantity 2 plus t, and at the same time empties out through a hole in the bottom at the rate E of t equals the quotient of the natural log of the quantity t plus 4 and the quantity t plus 2, with both F(t) and E(t) measured in pints per minute. How much water, to the nearest pint, is in the bucket at time t = 5 minutes. You must show your setup but can use your calculator for all evaluations.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
https://gyazo.com/d2a5ac63b91f596e6febfa3e8dbd91aa
anonymous
  • anonymous
@jim_thompson5910 @SolomonZelman
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle F(t)=\frac{t+7}{t+2} }\) \(\large\color{#000000 }{ \displaystyle E(t)=\frac{\ln(x+4)}{t+2} }\)

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More answers

SolomonZelman
  • SolomonZelman
are the functions like this?
anonymous
  • anonymous
Yes
SolomonZelman
  • SolomonZelman
The amount of water is the area under the curve.... \(\large\color{#000000 }{ \displaystyle \int \left[F(t)-E(t)\right]dt }\)
anonymous
  • anonymous
Ohh. Ok. I got it from here
anonymous
  • anonymous
Unless you feel like doing it for me, I don't mind :p
SolomonZelman
  • SolomonZelman
EXAMPLE OF THE SAME CONCEPT: Same way if you were given the velocities of the cars, \(y_1(x)\) for car 1 and \(y_2(x)\) for car 2, then you will need an integral of \(y_1(x)-y_2(x)\) to find how much distance is car 1 ahead of car 2. (provided that car 1 is indeed ahead)
SolomonZelman
  • SolomonZelman
I do like integrating, especially if someone approaches and tells me that the problem is impossible. Even more do I enjoy using elemnatry properties for harder problems, but according to the policy I can't do it. (Afterall you have to integrate too)
SolomonZelman
  • SolomonZelman
oh, forgot to mention your limits of integration are 0 and 5.
SolomonZelman
  • SolomonZelman
because you are looking for the water in the tank in 5 minutes.
anonymous
  • anonymous
Ughh I have to use quotient rule right?
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \int_0^5\left[\frac{t+7}{t+2} -\frac{\ln(x+4)}{t+2} \right]dt }\)
anonymous
  • anonymous
Oh yeah I have a neato calculator no need for me to use quotient rule.
anonymous
  • anonymous
9.056 final answer
SolomonZelman
  • SolomonZelman
you can't use the quotient rule
SolomonZelman
  • SolomonZelman
it is integration (not differentiation)
SolomonZelman
  • SolomonZelman
\(\large\color{#000000 }{ \displaystyle \int_0^5\left[\frac{t+7}{t+2} -\frac{\ln(t+4)}{t+2} \right]dt }\)
anonymous
  • anonymous
Oh my mistake. If I wanted to manually do it I would have subtract the two and find a way to simplify it so I may integrate.
anonymous
  • anonymous
I hope you're not integrating (unless you did it for fun) as I am aware of how it is done, no need to teach me :)
SolomonZelman
  • SolomonZelman
I don't you think you can hande the last component ln(t+4)/(t+2). If it were ln(t+4)/(t+4) or ln(t+2)/(t+2), then you would.
SolomonZelman
  • SolomonZelman
are you familiar with polylogarithmic functions?
anonymous
  • anonymous
No, I am not. I don't think I need to be either at least not in my current course.

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