anonymous
  • anonymous
this one should be some what fun Water flows into a tank according to the rate F(t) = (6 + t)/(1 + t), and at the same time empties out at the rate E(t) = (ln(t+2))/(t+1) , with both F(t) and E(t) measured in gallons per minute. How much water, to the nearest gallon, is in the tank at time t = 10 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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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
presumably the tank is empty to start with..
anonymous
  • anonymous
do i just evaluate both functions at t =10 and then subtract f(10) - E(10)? and Id assume the tank was empty i wasn't given anymore information
IrishBoy123
  • IrishBoy123
\(\frac{dV}{dt} = F(t) - E(t)\)

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IrishBoy123
  • IrishBoy123
build and solve integral
anonymous
  • anonymous
\[\int\limits \frac{ (t+6)-(\ln(t+2)) }{ (t+1) }\]?
ganeshie8
  • ganeshie8
Looks good, but that wont evaluate into elementary functions so you may simply use wolfram http://www.wolframalpha.com/input/?i=%5Cint_0%5E%2810%29+%5Cfrac%7B+%28t%2B6%29-%28%5Cln%28t%2B2%29%29+%7D%7B+%28t%2B1%29+%7D
anonymous
  • anonymous
:( i was hoping it would be more complicated
ganeshie8
  • ganeshie8
evaluating it is complicated indeed but i think you should not waste time messing with special functions at this point..
anonymous
  • anonymous
yeah your probably right , anyway thanks once again
ganeshie8
  • ganeshie8
np
ganeshie8
  • ganeshie8
maybe just double check the problem has no typoes because usually you should expect to see easily workable integrals in these type of problems.. the focus should be on setting up the integral, not evaluating it..
anonymous
  • anonymous
okay one second,
anonymous
  • anonymous
all seems clear to me , do you see anything out of place ?
ganeshie8
  • ganeshie8
integral becomes easy if E(t) is like below : \(E(t) = (\ln(t+\color{red}{1}))/(t+1)\)
anonymous
  • anonymous
nope triple checked its t + 2
ganeshie8
  • ganeshie8
then we're good, nearest to gallon, the water in the tank is 18 gallon at t = 10
anonymous
  • anonymous
@ganeshie8 can i ask you something?
ganeshie8
  • ganeshie8
sure ask
anonymous
  • anonymous
why are you so helpfull? im serious you clearly are on a higher level of math, why do you keep helping people with silly linear calculus I problems, you couldn't possibly be learning anything and i'm sure your own work keeps you busy you have infinity medals what keeps you here ?
ganeshie8
  • ganeshie8
Haha thanks for the good words! But you have no idea, I suck at math, thats the only reason I'm still here ;p
anonymous
  • anonymous
god , i must be truly awful then
ganeshie8
  • ganeshie8
I think you're doing great!
anonymous
  • anonymous
:)

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