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.

Question

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.

ganeshie8 · Answer

presumably the tank is empty to start with..

anonymous · Answer

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 · Answer

$\frac{dV}{dt} = F(t) - E(t)$

irishboy123 · Answer

build and solve integral

anonymous · Answer

$$\int\limits \frac{ (t+6)-(\ln(t+2)) }{ (t+1) }$$?

ganeshie8 · Answer

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 · Answer

:( i was hoping it would be more complicated

ganeshie8 · Answer

evaluating it is complicated indeed but i think you should not waste time messing with special functions at this point..

anonymous · Answer

yeah your probably right , anyway thanks once again

ganeshie8 · Answer

np

ganeshie8 · Answer

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 · Answer

okay one second,

anonymous · Answer

all seems clear to me , do you see anything out of place ?

ganeshie8 · Answer

integral becomes easy if E(t) is like below :

$E(t) = (\ln(t+\color{red}{1}))/(t+1)$

anonymous · Answer

nope triple checked its t + 2

ganeshie8 · Answer

then we're good, nearest to gallon, the water in the tank is 18 gallon at t = 10

anonymous · Answer

@ganeshie8 can i ask you something?

ganeshie8 · Answer

sure ask

anonymous · Answer

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 · Answer

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 · Answer

god , i must be truly awful then

ganeshie8 · Answer

I think you're doing great!

anonymous · Answer

:)