## anonymous one year ago 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.

1. ganeshie8

2. 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

3. IrishBoy123

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

4. IrishBoy123

build and solve integral

5. anonymous

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

6. 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

7. anonymous

:( i was hoping it would be more complicated

8. ganeshie8

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

9. anonymous

yeah your probably right , anyway thanks once again

10. ganeshie8

np

11. 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..

12. anonymous

okay one second,

13. anonymous

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

14. ganeshie8

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

15. anonymous

nope triple checked its t + 2

16. ganeshie8

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

17. anonymous

@ganeshie8 can i ask you something?

18. ganeshie8

19. 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 ?

20. 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

21. anonymous

god , i must be truly awful then

22. ganeshie8

I think you're doing great!

23. anonymous

:)