Question

@perl

Answer 1

please can you help me solve this step by step??

Answer 2

you want the integral F(t) - E(t)

Answer 3

can you please help me solve this, ive posted this question like 5 times in the past 5 hours and nobody has responded hahah

Answer 4

@perl

Answer 5

correct

Answer 6

and i just solve that?

Answer 7

i think we have to assume that the tank started as empty , at time zero

Answer 8

yeah cause it doesnt say

Answer 9

what do i do next?

Answer 10

now we use our calculator

Answer 11

my calculator gave me
18.38098087

Answer 12

@Loser66 did you get that too?

Answer 13

alright i guess im going with that hahah thanks

Answer 14

@SolomonZelman can you check this too

Answer 15

the integral would be simpler if you used one integral though

Answer 16

why do we need to use a calculator?
\(\large\color{slate}{\displaystyle\int\limits_{0}^{10}\frac{t+6}{t+1}~dt-\int\limits_{0}^{10}\frac{\ln(t+1)}{t+1}~dt}\)

\(\large\color{slate}{\displaystyle t+5\ln(t+1){{\huge |}_{ t=0}^{t=10}}-\int\limits_{0}^{10}\frac{\ln(t+1)}{t+1}~dt}\)

no need for abs value since it is positive.

\(\large\color{slate}{\displaystyle 10+5\ln(11)-\int\limits_{0}^{10}\frac{\ln(t+1)}{t+1}~dt}\)

\(\large\color{slate}{\displaystyle 10+5\ln(11)-\frac{1}{2}\ln^2(t+1){{\huge |}_{ t=0}^{t=10}}}\)


\(\large\color{slate}{\displaystyle 10+5\ln(11)-\frac{1}{2}\ln^2(11)}\)

Answer 17

http://www.wolframalpha.com/input/?i=10%2B5ln%2811%29-%281%2F2%29%28ln%5E2%2811%29%29+approximation
19.11

Answer 18

the integral is ln(t+2) / ( t + 1 )

Answer 19

is what I got

Answer 20

oh, there I go with my famous mistakes

Answer 21

I will redo it

Answer 22

its okay(:

Answer 23

18.381

Answer 24

yes, that is same answer then

Answer 25

@perl is right once again (:

Answer 26

I don't want to do that second integral by hand right now.

Answer 27

$$

\large\color{slate} {\displaystyle\int\limits_{0}^{10}\frac{t+6}{t+1}-\frac{\ln(t+2)}{t+1}~~dt}

$$

Answer 28

thank you both!!!

Answer 29

yes, I re-did it and came up with 18.3810

Answer 30

i dont mean to be nitpicky, sorry

Answer 31

$$
\int_D F(t) - E(t)

$$

Answer 32

was gonna say something, but I guess there is no need.
tnx and yw

Answer 33

@perl can you plz go to the question i tagged you in??

Answer 34

my computer is frozen, but you can post it here

Answer 35

it says loading when i try to click on anything

Answer 36

did you get x=2 as the answer? i did this problem with someone else earlier and they told me it was -2 but that doesnt really make sense to me

Answer 37

ok we have to test the endpoints and critical points to find absolute maximum

Answer 38

did you get 2 as the max?

Answer 39

give me a minute to think about this, i just realized we were not given f(x)

Answer 40

okk(:

Answer 41

yes i think that is right, the absolute maximum is -3

Answer 42

this is tricky though

Answer 43

-3??

Answer 44

@Loser66

Answer 45

the graph of f(x) starts falling at x = -2, and keeps falling because the derivative is negative there, until x = 5