Question

A long time ago, in a galaxy far, far away, Lama Su takes Obi-Wan Kenobi on a tour of the clone factory in Tipoca City on Kamino. In order to obtain the biomass necessary to construct the clones, a gigantic vat is filled with 700 gallons of a solution of liquefied Hutt fat containing 80 pounds of granulated Wookie hair. Then, pure liquefied Hutt fat is pumped into the vat at a rate of 6 gallons per minute, while the well-stirred mixture is removed from the vat at a rate of 9 gallons per minute. After 3 hours of pumping pure Hutt fat into the vat, how many pounds of granulated Wookie hair are left in the vat?

Answer 1

who ever came up with this question should be killed,they screwed up star wars worse than Disney did making that musical

Answer 2

http://www.wolframalpha.com/input/?i=dy%2Fdt+%3D++0+-++++9y%2F%28+700-3t%29

Answer 3

plugin the initial value,
solve the constant c

Answer 4

Ok here's how I did it: t=180mins
Let H(t)=amount of liquefied Huttfat (in gallons) after t minutes
Let W(t)=amount of wookie hair (in pounds) after t minutes
\[\frac{ dw }{ dt }\]=rate in(of hair) - rate out(of hair)
=[(rate in(of soln)*concentration of soln. coming in)-(rate out (of soln)*concentration of soln coming out)]
=(6gal/min*0bl/gal)-(9gal/min*(hair at time t/soln of time t)
=0lb/min-9gal*(W lb/ H gal)
dW/dt=-9W/(700-3t)=(-9/(700-3t))*dt=dW/W
\[\int\limits \frac{ dW }{W }=\int\limits \frac{ -9 }{ 700-3t }dt \rightarrow \ln \left| W \right|=-9\ln \left| 700-3t \right|+c\]
\[e^{\ln \left| W \right|}=e^{-9\ln \left| 700-3t \right|} +e^{C}\]
are these the right steps to find C and find the amount of wookie hair? If not what steps do I need to add or revise?

Answer 5

this is the worst star wars question ever

Answer 6

scary lol

Answer 7

it looks okay, except for a minor mistake when evaluating integral

Answer 8

you should get :

\(\large \int\limits \frac{ dW }{W }=\int\limits \frac{ -9 }{ 700-3t }dt \rightarrow \ln \left| W \right|=\dfrac{-9\ln \left| 700-3t \right|}{-3}+c\)

Answer 9

right ?

Answer 10

Oh yah and the 9 cancelles out 3 yah I see

Answer 11

yes and it simplifies to the wolfram solution
click my first reply