Homework Help: math please help

Posted by lucy on Tuesday, February 2, 2010 at 8:03am.

i posted this

can you explain to me how to do this question i know i have to use differential equations but im not sure how to form an equation for inversely proportional

question states

grain is being poured at a steady rate to form a pile with height h, the rate at which the height is increasing is inversely proportional to h^3.
the initial height of the pile is ho and the height doubles after time T.

find in terms of T, the time after which the height of the pile is 3ho

if you could explain it as much as possible

thanks

Damon replied

dh/dt = k/h^3 where k is unknown constant
h^3 dh = k dt
h^4/4 + c = kt
at t = 0, h = ho
ho^4/4 + c = 0
c = -ho^4/4
so
h^4/4 -ho^4/4 = k t
at t = T, h = 2 ho
16 ho^4/4 -ho^4/4 = k T
15 ho^4/4 = k T
k = (1/T)(15 ho^4/4)
so
h^4 - ho^4 = 25 ho^4 (t/T)
when is h = 3 ho ?
81 ho^4 - ho^4 = 25 ho^4 (t/T)
80 = 25 (t/T)
t = 80T/25 = 16 T/5

i follow it up to this point

h^4 - ho^4 = 25 ho^4 (t/T)
when is h = 3 ho ?
81 ho^4 - ho^4 = 25 ho^4 (t/T)
80 = 25 (t/T)
t = 80T/25 = 16 T/5

where do you get 25 from and 81

could someone help??

math please help - drwls, Tuesday, February 2, 2010 at 9:30am
81 = 3^4
The "25" comes from previous step, canceling out ho^4.
81 ho^4 - ho^4 = 25 ho^4 (t/T)
80 = 25 (t/T)

Answer this Question

Related Questions

physics - please explain further - Can someone please explain the answer I got ...
financial Matters - I need help in understanding this question given by my ...
financial Matters - I need help in understanding this question given by my ...
math - Posted by mota THE MASS OF THE SUN IS ABOUT 10^27 METRIC TONS , OR 10^30 ...
READ THIS! - Please answer my question that I posted at 6:10 quickly because I ...
calorimetry - please, someone answer my question i posted already I answered ...
Algebra-drwls please check! - Posted by Megan on Tuesday, October 12, 2010 at 3:...
year 8 re-Re teachers - i posted this question before but can`t see it on the ...
Math PLEASE HELP - No one was answering my questions for the first question I ...
Math Rational Functions-Please Clarify =) - I have a question about the rational...

For Further Reading

First Name:
School Subject:
Answer: