# math

posted by lucy

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??

## Similar Questions

1. ### Pre Calc (question was never answered)

Write the statement as a power function equation. Use k for constant of variation if one is not given. a. Charles's law states the volume V of an enclosed ideal gas at a constant pressure varies directly as the absolute temperature …
2. ### maths

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 …
3. ### math

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 …

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 …
5. ### Inverse Variation

Help me please.. Explain also :( 1. E is inversely proportional to Z and Z = 4 when E = 6. 2. P varies inversely as Q and Q = 2/3 when P = 1/2. 3.R is inversely proportional to the square of I and I = 25 when R = 100. 4. F varies inversely …
6. ### SAT math

Can someone please help me with this question: Write an equation that describes the following variation statement, and then find the constant of proportionality k . z is inversely proportional to x and directly proportional to y ; …
7. ### math

4. Which equation represents a proportional relationship?
8. ### Math Ratios

Suppose A is directly proportional to B, B is inversely proportional to C and C is inversely proportional to D. Determine whether A and D are directly proportional, inversely proportional, or neither.
9. ### Calculus II

Suppose a cell of volume V cc is surrounded by a homogeneous chemical solution of concentration C g/cc. Let y denote the concentration of the solute inside the cell at any time t and suppose that, initially, the concentration is y0. …
10. ### Calculus II

I'm having trouble getting started. Steve said it's similar to another question I asked but I don't know how to begin. Any help?

More Similar Questions