# 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 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??

posted by drwls

First Name

## Similar Questions

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
2. ### 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
3. ### 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
4. ### 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 ;
5. ### 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? Suppose a cell of volume V cc is surrounded by a homogeneous chemical solution of concentration C
6. ### 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
7. ### maths

A mixture contains two chemicals, A and B, with masses mA and mB. The total mass of the mixture, m, remains constant. B is converted into A at a rate that is inversely proportional to the mass of A and directly proportional to the
8. ### calculus

I posted this below, and no one answered. Please help with this very complicated question! Using 3(x-3)(x^2-6x+23)^1/2, as the chain rule differentiation of f(x)=(x^2-6x+23). Please explain how I find the general solution to the
9. ### calculus

I posted this below, and no one answered. Please help with this very complicated question! Using 3(x-3)(x^2-6x+23)^1/2, as the chain rule differentiation of f(x)=(x^2-6x+23). Please explain how I find the general solution to the
10. ### Calculus

1) yy'-e^x= 0, and y=4 when x=0 means that: A)y=x-lnx^2+4 B)y^2=4x^2+3 C)y=-2x+1/2x^3 D)y^2=2e^x+14 E)1/2ln|x^2+4|+6 2) The rate of change of P with respect to t is directly proportional to (10-t) and inversely proportional to the

More Similar Questions