Originally posted by joe shmoif my notation doesnt make sence, I'll be happy to clarify what I thought it meant..
I haven't done these types of problems yet, so the math I have done on it so far may be incorrect, but i'll let you be the judge of that.
This is just for fun
Ok, here it is broken into two parts
start with a cube(A) of side length x, nested inside a cube(B) of side lenght (x+1), at what side lengths will their rates of change in volume be equal
...[text shortened]... to add another piece of information, like one of the original starting volumes to deduce this?
Originally posted by wolfgang59sorry, I think I meant to ask, when are their rates of change in volume with respect to time equal
I cant follow this. If the rates of change of the sides are constant then the rates of change of the volumes will be constant. Namely 8 and 27. They are never going to be equal!
The volume (V) is equal to x^3 so
DV/dx = 3x^2
DV/dt = DV/dx * dx/dt
= (3x^2) * 3
I'm unclear as to the realtionship between the two cubes - ...[text shortened]... constantly 1 unit larger than the smaller?
ie does y = x+1 (y is side length of larger cube)
Originally posted by joe shmoHow can x^3 be greater than (x+1)^3 ????
sorry, I think I meant to ask, when are their rates of change in volume with respect to time equal
And yes, the side of the larger cube is (x+1)
so the two volumes are V= x^3 & V = (x+1)^3
the cubes are growing at different rates relative to each other, so the larger cube isnt always 1 unit larger
given enough time V= x^3 should become greater than V = (x+1)^3 right?
Originally posted by wolfgang59yeah, your right about that..all logic escapes me somtimes. haha
How can x^3 be greater than (x+1)^3 ????
Your problem I think is that you are using x as a variable as well as using it as a discrete value.
Originally posted by wolfgang59thanks wolfgang, That is ( as far as i can tell ) the mathematics I was thinking of, or at least, trying to think of!!!LOL
You have 2 variables which vary with time; the length of small cube (lets call it 'a' and the length of the larger (lets call that 'b'
Lets call their respective volumes A and B.
We are given that
da/dt = 3; a=3t + C (where C is a constant)
db/dt = 2; b=2t + K (where K is a constant)
initial value t=0, a=x, b=x+1
At time t, a=C = x and b= ...[text shortened]... x)^2 = 2 (2t+x+1)^2
Then solve for t in terms of x.
REMEMBER that x IS NOT A VARIABLE!!!