Homework Statement
The particles of an ink blob dropped into a large container of water diffuse outward and obey the radial diffusion equation:
dn/dt = (D/r2) (d/dr) (r2* (dn/dr) )
where n(r,t) is the density of ink particles at point r at time t and D is the diffusion constant.
Verify, by...
ok - could someone validate my answer please?
i got 4 atoms in one crystal,
the volume of one atom: ( pi * (2^(3/2)) * (a^3) ) / 48
the volume of the crystal is a^3
giving a packing fraction of 0.236?
Homework Statement
Write down the number of nearest neighbours in a FCC structure, calculate the angle between the bonds and the packing fraction.
Homework Equations
Literally don't know where to start!
The Attempt at a Solution
Very confused at the moment. Tried to look up...
Homework Statement
Show that the set of functions:
x^2
3x+2
x-1
2x+5
are linearly dependent.
Homework Equations
-
The Attempt at a Solution
I know that you have to show that you can put constants in front of each equation (that aren't all zero) such that:
c1y1 + c2y2...
oh and i can't see where a 2y would come from??
the LHS integral is (y^2) / 2 + y
which factorizes to 0.5y(y+1) ?
then re-arranges to what i said earlier.
yes i did mean y = 2(x^2) / (y+1) sorry.
and there should be a +c on the end, granted.
but my solution is still wrong isn't it?
you can't have a y on both sides?
argh I've literally been thinking about this for like two hours, it's ridiculous.
integrating (y+1) wrt y gives: (y^2)/2 + y
and integrating 2x wrt x gives: x^2
giving (y^2)/2 + y = x^2
and rearranged gives y = 2x / (y+1)
i still get it no matter how many times i think of it :(
arrgghhh