are you not already a chem major at your uni? organic is like intro chem for chem majors. even after undergrad and you take some higher level courses you've still got a long ass way to go.
study hard in your physics and math classes so you don't die in physical chemistry. learn programming because computation is really important. you kind of sound like either a freshman or someone who just finished breaking bad
I need to combine linear falloff of explosion force with distance and inverse square falloff of explosion force with distance.
Obviously it's impossible to have true inverse square that is zero when distance = blast radius, but what would be a good imitation?
The points (1, 3) and (−2, 6) lie on a line. Where does the line cross the x-axis?
Ik how to do this easily with y =mx+b, but I'm in a linear algebra course and I need to do it using a matrix.
I set up the matrix
1 -2
3 6
But then what? If I try to make it go to reduce form, it just becomes
1 0
0 1
you have the equations
3=m+b
6=-2m+b
so the matrix equation is
[1 1][m]=[3]
[-2 1][b]=[6]
invert the matrix on the left to solve for the vector
[m]
[b]
or i guess you want to solve
(1,3)+t[(1,3)-(-2,6)]=(x,0)
(1,3)+t(3,-3)=(x,0)
(1+3t, 3-3t)=(x,0)
so need t=1
so x=4
Watch this entire series.
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Thanks, this helped
What about something like this?
"The points (3, −1, −5), (1, 4, 14), and (5, 3, 3) lie on a unique plane. Where does this plane cross the z-axis?"
I got the answer as z = 4 but I had to use vectors and cross products (I'm supposed to use matrices in linear alg or something else, not cross product).
I tried setting up a matrix in the form
ax + by + cz + d = 0
1 4 14 1 0
3 -1 -5 1 0
5 3 3 1 0
But I think I did it wrong.
I then tried again without the zeroes at the end (ax + by +cz = d) and I got nice looking answers (a = 1/2, b = -3/4, c = 1/4, but I'm not sure what to do with those answers)
>(3, −1, −5), (1, 4, 14), and (5, 3, 3)
you can write
(0,0,z)=(3,-1,5)+t[(3,-1,5)-(1,4,14)]+u[(3,-1,-5)-(5,3,3)]
use the first two equations to solve for t and u, then substitute it in to get z=4
just looking for a hint, not a solution
given a continuous function f from the unit sphere embedded in R^3 to R, show there exists an orthonormal basis u1,u2,u3 of R^3 with f(u1)=f(u2)=f(u3)
i can do it when its a function f(theta):[0,2pi] to R from the unit circle in R^2 instead of the sphere in R^3 but i don't know if the proof is adaptable.
an orthonormal basis u1, u2 in R^2 has a pi/2 angle between them so we can consider the function f(theta)-f(theta+pi/2)
since the circle is compact f has a maximum u and a minimum v
these satisfy f(u)-f(u+pi/2)>0 and f(v)-f(v+pi/2)
Use the inverse of the CDF (inverse transform sampling).